CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW216+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n001.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 05:30:04 PM UTC 2026

% Result   : Theorem 0.97s 5.79s
% Output   : CNFRefutation 5.23s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1448)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_not__sum__power2__lt__zero,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__less__0,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [X4,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ~ c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => ~ c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_real__sqrt__sum__squares__mult__squared__eq,axiom,
    ! [X42,X40,X19,X11] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,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,X40,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,X42,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)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,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,X40,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,X42,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__squared__eq) ).

fof(fact_succ__Bit0,axiom,
    ! [X31] : c_Int_Osucc(c_Int_OBit0(X31)) = c_Int_OBit1(X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [X31] : c_Int_OBit0(X31) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_succ__def,axiom,
    ! [X31] : c_Int_Osucc(X31) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).

fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
    ! [X42,X40,X19,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,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,X40,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,X42,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).

fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
    ! [X34,X12,X26,X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,X9,X26),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,X12,X34),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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X9,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,X12,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X26,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,X34,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).

fof(fact_arctan__half,axiom,
    ! [X11] : hAPP(c_Transcendental_Oarctan,X11) = hAPP(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)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__half) ).

fof(fact_cos__x__y__le__one,axiom,
    ! [X19,X11] : 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,X11,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,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/sandbox2/benchmark/theBenchmark.p',fact_cos__x__y__le__one) ).

fof(fact_real__sqrt__sum__squares__less,axiom,
    ! [X19,X38,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X38,hAPP(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,X19),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X38,hAPP(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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__less) ).

fof(fact_power2__sum,axiom,
    ! [X19,X11,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Oplus__class_Oplus(X10,X11,X19),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).

fof(fact_real__sum__squared__expand,axiom,
    ! [X19,X11] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X19),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,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(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)))),X11)),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).

fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
    ! [X19,X11,X38] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X38)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X38,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,X19,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X38,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),X11)
           => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
             => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X38) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).

fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
    ! [X19,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).

fof(fact_real__sqrt__sum__squares__ge1,axiom,
    ! [X19,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).

fof(fact_real__sqrt__sum__squares__ge2,axiom,
    ! [X11,X19] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).

fof(fact_four__x__squared,axiom,
    ! [X11] : hAPP(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,X11,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,hAPP(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)))),X11),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_four__x__squared) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> ( X21 != c_Groups_Ozero__class_Ozero(X10)
          | X20 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X10))
      <=> ( X21 = c_Groups_Ozero__class_Ozero(X10)
          & X20 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
    ! [X19,X11] :
      ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = X19
     => X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).

fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
    ! [X19,X11] :
      ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,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,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = X11
     => X19 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).

fof(fact_even__power__le__0__imp__0,axiom,
    ! [X31,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,hAPP(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)))),X31)),c_Groups_Ozero__class_Ozero(X10))
       => X9 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).

fof(fact_eq__divide__2__times__iff,axiom,
    ! [X22,X20,X21] :
      ( X21 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X20,hAPP(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)))),X22))
    <=> hAPP(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)))),X21) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X20,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).

fof(fact_DERIV__arctan,axiom,
    ! [X21] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,X21,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__arctan) ).

fof(fact_sum__power2__ge__zero,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,X9,hAPP(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)))),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_ring__1__class_Opower__minus__even,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Oring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),hAPP(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)))),X28)) = c_Power_Opower__class_Opower(X10,X9,hAPP(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)))),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ring__1__class_Opower__minus__even) ).

fof(fact_power2__le__imp__le,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless__eq(X10,X11,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_power2__less__imp__less,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless(X10,X11,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X21 = c_Groups_Ozero__class_Ozero(X10)
          & X20 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_realpow__two__sum__zero__iff,axiom,
    ! [X20,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X21,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,X20,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)
    <=> ( X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X20 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).

fof(fact_realpow__square__minus__le,axiom,
    ! [X11,X38] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__square__minus__le) ).

fof(fact_power__even__eq,axiom,
    ! [X28,X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,hAPP(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)))),X28)) = c_Power_Opower__class_Opower(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [X28,X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Power_Opower__class_Opower(X10,X11,hAPP(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)))),X28)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X11,X28)),c_Power_Opower__class_Opower(X10,X11,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_lemma__real__divide__sqrt__less,axiom,
    ! [X38] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X38)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X38,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).

fof(fact_real__sum__of__halves,axiom,
    ! [X11] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,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,X11,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).

fof(fact_power__minus1__even,axiom,
    ! [X28,X10] :
      ( class_Rings_Oring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)),hAPP(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)))),X28)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).

fof(fact_DERIV__const__average,axiom,
    ! [X50,X48,X16,X17] :
      ( X17 != X16
     => ( ! [X3] : c_Deriv_Oderiv(tc_RealDef_Oreal,X48,X3,X50)
       => hAPP(X48,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X17,X16),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(X48,X17),hAPP(X48,X16)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__const__average) ).

fof(fact_DERIV__real__sqrt__generic,axiom,
    ! [X57,X21] :
      ( X21 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
         => X57 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21)),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,X21,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
           => X57 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
         => c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X21,X57) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__real__sqrt__generic) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
           => X11 = X19 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X74,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber__ring(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X74,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X74) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_zero__less__power2,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      <=> X17 != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).

fof(fact_DERIV__real__sqrt,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
     => c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X21,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__real__sqrt) ).

fof(fact_power3__eq__cube,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9)),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_real__gt__half__sum,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X19),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).

fof(fact_real__less__half__sum,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X19),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__half__sum) ).

fof(fact_real__sqrt__pow2__gt__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).

fof(fact_half__gt__zero,axiom,
    ! [X30,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber__ring(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X30)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X30,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).

fof(fact_half,axiom,
    ! [X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber__ring(X10) )
     => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half) ).

fof(fact_zero__le__power2,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power2) ).

fof(fact_two__realpow__ge__one,axiom,
    ! [X28] : 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))),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).

fof(fact_power2__minus,axiom,
    ! [X9,X10] :
      ( class_Rings_Oring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__minus) ).

fof(fact_mult__2,axiom,
    ! [X5,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5) = c_Groups_Oplus__class_Oplus(X10,X5,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).

fof(fact_nat__mult__2,axiom,
    ! [X5] : hAPP(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)))),X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).

fof(fact_eq__special_I4_J,axiom,
    ! [X21,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Int_Onumber__class_Onumber__of(X10,X21) = c_Groups_Oone__class_Oone(X10)
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).

fof(fact_real__sqrt__unique,axiom,
    ! [X11,X19] :
      ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X11
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
       => hAPP(c_NthRoot_Osqrt,X11) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).

fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( X11 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | X11 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).

fof(fact_real__sqrt__pow2__iff,axiom,
    ! [X21] :
      ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [X17,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( c_Power_Opower__class_Opower(X10,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X10)
      <=> ( X17 = c_Groups_Oone__class_Oone(X10)
          | X17 = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_zero__eq__power2,axiom,
    ! [X17,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( c_Power_Opower__class_Opower(X10,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X10)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_real__inv__sqrt__pow2,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__inv__sqrt__pow2) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [X4,X35] :
      ( ( class_Groups_Omonoid__mult(X35)
        & class_Int_Onumber(X35) )
     => c_Power_Opower__class_Opower(X35,c_Int_Onumber__class_Onumber__of(X35,X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X35,c_Int_Onumber__class_Onumber__of(X35,X4)),c_Int_Onumber__class_Onumber__of(X35,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_real__sqrt__pow2,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2) ).

fof(fact_mult__2__right,axiom,
    ! [X5,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X5),c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X10,X5,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).

fof(fact_power2__eq__square,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X11) = c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_nat__mult__2__right,axiom,
    ! [X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5),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,X5,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_one__power2,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).

fof(fact_zero__power2,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).

fof(fact_csqrt,axiom,
    ! [X5] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_csqrt) ).

fof(fact_eq__special_I2_J,axiom,
    ! [X20,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Groups_Oone__class_Oone(X10) = c_Int_Onumber__class_Onumber__of(X10,X20)
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_one__add__one__is__two,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10)) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [X66,X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X31),c_Int_OBit1(X66)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Int_Osucc(X66))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_mult__numeral__1,axiom,
    ! [X9,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_rel__simps_I34_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X68),c_Int_OBit1(X67))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X68),c_Int_OBit1(X67))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I17_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_mult__Bit1,axiom,
    ! [X66,X31] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X31)),X66) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X31),X66)),X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [X27,X18,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [X27,X18,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [X18,X16,X27,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [X18,X16,X27,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X66,X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X31),c_Int_OBit0(X66)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X66)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X66,X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X31),c_Int_OBit1(X66)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X66)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_inverse__numeral__1,axiom,
    ! [X10] :
      ( ( class_Fields_Ofield(X10)
        & class_Int_Onumber__ring(X10) )
     => c_Rings_Oinverse__class_Oinverse(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__numeral__1) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [X17,X27,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [X17,X27,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [X27,X16,X17,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [X27,X16,X17,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_number__of1,axiom,
    ! [X28] :
      ( 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,X28))
     => ( 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(X28)))
        & 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(X28))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).

fof(fact_add__special_I3_J,axiom,
    ! [X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,X37),c_Groups_Oone__class_Oone(X10)) = c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X4)) = c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X68),c_Int_OBit0(X67))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_rel__simps_I33_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X68),c_Int_OBit0(X67))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_rel__simps_I32_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X68),c_Int_OBit1(X67))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X68),c_Int_OBit1(X67))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I15_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X19)),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_divide__numeral__1,axiom,
    ! [X9,X10] :
      ( ( class_Fields_Ofield(X10)
        & class_Int_Onumber__ring(X10) )
     => c_Rings_Oinverse__class_Odivide(X10,X9,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_divide__Numeral1,axiom,
    ! [X11,X10] :
      ( ( class_Fields_Ofield(X10)
        & class_Int_Onumber__ring(X10) )
     => c_Rings_Oinverse__class_Odivide(X10,X11,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_minus__Bit1,axiom,
    ! [X31] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(X31)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X31))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit1) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [X9,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_divide__le__eq,axiom,
    ! [X17,X18,X16,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [X17,X18,X16,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

fof(fact_le__divide__eq,axiom,
    ! [X18,X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [X18,X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [X31,X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)),X31)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)),X31)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X65))),X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_le__special_I4_J,axiom,
    ! [X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Groups_Oone__class_Oone(X10))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Int_OBit1(c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_less__special_I4_J,axiom,
    ! [X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Groups_Oone__class_Oone(X10))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Int_OBit1(c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [X20,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [X20,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_succ__Bit1,axiom,
    ! [X31] : c_Int_Osucc(c_Int_OBit1(X31)) = c_Int_OBit0(c_Int_Osucc(X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit1) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X27),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X50))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X50))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_number__of__Bit1,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(X4)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X4)),c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X66,X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X31),c_Int_OBit0(X66)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X66)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X49,X50] :
      ( c_Int_OBit1(X50) = c_Int_OBit1(X49)
    <=> X50 = X49 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_rel__simps_I31_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X68),c_Int_OBit0(X67))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X67,X68] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X68),c_Int_OBit0(X67))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I14_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))),c_Int_Onumber__class_Onumber__of(X10,X4)) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [X27,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ( c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(X27)))
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_mult__Bit0,axiom,
    ! [X66,X31] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X31)),X66) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X31),X66)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).

fof(fact_number__of__Bit0,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(X4)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X4)),c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_pred__Bit1,axiom,
    ! [X31] : c_Int_Opred(c_Int_OBit1(X31)) = c_Int_OBit0(X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [X27,X48,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Olinorder(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X48),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Int_Onumber__class_Onumber__of(X10,X48)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X66,X31] : c_Int_OBit0(X31) != c_Int_OBit1(X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X66,X31] : c_Int_OBit1(X31) != c_Int_OBit0(X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oone__class_Oone(X10) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_Bit1__def,axiom,
    ! [X31] : c_Int_OBit1(X31) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X31),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(fact_add__nat__number__of,axiom,
    ! [X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X65)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X27),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_add__leE,axiom,
    ! [X28,X31,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X31),X28)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X50))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X50))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_less__fun__def,axiom,
    ! [X1,X2,X10,X35] :
      ( class_Orderings_Oord(X35)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X10,X35),X2,X1)
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X2,X1)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_pred__Bit0,axiom,
    ! [X31] : c_Int_Opred(c_Int_OBit0(X31)) = c_Int_OBit1(c_Int_Opred(X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit0) ).

fof(fact_le__nat__number__of,axiom,
    ! [X64,X48] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X64)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X31] : c_Int_OBit1(X31) != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X66] : c_Int_OPls != c_Int_OBit1(X66),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_not__add__less1,axiom,
    ! [X32,X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X33,X32] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_mult__nat__number__of,axiom,
    ! [X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X65)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_not__square__less__zero,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_number__of__succ,axiom,
    ! [X31,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_Osucc(X31)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).

fof(fact_minus__Bit0,axiom,
    ! [X31] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X31)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_not__real__square__gt__zero,axiom,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21),X21))
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

fof(fact_less__le__not__le,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
          & ~ c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
       => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_xt1_I9_J,axiom,
    ! [X9,X12,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ~ c_Orderings_Oord__class_Oless(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_linorder__not__le,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
      <=> c_Orderings_Oord__class_Oless(X10,X20,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_leD,axiom,
    ! [X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => ~ c_Orderings_Oord__class_Oless(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless(X10,X20,X21)
          | X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_order__less__not__sym,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__asym_H,axiom,
    ! [X12,X9,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ~ c_Orderings_Oord__class_Oless(X10,X12,X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__asym,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [X49,X50] :
      ( c_Int_OBit0(X50) = c_Int_OBit0(X49)
    <=> X50 = X49 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X24] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
         => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_not__exp__le__zero,axiom,
    ! [X11] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__exp__le__zero) ).

fof(fact_not__exp__less__zero,axiom,
    ! [X11] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__exp__less__zero) ).

fof(fact_abs__if,axiom,
    ! [X9,X10] :
      ( class_Groups_Oabs__if(X10)
     => ( ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
         => c_Groups_Oabs__class_Oabs(X10,X9) = c_Groups_Ouminus__class_Ouminus(X10,X9) )
        & ( ~ c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
         => c_Groups_Oabs__class_Oabs(X10,X9) = X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_sgn__if,axiom,
    ! [X11,X10] :
      ( class_Groups_Osgn__if(X10)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(X10)
         => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Ozero__class_Ozero(X10) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X10)
         => ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
             => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Oone__class_Oone(X10) )
            & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
             => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X21,X20,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X20,X21)
       => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( X11 != X19
       => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__cases,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ( X11 != X19
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( X11 != X19
       => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__le__cases,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_leI,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_not__leE,axiom,
    ! [X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => c_Orderings_Oord__class_Oless(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_not__one__le__zero,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_not__one__less__zero,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X19,X11] :
      ( X11 != X19
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_zsgn__def,axiom,
    ! [X33] :
      ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X33 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).

fof(fact_real__sgn__def,axiom,
    ! [X11] :
      ( ( X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X11 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__def) ).

fof(fact_sgn__real__def,axiom,
    ! [X9] :
      ( ( X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__real__def) ).

fof(fact_order__less__irrefl,axiom,
    ! [X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,X11,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_not__less0,axiom,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__zeroE,axiom,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [X49] :
      ( c_Int_OPls = c_Int_OBit0(X49)
    <=> c_Int_OPls = X49 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X50] :
      ( c_Int_OBit0(X50) = c_Int_OPls
    <=> X50 = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_less__not__refl,axiom,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_succ__pred,axiom,
    ! [X11] : c_Int_Osucc(c_Int_Opred(X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).

fof(fact_not__iszero__1,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => ~ c_Int_Oiszero(X10,c_Groups_Oone__class_Oone(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

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),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).

fof(fact_real__sqrt__two__gt__one,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/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),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__zero) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X10,X35] :
      ( class_Orderings_Oord(X35)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X2,X1)
      <=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X35,hAPP(X2,X3),hAPP(X1,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_pos2,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos2) ).

fof(fact_incr__mult__lemma,axiom,
    ! [X50,X71,X43] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
     => ( ! [X3] :
            ( hBOOL(hAPP(X71,X3))
           => hBOOL(hAPP(X71,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X43))) )
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X50)
         => ! [X3] :
              ( hBOOL(hAPP(X71,X3))
             => hBOOL(hAPP(X71,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X50),X43)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__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/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_inverse__add,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => ( X12 != c_Groups_Ozero__class_Ozero(X10)
         => c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)),c_Rings_Oinverse__class_Oinverse(X10,X9))),c_Rings_Oinverse__class_Oinverse(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [X60,X61,X39,X30,X62,X12] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X62),X30) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X12)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X60)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X12)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X62) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [X60,X61,X39,X30,X62,X12] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X62),X30) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60)
     => ( 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X39)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X30)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X12)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X62,X61) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [X30,X62,X60,X61,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X61),X60),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X62),X30))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X60)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X12)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X12)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X62) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [X30,X62,X60,X61,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X61),X60),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12),X62),X30))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X30,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X30)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X60)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X62,X61) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_DERIV__neg__dec__right,axiom,
    ! [X49,X21,X2] :
      ( c_Deriv_Oderiv(tc_RealDef_Oreal,X2,X21,X49)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X49,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => ? [X24] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
            & ! [X63] :
                ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
               => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X63,X24)
                 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X63)),hAPP(X2,X21)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__neg__dec__right) ).

fof(fact_DERIV__pos__inc__right,axiom,
    ! [X49,X21,X2] :
      ( c_Deriv_Oderiv(tc_RealDef_Oreal,X2,X21,X49)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49)
       => ? [X24] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
            & ! [X63] :
                ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
               => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X63,X24)
                 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X2,X21),hAPP(X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X63))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__pos__inc__right) ).

fof(fact_division__ring__inverse__add,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => ( X12 != c_Groups_Ozero__class_Ozero(X10)
         => c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)),c_Groups_Oplus__class_Oplus(X10,X9,X12))),c_Rings_Oinverse__class_Oinverse(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).

fof(fact_combine__common__factor,axiom,
    ! [X26,X12,X44,X9,X10] :
      ( class_Rings_Osemiring(X10)
     => c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X44),c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X44),X26)) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)),X44),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( ! [X36] :
            ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X36)
           => ( c_Orderings_Oord__class_Oless(X10,X36,c_Groups_Oone__class_Oone(X10))
             => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X36),X11),X19) ) )
       => c_Orderings_Oord__class_Oless__eq(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_convex__bound__le,axiom,
    ! [X37,X38,X19,X9,X11,X10] :
      ( class_Rings_Olinordered__semiring__1(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X9)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X38)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X37)
             => ( c_Groups_Oplus__class_Oplus(X10,X38,X37) = c_Groups_Oone__class_Oone(X10)
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X38),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X37),X19)),X9) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

fof(fact_convex__bound__lt,axiom,
    ! [X37,X38,X19,X9,X11,X10] :
      ( class_Rings_Olinordered__semiring__1__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X9)
       => ( c_Orderings_Oord__class_Oless(X10,X19,X9)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X38)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X37)
             => ( c_Groups_Oplus__class_Oplus(X10,X38,X37) = c_Groups_Oone__class_Oone(X10)
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X38),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X37),X19)),X9) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [X31,X32,X38,X33] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33),X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X32),X38),X31)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32)),X38),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_real__mult__inverse__cancel,axiom,
    ! [X38,X19,X47,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X47)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47),X19),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X38))
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)),X19),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X47)),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).

fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
    ! [X19,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X11),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X19),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).

fof(fact_le__real__sqrt__sumsq,axiom,
    ! [X19,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X11),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X19),X19)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__real__sqrt__sumsq) ).

fof(fact_add__frac__eq,axiom,
    ! [X4,X11,X5,X19,X10] :
      ( class_Fields_Ofield(X10)
     => ( X19 != c_Groups_Ozero__class_Ozero(X10)
       => ( X5 != c_Groups_Ozero__class_Ozero(X10)
         => c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),c_Rings_Oinverse__class_Odivide(X10,X4,X5)) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X5),hAPP(c_Groups_Otimes__class_Otimes(X10,X4),X19)),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

fof(fact_DERIV__unique,axiom,
    ! [X56,X57,X21,X2,X10] :
      ( class_RealVector_Oreal__normed__field(X10)
     => ( c_Deriv_Oderiv(X10,X2,X21,X57)
       => ( c_Deriv_Oderiv(X10,X2,X21,X56)
         => X57 = X56 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__unique) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X21),hAPP(c_Groups_Otimes__class_Otimes(X10,X20),X20)))
      <=> ( X21 != c_Groups_Ozero__class_Ozero(X10)
          | X20 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_real__mult__inverse__cancel2,axiom,
    ! [X38,X19,X47,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X47)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47),X19),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X38))
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X19),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X38),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X47))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X21),hAPP(c_Groups_Otimes__class_Otimes(X10,X20),X20)),c_Groups_Ozero__class_Ozero(X10))
      <=> ( X21 = c_Groups_Ozero__class_Ozero(X10)
          & X20 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_gt__half__sum,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_less__half__sum,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => c_Orderings_Oord__class_Oless(X10,X9,c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_q__neg__lemma,axiom,
    ! [X60,X61,X39] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60),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),X60)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X13,X14,X23,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X14),hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_q__pos__lemma,axiom,
    ! [X60,X61,X39] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39),X61),X60))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X60,X39)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X61) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_divide__left__mono,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12))
           => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X26,X9),c_Rings_Oinverse__class_Odivide(X10,X26,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12))
           => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X26,X9),c_Rings_Oinverse__class_Odivide(X10,X26,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12))
           => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X26,X9),c_Rings_Oinverse__class_Odivide(X10,X26,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_divide__strict__left__mono__neg,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12))
           => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X26,X9),c_Rings_Oinverse__class_Odivide(X10,X26,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X43,X18,X16,X17,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( ( X17 != X16
          & X18 != X43 )
      <=> c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),hAPP(c_Groups_Otimes__class_Otimes(X10,X16),X43)) != c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X43),hAPP(c_Groups_Otimes__class_Otimes(X10,X16),X18)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X22,X21,X20,X27,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X27),X20),hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X22)) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X27),X22),hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X20))
      <=> ( X27 = X21
          | X20 = X22 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_mult__number__of__left,axiom,
    ! [X5,X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X37)),hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X4)),X5)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X4))),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_odd__less__0,axiom,
    ! [X22] :
      ( 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),X22),X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(fact_power__Suc__less,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oone__class_Oone(X10))
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Power_Opower__class_Opower(X10,X9,X28)),c_Power_Opower__class_Opower(X10,X9,X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

fof(fact_field__le__epsilon,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( ! [X25] :
            ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X25)
           => c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Oplus__class_Oplus(X10,X19,X25)) )
       => c_Orderings_Oord__class_Oless__eq(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_frac__le,axiom,
    ! [X5,X4,X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
           => ( c_Orderings_Oord__class_Oless__eq(X10,X4,X5)
             => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X5),c_Rings_Oinverse__class_Odivide(X10,X19,X4)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_frac__less,axiom,
    ! [X5,X4,X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
           => ( c_Orderings_Oord__class_Oless__eq(X10,X4,X5)
             => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X5),c_Rings_Oinverse__class_Odivide(X10,X19,X4)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_frac__less2,axiom,
    ! [X5,X4,X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X4)
           => ( c_Orderings_Oord__class_Oless(X10,X4,X5)
             => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X5),c_Rings_Oinverse__class_Odivide(X10,X19,X4)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X26,X12,X37,X35] :
      ( ( class_Int_Onumber(X35)
        & class_Rings_Osemiring(X35) )
     => hAPP(c_Groups_Otimes__class_Otimes(X35,c_Int_Onumber__class_Onumber__of(X35,X37)),c_Groups_Oplus__class_Oplus(X35,X12,X26)) = c_Groups_Oplus__class_Oplus(X35,hAPP(c_Groups_Otimes__class_Otimes(X35,c_Int_Onumber__class_Onumber__of(X35,X37)),X12),hAPP(c_Groups_Otimes__class_Otimes(X35,c_Int_Onumber__class_Onumber__of(X35,X37)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_abs__mult__less,axiom,
    ! [X34,X12,X26,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X9),X26)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X12),X34)
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oabs__class_Oabs(X10,X9)),c_Groups_Oabs__class_Oabs(X10,X12)),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X37,X12,X9,X35] :
      ( ( class_Int_Onumber(X35)
        & class_Rings_Osemiring(X35) )
     => hAPP(c_Groups_Otimes__class_Otimes(X35,c_Groups_Oplus__class_Oplus(X35,X9,X12)),c_Int_Onumber__class_Onumber__of(X35,X37)) = c_Groups_Oplus__class_Oplus(X35,hAPP(c_Groups_Otimes__class_Otimes(X35,X9),c_Int_Onumber__class_Onumber__of(X35,X37)),hAPP(c_Groups_Otimes__class_Otimes(X35,X12),c_Int_Onumber__class_Onumber__of(X35,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_power__minus,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Oring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X28) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)),X28)),c_Power_Opower__class_Opower(X10,X9,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

fof(fact_mult__mono_H,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Oordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Oordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
           => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__strict__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,X34)
         => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12)
           => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
             => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X34)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [X12,X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X12,X28))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [X28,X29,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,X29),c_Power_Opower__class_Opower(X10,X9,X28))
         => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [X20,X21,X16,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X16)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X16,X21),c_Power_Opower__class_Opower(X10,X16,X20))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [X28,X29,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X29),c_Power_Opower__class_Opower(X10,X9,X28))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [X20,X21,X16,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X16)
       => ( c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X16,X21),c_Power_Opower__class_Opower(X10,X16,X20))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_times__divide__times__eq,axiom,
    ! [X4,X5,X19,X11,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19)),c_Rings_Oinverse__class_Odivide(X10,X5,X4)) = c_Rings_Oinverse__class_Odivide(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X5),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_eq__number__of__eq,axiom,
    ! [X20,X21,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Int_Onumber__class_Onumber__of(X10,X21) = c_Int_Onumber__class_Onumber__of(X10,X20)
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_power__less__power__Suc,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
       => c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X28),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Power_Opower__class_Opower(X10,X9,X28))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X13,X14,X23,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13)) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X14)),hAPP(c_Groups_Otimes__class_Otimes(X10,X23),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X13,X14,X23,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X15),hAPP(c_Groups_Otimes__class_Otimes(X10,X23),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [X28,X29,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X33,X29),c_Power_Opower__class_Opower(tc_Nat_Onat,X33,X28))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_power__decreasing,axiom,
    ! [X9,X76,X28,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X76)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Oone__class_Oone(X10))
           => c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,X76),c_Power_Opower__class_Opower(X10,X9,X28)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(fact_power__strict__decreasing,axiom,
    ! [X9,X76,X28,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X76)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oone__class_Oone(X10))
           => c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X76),c_Power_Opower__class_Opower(X10,X9,X28)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_eq__special_I1_J,axiom,
    ! [X20,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = c_Int_Onumber__class_Onumber__of(X10,X20)
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_power__strict__mono,axiom,
    ! [X28,X12,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
           => c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X12,X28)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Oplus__class_Oplus(X10,X26,X34)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_eq__special_I3_J,axiom,
    ! [X21,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Int_Onumber__class_Onumber__of(X10,X21) = c_Groups_Ozero__class_Ozero(X10)
      <=> c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).

fof(fact_add__number__of__left,axiom,
    ! [X5,X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,X37),c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,X4),X5)) = c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X4)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [X62,X75,X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X11,X75)),c_Power_Opower__class_Opower(X10,X11,X62)) = c_Power_Opower__class_Opower(X10,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X75,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_power__add,axiom,
    ! [X28,X29,X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X9,X29)),c_Power_Opower__class_Opower(X10,X9,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [X5,X19,X11] : c_Power_Opower__class_Opower(tc_Int_Oint,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X11,X19)),c_Power_Opower__class_Opower(tc_Int_Oint,X11,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_power__mult__distrib,axiom,
    ! [X28,X12,X9,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),X28) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X9,X28)),c_Power_Opower__class_Opower(X10,X12,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [X62,X19,X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Power_Opower__class_Opower(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X19),X62) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X11,X62)),c_Power_Opower__class_Opower(X10,X19,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [X19,X11,X5,X10] :
      ( class_Fields_Ofield(X10)
     => ( X5 != c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X5),X19) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19)),X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X19 != c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),X5) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [X19,X11,X5,X10] :
      ( class_Fields_Ofield(X10)
     => ( X5 != c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Oplus__class_Oplus(X10,X11,c_Rings_Oinverse__class_Odivide(X10,X19,X5)) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X11),X19),X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_add__num__frac,axiom,
    ! [X11,X5,X19,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X19 != c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Oplus__class_Oplus(X10,X5,c_Rings_Oinverse__class_Odivide(X10,X11,X19)) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19)),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
        <=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
        <=> c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [X17,X16,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
        <=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [X17,X16,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
        <=> c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [X17,X16,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
        <=> c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [X17,X16,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
        <=> c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
        <=> c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
        <=> c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [X12,X26,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X17),hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X16))
        <=> c_Orderings_Oord__class_Oless__eq(X10,X17,X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [X12,X26,X9,X10] :
      ( class_Rings_Olinordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [X12,X26,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Rings_Olinordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
       => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X17),hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X16))
        <=> c_Orderings_Oord__class_Oless(X10,X17,X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X17),hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X16))
        <=> c_Orderings_Oord__class_Oless__eq(X10,X16,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X17),hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X16))
        <=> c_Orderings_Oord__class_Oless(X10,X16,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X19))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X16,X18,X17,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X17,X18),c_Groups_Oplus__class_Oplus(X10,X16,X18))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X12,X26,X9,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X26))
       => c_Orderings_Oord__class_Oless__eq(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X18,X17),c_Groups_Oplus__class_Oplus(X10,X18,X16))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X26,X9),c_Groups_Oplus__class_Oplus(X10,X26,X12))
       => c_Orderings_Oord__class_Oless__eq(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X12,X26,X9,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X26))
       => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X16,X18,X17,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X18),c_Groups_Oplus__class_Oplus(X10,X16,X18))
      <=> c_Orderings_Oord__class_Oless(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X26,X9),c_Groups_Oplus__class_Oplus(X10,X26,X12))
       => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X18,X17),c_Groups_Oplus__class_Oplus(X10,X18,X16))
      <=> c_Orderings_Oord__class_Oless(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
       => ( c_Orderings_Oord__class_Oless(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19))
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [X11,X5,X19,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
       => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19),X11)
         => c_Orderings_Oord__class_Oless__eq(X10,X5,c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [X11,X5,X19,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
       => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X5),X19),X11)
         => c_Orderings_Oord__class_Oless(X10,X5,c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X12,X29,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X29),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X29)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Ocomm__semiring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)),X26) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_mult__left_Oadd,axiom,
    ! [X42,X19,X11,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X11,X19)),X42) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X42),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

fof(fact_mult_Oadd__left,axiom,
    ! [X12,X41,X9,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X41)),X12) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),hAPP(c_Groups_Otimes__class_Otimes(X10,X41),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)),X26) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X53),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X52))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X53),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X52))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [X12,X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Power_Opower__class_Opower(X10,X9,X28) = c_Power_Opower__class_Opower(X10,X12,X28)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
             => X9 = X12 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X17),hAPP(c_Groups_Otimes__class_Otimes(X10,X18),X16))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
            & c_Orderings_Oord__class_Oless(X10,X17,X16) )
          | ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless(X10,X16,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X16,X18,X17,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),hAPP(c_Groups_Otimes__class_Otimes(X10,X16),X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
            & c_Orderings_Oord__class_Oless(X10,X17,X16) )
          | ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless(X10,X16,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_power__mono,axiom,
    ! [X28,X12,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X12,X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

fof(fact_divide__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X26),c_Rings_Oinverse__class_Odivide(X10,X12,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X26),c_Rings_Oinverse__class_Odivide(X10,X12,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X12,X26),c_Rings_Oinverse__class_Odivide(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X26),c_Rings_Oinverse__class_Odivide(X10,X12,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_power__increasing,axiom,
    ! [X9,X76,X28,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X76)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X9)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X9,X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(fact_power__strict__increasing,axiom,
    ! [X9,X76,X28,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X76)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
         => c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X9,X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__gt1__lemma,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Power_Opower__class_Opower(X10,X9,X28))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_mult__le__cancel2,axiom,
    ! [X52,X50,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X50),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X52),X50))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel1,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_real__mult__le__cancel__iff1,axiom,
    ! [X20,X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21),X22),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X20),X22))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

fof(fact_real__mult__le__cancel__iff2,axiom,
    ! [X20,X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X22),X21),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X22),X20))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_real__mult__less__iff1,axiom,
    ! [X20,X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21),X22),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X20),X22))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).

fof(fact_add__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Groups_Oordered__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,X34)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,X34)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,X34)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [X34,X26,X12,X9,X10] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X26,X34)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_DERIV__ln__divide,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
     => c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X21,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ln__divide) ).

fof(fact_nonzero__power__divide,axiom,
    ! [X28,X9,X12,X10] :
      ( class_Fields_Ofield(X10)
     => ( X12 != c_Groups_Ozero__class_Ozero(X10)
       => c_Power_Opower__class_Opower(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12),X28) = c_Rings_Oinverse__class_Odivide(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X12,X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_add__mult__distrib,axiom,
    ! [X31,X28,X29] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)),X31) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X31),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X28),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [X4,X7,X8] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7)),X4) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8),X4),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_real__add__mult__distrib,axiom,
    ! [X4,X7,X8] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,X7)),X4) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8),X4),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

fof(fact_power__divide,axiom,
    ! [X28,X12,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Power_Opower__class_Opower(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12),X28) = c_Rings_Oinverse__class_Odivide(X10,c_Power_Opower__class_Opower(X10,X9,X28),c_Power_Opower__class_Opower(X10,X12,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

fof(fact_divide_Oadd,axiom,
    ! [X42,X19,X11,X10] :
      ( class_RealVector_Oreal__normed__field(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X11,X19),X42) = c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X42),c_Rings_Oinverse__class_Odivide(X10,X19,X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).

fof(fact_add__divide__distrib,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),X26) = c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X26),c_Rings_Oinverse__class_Odivide(X10,X12,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X34,X26,X12,X9,X30,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( X30 != c_Groups_Ozero__class_Ozero(X10)
       => ( ( X9 = X12
            & X26 != X34 )
         => c_Groups_Oplus__class_Oplus(X10,X9,hAPP(c_Groups_Otimes__class_Otimes(X10,X30),X26)) != c_Groups_Oplus__class_Oplus(X10,X12,hAPP(c_Groups_Otimes__class_Otimes(X10,X30),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_self__quotient__aux2,axiom,
    ! [X62,X30,X9] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => ( X9 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9),X62))
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X30)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X62,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_add__le__mono,axiom,
    ! [X66,X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X66)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_add__less__mono,axiom,
    ! [X66,X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31,X66)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X5,X54,X4,X55] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X5)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => ( c_Orderings_Oord__class_Oless__eq(X10,X19,c_Groups_Oone__class_Oone(X10))
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X19),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => ( c_Orderings_Oord__class_Oless__eq(X10,X19,c_Groups_Oone__class_Oone(X10))
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X11),X11) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_self__quotient__aux1,axiom,
    ! [X62,X30,X9] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X9)
     => ( X9 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9),X62))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X30,X9)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X62) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X29,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X29),X29) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oone__class_Oone(X10))),X29) ),
    file('/export/starexec/sandbox2/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,
    ! [X9,X29,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X29,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X29)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oone__class_Oone(X10))),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_abs__eq__mult,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__ring__abs(X10)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
            | c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10)) )
          & ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
            | c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10)) ) )
       => c_Groups_Oabs__class_Oabs(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oabs__class_Oabs(X10,X9)),c_Groups_Oabs__class_Oabs(X10,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_power__commutes,axiom,
    ! [X28,X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X9,X28)),X9) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Power_Opower__class_Opower(X10,X9,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

fof(fact_mult__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Oordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Oordered__comm__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Oordered__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Olinordered__comm__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X26)
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ( c_Orderings_Oord__class_Oless(X10,X26,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X14,X23,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),X14) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X14)),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_rabs__ratiotest__lemma,axiom,
    ! [X19,X11,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,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,X11),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X19)))
       => X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).

fof(fact_zero__less__power__nat__eq__number__of,axiom,
    ! [X27,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X27)))
    <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X27) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X17,X16),c_Groups_Ozero__class_Ozero(X10))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Ozero__class_Ozero(X10)) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X17,X16),c_Groups_Ozero__class_Ozero(X10))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10)) )
          | ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X17,X16))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X16) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X17,X16))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X16) )
          | ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_ln__le__cancel__iff,axiom,
    ! [X20,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
       => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X21),hAPP(c_Transcendental_Oln,X20))
        <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).

fof(fact_ln__less__cancel__iff,axiom,
    ! [X20,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X21),hAPP(c_Transcendental_Oln,X20))
        <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).

fof(fact_minus__number__of__mult,axiom,
    ! [X5,X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Int_Onumber__class_Onumber__of(X10,X4))),X5) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4))),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_ln__add__one__self__le__self,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X9,X12,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X9))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_mult__less__cancel1,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__mono1,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33),X31),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X32),X31)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [X52,X50,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X50),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X52),X50))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_mult__less__mono2,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X33),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,X32)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X31)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X31),X33),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X31),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_real__mult__less__mono2,axiom,
    ! [X19,X11,X5] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5),X11),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless(X10,X19,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__neg__pos,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless(X10,X19,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_divide__pos__pos,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X19,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_divide__neg__neg,axiom,
    ! [X19,X11,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X19,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__le__mono,axiom,
    ! [X66,X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X66)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33),X31),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X32),X66)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

fof(fact_add__gr__0,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_real__0__le__divide__iff,axiom,
    ! [X20,X21] :
      ( 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,X21,X20))
    <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,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),X20) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
          | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).

fof(fact_mult__right_Oadd,axiom,
    ! [X19,X11,X40,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X40),c_Groups_Oplus__class_Oplus(X10,X11,X19)) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X40),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X40),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

fof(fact_mult_Oadd__right,axiom,
    ! [X39,X12,X9,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Oplus__class_Oplus(X10,X12,X39)) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X39)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X5,X19,X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X11),c_Groups_Oplus__class_Oplus(X10,X19,X5)) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X19),hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X29,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X29,X29) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_add__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X26,X9),c_Groups_Oplus__class_Oplus(X10,X26,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),c_Groups_Oplus__class_Oplus(X10,X12,X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X26,X9),c_Groups_Oplus__class_Oplus(X10,X26,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_ln__mult,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
       => hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X19)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X11),hAPP(c_Transcendental_Oln,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__mult) ).

fof(fact_one__less__power,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X9)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Power_Opower__class_Opower(X10,X9,X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

fof(fact_DERIV__ln,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
     => c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X21,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ln) ).

fof(fact_add__increasing,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X26)
         => c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Oplus__class_Oplus(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X9,X12,X26,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X26)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
         => c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Oplus__class_Oplus(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X26)
         => c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Oplus__class_Oplus(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X12,X26)
         => c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Oplus__class_Oplus(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_pos__add__strict,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X12,X26)
         => c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Oplus__class_Oplus(X10,X9,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X21),hAPP(c_Groups_Otimes__class_Otimes(X10,X20),X20)) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X21 = c_Groups_Ozero__class_Ozero(X10)
          & X20 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_power__one__over,axiom,
    ! [X28,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),c_Power_Opower__class_Opower(X10,X9,X28)) = c_Power_Opower__class_Opower(X10,c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),X9),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X16),c_Groups_Ozero__class_Ozero(X10))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Ozero__class_Ozero(X10)) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X16))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17)
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X16) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_add__le__mono1,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_zadd__left__mono,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X33),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_real__add__left__mono,axiom,
    ! [X5,X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X11),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,X32)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X33,X31),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X32,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__cancel__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__cancel__semiring(X10)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
            & c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10)) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12) ) )
       => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__cancel__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__cancel__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X9),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_mult__neg__pos,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X9),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
            & c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12) )
          | ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
            & c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10)) ) )
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__cancel__semiring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_less__1__mult,axiom,
    ! [X28,X29,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X29)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X28)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X29),X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_mult__pos__pos,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__semiring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X12)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_mult__neg__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_add__mult__distrib2,axiom,
    ! [X28,X29,X31] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X29),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [X7,X8,X4] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4),X8),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4),X7)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X17,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X17,X17))
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X17,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),X26) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oab__semigroup__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),X26) = c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,X12,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12),X26) = c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,X12,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X34,X26,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,X26,X34)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X34,X26,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,X26,X34)) = c_Groups_Oplus__class_Oplus(X10,X26,c_Groups_Oplus__class_Oplus(X10,X9,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_real__0__le__add__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

fof(fact_real__0__less__add__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

fof(fact_real__add__le__0__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

fof(fact_real__add__less__0__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

fof(fact_inverse__le__imp__le,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless__eq(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).

fof(fact_inverse__less__imp__less,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12))
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).

fof(fact_inverse__le__imp__le__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12))
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).

fof(fact_inverse__less__imp__less__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12))
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)),X26) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X14,X23,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X23)),X14) = hAPP(c_Groups_Otimes__class_Otimes(X10,X15),hAPP(c_Groups_Otimes__class_Otimes(X10,X23),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X13,X14,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X15),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13)) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X14)),X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_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/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).

fof(fact_one__code__numeral__code,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).

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/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).

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/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).

fof(fact_real__two__squares__add__zero__iff,axiom,
    ! [X20,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21),X21),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X20),X20)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X20 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

fof(fact_nat__add__assoc,axiom,
    ! [X31,X28,X29] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28),X31) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_zadd__assoc,axiom,
    ! [X6,X7,X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X5,X19,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_zadd__left__commute,axiom,
    ! [X5,X19,X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X5)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_zless__add1__eq,axiom,
    ! [X22,X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X22)
        | X27 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_zero__less__power__nat__eq,axiom,
    ! [X52,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X52))
    <=> ( X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [X52,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X52))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_add1__zle__eq,axiom,
    ! [X22,X27] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,c_Groups_Oone__class_Oone(tc_Int_Oint)),X22)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X22,X27] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_DERIV__exp,axiom,
    ! [X21,X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => c_Deriv_Oderiv(X10,c_Transcendental_Oexp(X10),X21,hAPP(c_Transcendental_Oexp(X10),X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__exp) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X52))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_real__mult__order,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X19)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

fof(fact_abs__div__pos,axiom,
    ! [X11,X19,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X19)
       => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oabs__class_Oabs(X10,X11),X19) = c_Groups_Oabs__class_Oabs(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_less__add__eq__less,axiom,
    ! [X28,X29,X66,X31] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X31,X66)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X66) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X31,X28)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_abs__power__minus,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Groups_Oabs__class_Oabs(X10,c_Power_Opower__class_Opower(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X28)) = c_Groups_Oabs__class_Oabs(X10,c_Power_Opower__class_Opower(X10,X9,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

fof(fact_add__leD1,axiom,
    ! [X28,X31,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X31),X28)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X28,X31,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X31),X28)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_add__lessD1,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32),X31)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X31) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X21)
       => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X20)
         => ( c_Groups_Oplus__class_Oplus(X10,X21,X20) = c_Groups_Ozero__class_Ozero(X10)
          <=> ( X21 = c_Groups_Ozero__class_Ozero(X10)
              & X20 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_le__imp__inverse__le,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X12),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).

fof(fact_less__imp__inverse__less,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X12),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).

fof(fact_le__imp__inverse__le__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X12),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).

fof(fact_less__imp__inverse__less__neg,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ( c_Orderings_Oord__class_Oless(X10,X12,c_Groups_Ozero__class_Ozero(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X12),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).

fof(fact_mult__exp__exp,axiom,
    ! [X19,X11,X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Transcendental_Oexp(X10),X11)),hAPP(c_Transcendental_Oexp(X10),X19)) = hAPP(c_Transcendental_Oexp(X10),c_Groups_Oplus__class_Oplus(X10,X11,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__exp__exp) ).

fof(fact_exp__add,axiom,
    ! [X19,X11,X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => hAPP(c_Transcendental_Oexp(X10),c_Groups_Oplus__class_Oplus(X10,X11,X19)) = hAPP(c_Groups_Otimes__class_Otimes(X10,hAPP(c_Transcendental_Oexp(X10),X11)),hAPP(c_Transcendental_Oexp(X10),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__add) ).

fof(fact_power__mult,axiom,
    ! [X28,X29,X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X28)) = c_Power_Opower__class_Opower(X10,c_Power_Opower__class_Opower(X10,X9,X29),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [X62,X75,X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Power_Opower__class_Opower(X10,c_Power_Opower__class_Opower(X10,X11,X75),X62) = c_Power_Opower__class_Opower(X10,X11,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X75),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_less__nat__number__of,axiom,
    ! [X64,X48] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X64)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X64) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X64) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_real__minus__mult__self__le,axiom,
    ! [X11,X38] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X38),X38)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

fof(fact_nat__mult__assoc,axiom,
    ! [X31,X28,X29] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X28)),X31) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X28),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_zmult__assoc,axiom,
    ! [X6,X7,X8] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8),X7)),X6) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7),X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

fof(fact_real__mult__assoc,axiom,
    ! [X6,X7,X8] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8),X7)),X6) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7),X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).

fof(fact_abs__mult__pos,axiom,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
       => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oabs__class_Oabs(X10,X19)),X11) = c_Groups_Oabs__class_Oabs(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_times__divide__eq__right,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Rings_Oinverse__class_Odivide(X10,X12,X26)) = c_Rings_Oinverse__class_Odivide(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_one__le__inverse__iff,axiom,
    ! [X21,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X21))
      <=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X21)
          & c_Orderings_Oord__class_Oless__eq(X10,X21,c_Groups_Oone__class_Oone(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).

fof(fact_one__le__inverse,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Oone__class_Oone(X10))
         => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).

fof(fact_one__less__inverse__iff,axiom,
    ! [X21,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X21))
      <=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X21)
          & c_Orderings_Oord__class_Oless(X10,X21,c_Groups_Oone__class_Oone(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).

fof(fact_one__less__inverse,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oone__class_Oone(X10))
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).

fof(fact_exp__ge__add__one__self__aux,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ge__add__one__self__aux) ).

fof(fact_zpower__zpower,axiom,
    ! [X5,X19,X11] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X11,X19),X5) = c_Power_Opower__class_Opower(tc_Int_Oint,X11,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19),X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

fof(fact_DERIV__cmult__Id,axiom,
    ! [X21,X18,X10] :
      ( class_RealVector_Oreal__normed__field(X10)
     => c_Deriv_Oderiv(X10,c_Groups_Otimes__class_Otimes(X10,X18),X21,X18) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult__Id) ).

fof(fact_mult__le__mono1,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33),X31),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X32),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X33),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X26 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Odivide(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X26),X12)) = c_Rings_Oinverse__class_Odivide(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X26 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Odivide(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26),hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X26)) = c_Rings_Oinverse__class_Odivide(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_power__inject__exp,axiom,
    ! [X52,X53,X17,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X17)
       => ( c_Power_Opower__class_Opower(X10,X17,X53) = c_Power_Opower__class_Opower(X10,X17,X52)
        <=> X53 = X52 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(fact_one__le__power,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X9)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Power_Opower__class_Opower(X10,X9,X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(fact_zero__le__power,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,X9,X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(fact_zero__less__power,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,X9,X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_ln__ge__zero__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X21))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).

fof(fact_ln__ge__zero__imp__ge__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X11))
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).

fof(fact_ln__gt__zero__iff,axiom,
    ! [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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X21))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).

fof(fact_ln__gt__zero__imp__gt__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X11))
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).

fof(fact_ln__less__zero__iff,axiom,
    ! [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,hAPP(c_Transcendental_Oln,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).

fof(fact_frac__eq__eq,axiom,
    ! [X27,X21,X22,X20,X10] :
      ( class_Fields_Ofield(X10)
     => ( X20 != c_Groups_Ozero__class_Ozero(X10)
       => ( X22 != c_Groups_Ozero__class_Ozero(X10)
         => ( c_Rings_Oinverse__class_Odivide(X10,X21,X20) = c_Rings_Oinverse__class_Odivide(X10,X27,X22)
          <=> hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X22) = hAPP(c_Groups_Otimes__class_Otimes(X10,X27),X20) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_le__cube,axiom,
    ! [X29] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

fof(fact_inverse__le__1__iff,axiom,
    ! [X21,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X21),c_Groups_Oone__class_Oone(X10))
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,c_Groups_Ozero__class_Ozero(X10))
          | c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).

fof(fact_inverse__less__1__iff,axiom,
    ! [X21,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X21),c_Groups_Oone__class_Oone(X10))
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,c_Groups_Ozero__class_Ozero(X10))
          | c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).

fof(fact_odd__nonzero,axiom,
    ! [X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5),X5) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [X27,X18,X16,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Rings_Oinverse__class_Odivide(X10,X16,X18) = c_Int_Onumber__class_Onumber__of(X10,X27)
      <=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
           => X16 = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18) )
          & ( X18 = c_Groups_Ozero__class_Ozero(X10)
           => c_Int_Onumber__class_Onumber__of(X10,X27) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [X18,X16,X27,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Int_Onumber__class_Onumber__of(X10,X27) = c_Rings_Oinverse__class_Odivide(X10,X16,X18)
      <=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18) = X16 )
          & ( X18 = c_Groups_Ozero__class_Ozero(X10)
           => c_Int_Onumber__class_Onumber__of(X10,X27) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_ln__less__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero) ).

fof(fact_le__imp__0__less,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_real__divide__square__eq,axiom,
    ! [X9,X30] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X30),X9),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X30),X30)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X9,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [X28,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
     => 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,X11,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X5,X4] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X5)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X13,X14,X15,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X15),hAPP(c_Groups_Otimes__class_Otimes(X10,X14),X13)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X14),hAPP(c_Groups_Otimes__class_Otimes(X10,X15),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_le__funE,axiom,
    ! [X21,X1,X2,X10,X35] :
      ( class_Orderings_Oord(X35)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X35,hAPP(X2,X21),hAPP(X1,X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_le__funD,axiom,
    ! [X21,X1,X2,X10,X35] :
      ( class_Orderings_Oord(X35)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X35,hAPP(X2,X21),hAPP(X1,X21)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X5,X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X19)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X29,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X19,X5,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X5)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X29,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X5,X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add1,axiom,
    ! [X29,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X19,X5,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X5)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X29,X32,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X32)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_exp__le__cancel__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__le__cancel__iff) ).

fof(fact_exp__less__cancel,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X19))
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__cancel) ).

fof(fact_exp__less__cancel__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__cancel__iff) ).

fof(fact_le__number__of,axiom,
    ! [X20,X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_less__number__of,axiom,
    ! [X20,X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_order__trans,axiom,
    ! [X5,X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X5)
         => c_Orderings_Oord__class_Oless__eq(X10,X11,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X5,X19)
         => c_Orderings_Oord__class_Oless__eq(X10,X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_order__less__le__trans,axiom,
    ! [X5,X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X5)
         => c_Orderings_Oord__class_Oless(X10,X11,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X5,X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless(X10,X19,X5)
         => c_Orderings_Oord__class_Oless(X10,X11,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__trans,axiom,
    ! [X5,X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless(X10,X19,X5)
         => c_Orderings_Oord__class_Oless(X10,X11,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I7_J,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X19,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X5,X19)
         => c_Orderings_Oord__class_Oless(X10,X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => ( c_Orderings_Oord__class_Oless(X10,X5,X19)
         => c_Orderings_Oord__class_Oless(X10,X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I10_J,axiom,
    ! [X5,X11,X19,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X19,X11)
       => ( c_Orderings_Oord__class_Oless(X10,X5,X19)
         => c_Orderings_Oord__class_Oless(X10,X5,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_minus__add__distrib,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oab__group__add(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X9,X12)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X12),c_Groups_Ouminus__class_Ouminus(X10,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_add__number__of__eq,axiom,
    ! [X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,X37),c_Int_Onumber__class_Onumber__of(X10,X4)) = c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_number__of__add,axiom,
    ! [X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X4)) = c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,X37),c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X21),c_Groups_Ouminus__class_Ouminus(X10,X20))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X17,X16,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X16),c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_neg__less__iff__less,axiom,
    ! [X17,X16,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X16),c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless(X10,X17,X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [X27,X16,X17,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( X17 = c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ( ( c_Int_Onumber__class_Onumber__of(X10,X27) != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)) = X16 )
          & ( c_Int_Onumber__class_Onumber__of(X10,X27) = c_Groups_Ozero__class_Ozero(X10)
           => X17 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [X17,X27,X16,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)) = X17
      <=> ( ( c_Int_Onumber__class_Onumber__of(X10,X27) != c_Groups_Ozero__class_Ozero(X10)
           => X16 = hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)) )
          & ( c_Int_Onumber__class_Onumber__of(X10,X27) = c_Groups_Ozero__class_Ozero(X10)
           => X17 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_nonzero__inverse__mult__distrib,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => ( X12 != c_Groups_Ozero__class_Ozero(X10)
         => c_Rings_Oinverse__class_Oinverse(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Oinverse(X10,X12)),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).

fof(fact_zero__le__power__abs,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Power_Opower__class_Opower(X10,c_Groups_Oabs__class_Oabs(X10,X9),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_add__minus__cancel,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_le__trans,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,X31)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_zle__trans,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X31)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_real__le__trans,axiom,
    ! [X31,X32,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X32)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X32,X31)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

fof(fact_ln__inj__iff,axiom,
    ! [X20,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
       => ( hAPP(c_Transcendental_Oln,X21) = hAPP(c_Transcendental_Oln,X20)
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inj__iff) ).

fof(fact_sgn__mult,axiom,
    ! [X19,X11,X10] :
      ( class_RealVector_Oreal__normed__div__algebra(X10)
     => c_Groups_Osgn__class_Osgn(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X19)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Osgn__class_Osgn(X10,X11)),c_Groups_Osgn__class_Osgn(X10,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).

fof(fact_sgn__times,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Groups_Osgn__class_Osgn(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Osgn__class_Osgn(X10,X9)),c_Groups_Osgn__class_Osgn(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_inverse__mult__distrib,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)),c_Rings_Oinverse__class_Oinverse(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).

fof(fact_minus__le__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X16)
      <=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X16),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_minus__less__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X16)
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X16),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_le__minus__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X16))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X16,c_Groups_Ouminus__class_Ouminus(X10,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(fact_less__minus__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X16))
      <=> c_Orderings_Oord__class_Oless(X10,X16,c_Groups_Ouminus__class_Ouminus(X10,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X4,X37] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X37),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X4,X5] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,X4)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_real__sqrt__divide,axiom,
    ! [X19,X11] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,X19)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),hAPP(c_NthRoot_Osqrt,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__divide) ).

fof(fact_nonzero__power__inverse,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,c_Power_Opower__class_Opower(X10,X9,X28)) = c_Power_Opower__class_Opower(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X9,X12,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X12 != c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12)) = c_Rings_Oinverse__class_Odivide(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X37)),c_Int_Onumber__class_Onumber__of(X10,X4)) = c_Int_Onumber__class_Onumber__of(X10,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_number__of__mult,axiom,
    ! [X4,X37,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X4)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X37)),c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_inverse__positive__imp__positive,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X9))
       => ( X9 != c_Groups_Ozero__class_Ozero(X10)
         => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).

fof(fact_inverse__negative__imp__negative,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Groups_Ozero__class_Ozero(X10))
       => ( X9 != c_Groups_Ozero__class_Ozero(X10)
         => c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X50),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_real__sqrt__le__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__iff) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X50),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_real__sqrt__less__iff,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__iff) ).

fof(fact_divide_Ominus,axiom,
    ! [X19,X11,X10] :
      ( class_RealVector_Oreal__normed__field(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X19) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Odivide(X10,X11,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).

fof(fact_power__abs,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Groups_Oabs__class_Oabs(X10,c_Power_Opower__class_Opower(X10,X9,X28)) = c_Power_Opower__class_Opower(X10,c_Groups_Oabs__class_Oabs(X10,X9),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

fof(fact_minus__divide__left,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12)) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_power__inverse,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Power_Opower__class_Opower(X10,X9,X28)) = c_Power_Opower__class_Opower(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).

fof(fact_minus__divide__right,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12)) = c_Rings_Oinverse__class_Odivide(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Pls) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [X52,X53,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
     => ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52)
      <=> X53 = X52 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
    ! [X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).

fof(fact_sgn__greater,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Osgn__class_Osgn(X10,X17))
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(fact_inverse__positive__iff__positive,axiom,
    ! [X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X17))
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
    ! [X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).

fof(fact_sgn__less,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Osgn__class_Osgn(X10,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(fact_inverse__negative__iff__negative,axiom,
    ! [X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X17),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [X17,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_le__special_I1_J,axiom,
    ! [X20,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [X20,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X20))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X21),c_Groups_Ozero__class_Ozero(X10))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_exp__less__mono,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__mono) ).

fof(fact_compl__mono,axiom,
    ! [X19,X11,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X19),c_Groups_Ouminus__class_Ouminus(X10,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X12),c_Groups_Ouminus__class_Ouminus(X10,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_sqrt__divide__self__eq,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),X11) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sqrt__divide__self__eq) ).

fof(fact_zero__less__two,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_minus__add__cancel,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Groups_Oplus__class_Oplus(X10,X9,X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_one__le__exp__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__exp__iff) ).

fof(fact_one__less__exp__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__exp__iff) ).

fof(fact_exp__le__one__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__le__one__iff) ).

fof(fact_exp__less__one__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__one__iff) ).

fof(fact_minus__le__self__iff,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X17)
      <=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_neg__less__nonneg,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X17),X17)
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_le__minus__self__iff,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_less__minus__self__iff,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ouminus__class_Ouminus(X10,X17))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_real__sqrt__power,axiom,
    ! [X31,X11] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X11,X31)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).

fof(fact_nat__less__cases,axiom,
    ! [X71,X52,X53] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52)
       => hBOOL(hAPP(hAPP(X71,X52),X53)) )
     => ( ( X53 = X52
         => hBOOL(hAPP(hAPP(X71,X52),X53)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X53)
           => hBOOL(hAPP(hAPP(X71,X52),X53)) )
         => hBOOL(hAPP(hAPP(X71,X52),X53)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_mult_Ominus__left,axiom,
    ! [X12,X9,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)),X12) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

fof(fact_mult__left_Ominus,axiom,
    ! [X19,X11,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)),X19) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

fof(fact_minus__mult__left,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oring(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_negative__imp__inverse__negative,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X9),c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).

fof(fact_positive__imp__inverse__positive,axiom,
    ! [X9,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [X4,X37] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X37)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_real__sqrt__mult,axiom,
    ! [X19,X11] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),X19)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11)),hAPP(c_NthRoot_Osqrt,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).

fof(fact_arctan__monotone_H,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X11),hAPP(c_Transcendental_Oarctan,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).

fof(fact_real__sqrt__le__mono,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),hAPP(c_NthRoot_Osqrt,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__mono) ).

fof(fact_arctan__monotone,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X11),hAPP(c_Transcendental_Oarctan,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone) ).

fof(fact_real__sqrt__less__mono,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X19)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11),hAPP(c_NthRoot_Osqrt,X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__mono) ).

fof(fact_inverse__divide,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Odivide(X10,X9,X12)) = c_Rings_Oinverse__class_Odivide(X10,X12,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).

fof(fact_xt1_I5_J,axiom,
    ! [X11,X19,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
         => X11 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__antisym,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
         => X11 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_order__antisym__conv,axiom,
    ! [X21,X20,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X20,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__eq__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Oorder(X10)
     => ( X21 = X20
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
          & c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_real__sqrt__ge__1__iff,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__1__iff) ).

fof(fact_real__sqrt__ge__0__iff,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).

fof(fact_real__sqrt__gt__1__iff,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__1__iff) ).

fof(fact_real__sqrt__gt__0__iff,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X20))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__0__iff) ).

fof(fact_real__sqrt__le__1__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__1__iff) ).

fof(fact_real__sqrt__le__0__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__0__iff) ).

fof(fact_real__sqrt__lt__1__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__1__iff) ).

fof(fact_real__sqrt__lt__0__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X21),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__0__iff) ).

fof(fact_less__add__one,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oone__class_Oone(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_power__eq__0__iff__number__of,axiom,
    ! [X27,X17,X10] :
      ( ( class_Power_Opower(X10)
        & class_Rings_Omult__zero(X10)
        & class_Rings_Ono__zero__divisors(X10)
        & class_Rings_Ozero__neq__one(X10) )
     => ( c_Power_Opower__class_Opower(X10,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X27)) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X27) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X26,X9,X12,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X12,X9) = c_Groups_Oplus__class_Oplus(X10,X26,X9)
       => X12 = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__right__cancel,axiom,
    ! [X18,X17,X16,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X16,X17) = c_Groups_Oplus__class_Oplus(X10,X18,X17)
      <=> X16 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__imp__eq,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Ocancel__ab__semigroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X9,X12) = c_Groups_Oplus__class_Oplus(X10,X9,X26)
       => X12 = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X26,X12,X9,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X9,X12) = c_Groups_Oplus__class_Oplus(X10,X9,X26)
       => X12 = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X18,X16,X17,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X17,X16) = c_Groups_Oplus__class_Oplus(X10,X17,X18)
      <=> X16 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_exp__gt__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__gt__one) ).

fof(fact_less__0__number__of,axiom,
    ! [X48] :
      ( 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,X48))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X48) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X9,X12,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X12 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) = c_Rings_Oinverse__class_Odivide(X10,X9,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_le__antisym,axiom,
    ! [X28,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
       => X29 = X28 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_zle__antisym,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X5)
       => X5 = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_real__le__antisym,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X5)
       => X5 = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X52,X50,X53] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X50) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X50)
    <=> X53 = X52 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X52,X53,X50] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X53) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X52)
    <=> X53 = X52 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_minus__divide__divide,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) = c_Rings_Oinverse__class_Odivide(X10,X9,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_real__sqrt__ge__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__one) ).

fof(fact_real__sqrt__ge__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__zero) ).

fof(fact_ln__ge__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero) ).

fof(fact_real__sqrt__gt__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__zero) ).

fof(fact_ln__gt__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero) ).

fof(fact_zmult__zminus,axiom,
    ! [X4,X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5)),X4) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(fact_minus__mult__minus,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)),c_Groups_Ouminus__class_Ouminus(X10,X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_mult__left__idem,axiom,
    ! [X12,X9,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).

fof(fact_minus__mult__commute,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oring(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)),X12) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_mult_Ominus__right,axiom,
    ! [X12,X9,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

fof(fact_mult__right_Ominus,axiom,
    ! [X11,X40,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X40),c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X40),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

fof(fact_minus__mult__right,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Oring(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12)) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ouminus__class_Ouminus(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_ln__less__self,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X11),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__self) ).

fof(fact_le__Suc__ex__iff,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50,X49)
    <=> ? [X73] : X49 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X73) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(fact_le__iff__add,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52)
    <=> ? [X72] : X52 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X72) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_ln__inverse,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inverse) ).

fof(fact_le__add1,axiom,
    ! [X29,X28] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X29,X28] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X53)
     => ( hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X53),X52) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X53 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X52 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X12,X9,X10] :
      ( class_Orderings_Oorder(X10)
     => ( X9 != X12
       => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
          | X11 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X12,X9,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,X12)
       => ( X9 != X12
         => c_Orderings_Oord__class_Oless(X10,X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_xt1_I11_J,axiom,
    ! [X9,X12,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
       => ( X9 != X12
         => c_Orderings_Oord__class_Oless(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__less,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless(X10,X21,X20)
          | X21 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
          & X21 != X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_xt1_I12_J,axiom,
    ! [X12,X9,X10] :
      ( class_Orderings_Oorder(X10)
     => ( X9 != X12
       => ( c_Orderings_Oord__class_Oless__eq(X10,X12,X9)
         => c_Orderings_Oord__class_Oless(X10,X12,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_square__eq__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Rings_Oidom(X10)
     => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X17) = hAPP(c_Groups_Otimes__class_Otimes(X10,X16),X16)
      <=> ( X17 = X16
          | X17 = c_Groups_Ouminus__class_Ouminus(X10,X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096,axiom,
    ? [X25] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096) ).

fof(fact_order__less__imp__le,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_le__iff__pred__less,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X50),X49) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_number__of__pred,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_Opred(X4)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)),c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__pred) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X9,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oabs__class_Oabs(X10,X9)),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_zero__le__square,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X22] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X22)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_eq__divide__eq,axiom,
    ! [X18,X16,X17,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X17 = c_Rings_Oinverse__class_Odivide(X10,X16,X18)
      <=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18) = X16 )
          & ( X18 = c_Groups_Ozero__class_Ozero(X10)
           => X17 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [X16,X17,X18,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X18 != c_Groups_Ozero__class_Ozero(X10)
       => ( X17 = c_Rings_Oinverse__class_Odivide(X10,X16,X18)
        <=> hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18) = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_divide__eq__eq,axiom,
    ! [X17,X18,X16,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( c_Rings_Oinverse__class_Odivide(X10,X16,X18) = X17
      <=> ( ( X18 != c_Groups_Ozero__class_Ozero(X10)
           => X16 = hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18) )
          & ( X18 = c_Groups_Ozero__class_Ozero(X10)
           => X17 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X17,X16,X18,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X18 != c_Groups_Ozero__class_Ozero(X10)
       => ( c_Rings_Oinverse__class_Odivide(X10,X16,X18) = X17
        <=> X16 = hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_inverse__eq__divide__number__of,axiom,
    ! [X4,X35] :
      ( ( class_Int_Onumber(X35)
        & class_Rings_Odivision__ring(X35) )
     => c_Rings_Oinverse__class_Oinverse(X35,c_Int_Onumber__class_Onumber__of(X35,X4)) = c_Rings_Oinverse__class_Odivide(X35,c_Groups_Oone__class_Oone(X35),c_Int_Onumber__class_Onumber__of(X35,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide__number__of) ).

fof(fact_nat__less__le,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52)
        & X53 != X52 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X52,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X52)
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52)
        | X53 = X52 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X28,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
     => ( X29 != X28
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_zless__le,axiom,
    ! [X27,X22] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X27)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X27)
        & X22 != X27 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_less__eq__real__def,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
        | X21 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

fof(fact_real__less__def,axiom,
    ! [X20,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X21,X20)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
        & X21 != X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(fact_uminus__apply,axiom,
    ! [X21,X51,X35,X10] :
      ( class_Groups_Ouminus(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X35,X10),X51),X21) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(X51,X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [X11,X10] :
      ( class_Rings_Ocomm__ring__1(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,X11) = hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_sgn__1__neg,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X17) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))
      <=> c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_sgn__neg,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => c_Groups_Osgn__class_Osgn(X10,X9) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X19)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X28,X29] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X28,X29] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28)
        | X29 = X28 )
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_divide__eq__imp,axiom,
    ! [X9,X12,X26,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X26 != c_Groups_Ozero__class_Ozero(X10)
       => ( X12 = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26)
         => c_Rings_Oinverse__class_Odivide(X10,X12,X26) = X9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_eq__divide__imp,axiom,
    ! [X12,X9,X26,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X26 != c_Groups_Ozero__class_Ozero(X10)
       => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X26) = X12
         => X9 = c_Rings_Oinverse__class_Odivide(X10,X12,X26) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X9,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => c_Groups_Oabs__class_Oabs(X10,X9) = c_Groups_Ouminus__class_Ouminus(X10,X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_abs__of__neg,axiom,
    ! [X9,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
       => c_Groups_Oabs__class_Oabs(X10,X9) = c_Groups_Ouminus__class_Ouminus(X10,X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_exp__ln__iff,axiom,
    ! [X21] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X21)) = X21
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln__iff) ).

fof(fact_exp__ln,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln) ).

fof(fact_ext,axiom,
    ! [X1,X2] :
      ( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
     => X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

fof(fact_divide__inverse,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Odivide(X10,X9,X12) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__inverse) ).

fof(fact_field__divide__inverse,axiom,
    ! [X12,X9,X10] :
      ( class_Fields_Ofield(X10)
     => c_Rings_Oinverse__class_Odivide(X10,X9,X12) = hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__divide__inverse) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X52,X17,X10] :
      ( ( class_Power_Opower(X10)
        & class_Rings_Omult__zero(X10)
        & class_Rings_Ono__zero__divisors(X10)
        & class_Rings_Ozero__neq__one(X10) )
     => ( c_Power_Opower__class_Opower(X10,X17,X52) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
          & X52 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_power__0__left__number__of,axiom,
    ! [X4,X10] :
      ( ( class_Power_Opower(X10)
        & class_Rings_Osemiring__0(X10) )
     => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4)) = c_Groups_Oone__class_Oone(X10) )
        & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4)) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).

fof(fact_real__add__minus__iff,axiom,
    ! [X17,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X21 = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

fof(fact_le__square,axiom,
    ! [X29] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(fact_mult__cancel2,axiom,
    ! [X52,X50,X53] :
      ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X50) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X52),X50)
    <=> ( X53 = X52
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(fact_real__mult__right__cancel,axiom,
    ! [X16,X17,X18] :
      ( X18 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17),X18) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16),X18)
      <=> X17 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [X52,X53,X50] :
      ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52)
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X53 = X52 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_mult__cancel1,axiom,
    ! [X52,X53,X50] :
      ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X53) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50),X52)
    <=> ( X53 = X52
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(fact_real__mult__left__cancel,axiom,
    ! [X16,X17,X18] :
      ( X18 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18),X17) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18),X16)
      <=> X17 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).

fof(fact_sgn__pos,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
       => c_Groups_Osgn__class_Osgn(X10,X9) = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_sgn__1__pos,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X17) = c_Groups_Oone__class_Oone(X10)
      <=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( X21 != X20
      <=> ( c_Orderings_Oord__class_Oless(X10,X21,X20)
          | c_Orderings_Oord__class_Oless(X10,X20,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
        | X11 = X19
        | c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_linorder__linear,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
        | c_Orderings_Oord__class_Oless__eq(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
        | c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_ln__eq__zero__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
     => ( hAPP(c_Transcendental_Oln,X21) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      <=> X21 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).

fof(fact_real__sqrt__eq__zero__cancel,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( hAPP(c_NthRoot_Osqrt,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X26,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,X26) = c_Groups_Oplus__class_Oplus(X10,X26,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_minus__unique,axiom,
    ! [X12,X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X9,X12) = c_Groups_Ozero__class_Ozero(X10)
       => c_Groups_Ouminus__class_Ouminus(X10,X9) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X16)
      <=> c_Groups_Oplus__class_Oplus(X10,X17,X16) = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_add__eq__0__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X21,X20) = c_Groups_Ozero__class_Ozero(X10)
      <=> X20 = c_Groups_Ouminus__class_Ouminus(X10,X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).

fof(fact_real__divide__def,axiom,
    ! [X45,X46] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X46,X45) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__def) ).

fof(fact_divide__real__def,axiom,
    ! [X19,X11] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,X19) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__real__def) ).

fof(fact_exp__minus,axiom,
    ! [X11,X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => hAPP(c_Transcendental_Oexp(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Rings_Oinverse__class_Oinverse(X10,hAPP(c_Transcendental_Oexp(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__minus) ).

fof(fact_real__sqrt__not__eq__zero,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => hAPP(c_NthRoot_Osqrt,X11) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__not__eq__zero) ).

fof(fact_nat__neq__iff,axiom,
    ! [X52,X53] :
      ( X53 != X52
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X52)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X53) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_zless__linear,axiom,
    ! [X19,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X19)
      | X11 = X19
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(fact_left__inverse,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)),X9) = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).

fof(fact_field__inverse,axiom,
    ! [X9,X10] :
      ( class_Fields_Ofield(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)),X9) = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).

fof(fact_right__inverse__eq,axiom,
    ! [X17,X16,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X16 != c_Groups_Ozero__class_Ozero(X10)
       => ( c_Rings_Oinverse__class_Odivide(X10,X17,X16) = c_Groups_Oone__class_Oone(X10)
        <=> X17 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_nat__le__linear,axiom,
    ! [X28,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zle__linear,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_real__le__linear,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5,X4)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(fact_nat__add__commute,axiom,
    ! [X28,X29] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_zadd__commute,axiom,
    ! [X4,X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,X4) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_field__power__not__zero,axiom,
    ! [X28,X9,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Power_Opower__class_Opower(X10,X9,X28) != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Groups_Oplus__class_Oplus(X10,X17,X17) = c_Groups_Ozero__class_Ozero(X10)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Oplus__class_Oplus(X10,X17,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_real__sgn__pos,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__pos) ).

fof(fact_square__eq__1__iff,axiom,
    ! [X21,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X21),X21) = c_Groups_Oone__class_Oone(X10)
      <=> ( X21 = c_Groups_Oone__class_Oone(X10)
          | X21 = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

fof(fact_real__add__eq__0__iff,axiom,
    ! [X20,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X20) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X20 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

fof(fact_add__0__iff,axiom,
    ! [X17,X16,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( X16 = c_Groups_Oplus__class_Oplus(X10,X16,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_less__imp__neq,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => X11 != X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => X11 != X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => X19 != X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_eq__number__of__0,axiom,
    ! [X48] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [X48] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_divide__Numeral0,axiom,
    ! [X11,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber__ring(X10) )
     => c_Rings_Oinverse__class_Odivide(X10,X11,c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_neq0__conv,axiom,
    ! [X52] :
      ( X52 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_nonzero__inverse__minus__eq,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).

fof(fact_le__0__eq,axiom,
    ! [X52] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_inverse__unique,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) = c_Groups_Oone__class_Oone(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,X9) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).

fof(fact_ab__left__minus,axiom,
    ! [X9,X10] :
      ( class_Groups_Oab__group__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X9) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_left__minus,axiom,
    ! [X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),X9) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_right__minus,axiom,
    ! [X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_add__is__0,axiom,
    ! [X52,X53] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X52) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X53 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_gr__implies__not0,axiom,
    ! [X28,X29] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X29,X28)
     => X28 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_real__mult__inverse__left,axiom,
    ! [X11] :
      ( X11 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)),X11) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X28,X29] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X28) = X29
     => X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_exp__ge__zero,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ge__zero) ).

fof(fact_exp__gt__zero,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__gt__zero) ).

fof(fact_real__sgn__eq,axiom,
    ! [X11] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__eq) ).

fof(fact_less__not__refl3,axiom,
    ! [X69,X70] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,X69)
     => X70 != X69 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [X29,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X29)
     => X29 != X28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Rings_Oring__no__zero__divisors(X10)
     => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X16) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X17 = c_Groups_Ozero__class_Ozero(X10)
          | X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_no__zero__divisors,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Ono__zero__divisors(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => ( X12 != c_Groups_Ozero__class_Ozero(X10)
         => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) != c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_divisors__zero,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Ono__zero__divisors(X10)
     => ( hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) = c_Groups_Ozero__class_Ozero(X10)
       => ( X9 = c_Groups_Ozero__class_Ozero(X10)
          | X12 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_nonzero__inverse__eq__divide,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),X9) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X12) = hAPP(c_Groups_Otimes__class_Otimes(X10,X12),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_sgn__minus,axiom,
    ! [X11,X10] :
      ( class_RealVector_Oreal__normed__vector(X10)
     => c_Groups_Osgn__class_Osgn(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Osgn__class_Osgn(X10,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).

fof(fact_inverse__minus__eq,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).

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/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_add__numeral__0,axiom,
    ! [X9,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X9,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_power__0__left,axiom,
    ! [X28,X10] :
      ( ( class_Power_Opower(X10)
        & class_Rings_Osemiring__0(X10) )
     => ( ( X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),X28) = c_Groups_Oone__class_Oone(X10) )
        & ( X28 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),X28) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(fact_number__of__minus,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)) = c_Groups_Ouminus__class_Ouminus(X10,c_Int_Onumber__class_Onumber__of(X10,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X4,X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Int_Onumber__class_Onumber__of(X10,X4)) = c_Int_Onumber__class_Onumber__of(X10,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_right__inverse,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Rings_Oinverse__class_Oinverse(X10,X9)) = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).

fof(fact_inverse__eq__divide,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).

fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
    ! [X9,X10] :
      ( class_Fields_Ofield(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Rings_Oinverse__class_Odivide(X10,c_Groups_Oone__class_Oone(X10),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5),X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_divide__self__if,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => ( ( X9 = c_Groups_Ozero__class_Ozero(X10)
         => c_Rings_Oinverse__class_Odivide(X10,X9,X9) = c_Groups_Ozero__class_Ozero(X10) )
        & ( X9 != c_Groups_Ozero__class_Ozero(X10)
         => c_Rings_Oinverse__class_Odivide(X10,X9,X9) = c_Groups_Oone__class_Oone(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_zero__le__one,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_zero__less__one,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_nat__mult__commute,axiom,
    ! [X28,X29] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X28) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X28),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_zmult__commute,axiom,
    ! [X4,X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5),X4) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(fact_real__mult__commute,axiom,
    ! [X4,X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5),X4) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

fof(fact_power__one,axiom,
    ! [X28,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,c_Groups_Oone__class_Oone(X10),X28) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(fact_divide_Ozero,axiom,
    ! [X19,X10] :
      ( class_RealVector_Oreal__normed__field(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ozero__class_Ozero(X10),X19) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).

fof(fact_divide__zero__left,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Odivide(X10,c_Groups_Ozero__class_Ozero(X10),X9) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_divide__zero,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => c_Rings_Oinverse__class_Odivide(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_divide__self,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Odivide(X10,X9,X9) = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X4] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_arctan__minus,axiom,
    ! [X11] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__minus) ).

fof(fact_real__sqrt__minus,axiom,
    ! [X11] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__minus) ).

fof(fact_real__sqrt__inverse,axiom,
    ! [X11] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__inverse) ).

fof(fact_mult__is__0,axiom,
    ! [X52,X53] :
      ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X52) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X53 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

fof(fact_power__0,axiom,
    ! [X9,X10] :
      ( class_Power_Opower(X10)
     => c_Power_Opower__class_Opower(X10,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Power_Opower__class_Opower(X10,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_add__0__left,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_add__0,axiom,
    ! [X9,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0__right,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X9,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Ozero__class_Ozero(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_divide__1,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Odivide(X10,X9,c_Groups_Oone__class_Oone(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [X28,X29] :
      ( X29 = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),X28)
     => ( X28 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X29 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [X52,X53] :
      ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X52) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X53 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X52 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [X52,X53] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53),X52)
    <=> ( X53 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X52 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_power__one__right,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => c_Power_Opower__class_Opower(X10,X9,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [X11,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => c_Power_Opower__class_Opower(X10,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_order__eq__refl,axiom,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( X11 = X19
       => c_Orderings_Oord__class_Oless__eq(X10,X11,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_nonzero__inverse__eq__imp__eq,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Rings_Oinverse__class_Oinverse(X10,X12)
       => ( X9 != c_Groups_Ozero__class_Ozero(X10)
         => ( X12 != c_Groups_Ozero__class_Ozero(X10)
           => X9 = X12 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).

fof(fact_mult_Ozero__left,axiom,
    ! [X12,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ozero__class_Ozero(X10)),X12) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).

fof(fact_mult__left_Ozero,axiom,
    ! [X19,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ozero__class_Ozero(X10)),X19) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

fof(fact_mult__zero__left,axiom,
    ! [X9,X10] :
      ( class_Rings_Omult__zero(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Ozero__class_Ozero(X10)),X9) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_order__refl,axiom,
    ! [X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => c_Orderings_Oord__class_Oless__eq(X10,X11,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_sgn__sgn,axiom,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Groups_Osgn__class_Osgn(X10,c_Groups_Osgn__class_Osgn(X10,X9)) = c_Groups_Osgn__class_Osgn(X10,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_eq__number__of,axiom,
    ! [X20,X21,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ( c_Int_Onumber__class_Onumber__of(X10,X21) = c_Int_Onumber__class_Onumber__of(X10,X20)
      <=> X21 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_mult__1__left,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_mult__1,axiom,
    ! [X9,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,c_Groups_Oone__class_Oone(X10)),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_gr0I,axiom,
    ! [X28] :
      ( X28 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_mult_Ozero__right,axiom,
    ! [X9,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

fof(fact_mult__right_Ozero,axiom,
    ! [X11,X10] :
      ( class_RealVector_Oreal__normed__algebra(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X11),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

fof(fact_mult__zero__right,axiom,
    ! [X9,X10] :
      ( class_Rings_Omult__zero(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X28] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_zadd__0,axiom,
    ! [X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X29] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_zadd__0__right,axiom,
    ! [X5] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_eq__imp__le,axiom,
    ! [X28,X29] :
      ( X29 = X28
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X28] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X28] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_exp__inj__iff,axiom,
    ! [X20,X21] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X20)
    <=> X21 = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__inj__iff) ).

fof(fact_mult__1__right,axiom,
    ! [X9,X10] :
      ( class_Groups_Omonoid__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X9,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X9,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),c_Groups_Oone__class_Oone(X10)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X20,X21,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => ( c_Groups_Ouminus__class_Ouminus(X10,X21) = c_Groups_Ouminus__class_Ouminus(X10,X20)
      <=> X21 = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Ouminus__class_Ouminus(X10,X17) = c_Groups_Ouminus__class_Ouminus(X10,X16)
      <=> X17 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_inverse__eq__imp__eq,axiom,
    ! [X12,X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Rings_Oinverse__class_Oinverse(X10,X12)
       => X9 = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).

fof(fact_inverse__eq__iff__eq,axiom,
    ! [X16,X17,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X17) = c_Rings_Oinverse__class_Oinverse(X10,X16)
      <=> X17 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).

fof(fact_nonzero__inverse__inverse__eq,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).

fof(fact_le__refl,axiom,
    ! [X28] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X28),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_zle__refl,axiom,
    ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_real__le__refl,axiom,
    ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(fact_exp__not__eq__zero,axiom,
    ! [X11,X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => hAPP(c_Transcendental_Oexp(X10),X11) != c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__not__eq__zero) ).

fof(fact_add__Pls,axiom,
    ! [X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X31) = X31,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_add__Pls__right,axiom,
    ! [X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Int_OPls) = X31,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_mult__idem,axiom,
    ! [X11,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X11) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).

fof(fact_times_Oidem,axiom,
    ! [X9,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).

fof(fact_double__compl,axiom,
    ! [X11,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X9,X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X9)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_inverse__inverse__eq,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X9)) = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).

fof(fact_minus__equation__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Ouminus__class_Ouminus(X10,X17) = X16
      <=> c_Groups_Ouminus__class_Ouminus(X10,X16) = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X16,X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X16)
      <=> X16 = c_Groups_Ouminus__class_Ouminus(X10,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_mult__0,axiom,
    ! [X28] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

fof(fact_ln__exp,axiom,
    ! [X11] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__exp) ).

fof(fact_exp__zero,axiom,
    ! [X10] :
      ( ( class_RealVector_Oreal__normed__field(X10)
        & class_SEQ_Obanach(X10) )
     => hAPP(c_Transcendental_Oexp(X10),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__zero) ).

fof(fact_iszero__Numeral0,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_nat__mult__1,axiom,
    ! [X28] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X28) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(fact_zmult__1,axiom,
    ! [X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(fact_real__mult__1,axiom,
    ! [X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X5) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(fact_mult__0__right,axiom,
    ! [X29] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X29),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(fact_ln__unique,axiom,
    ! [X11,X19] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X19) = X11
     => hAPP(c_Transcendental_Oln,X11) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__unique) ).

fof(fact_exp__ln__eq,axiom,
    ! [X11,X38] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X38) = X11
     => hAPP(c_Transcendental_Oln,X11) = X38 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln__eq) ).

fof(fact_real__sqrt__eq__iff,axiom,
    ! [X20,X21] :
      ( hAPP(c_NthRoot_Osqrt,X21) = hAPP(c_NthRoot_Osqrt,X20)
    <=> X21 = X20 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Ouminus__class_Ouminus(X10,X17)
      <=> c_Groups_Ozero__class_Ozero(X10) = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_inverse__eq__1__iff,axiom,
    ! [X21,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X21) = c_Groups_Oone__class_Oone(X10)
      <=> X21 = c_Groups_Oone__class_Oone(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [X17,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Ouminus__class_Ouminus(X10,X17) = c_Groups_Ozero__class_Ozero(X10)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_sgn__zero__iff,axiom,
    ! [X21,X10] :
      ( class_RealVector_Oreal__normed__vector(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X21) = c_Groups_Ozero__class_Ozero(X10)
      <=> X21 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

fof(fact_sgn__0__0,axiom,
    ! [X17,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X17) = c_Groups_Ozero__class_Ozero(X10)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(fact_inverse__nonzero__iff__nonzero,axiom,
    ! [X17,X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X17) = c_Groups_Ozero__class_Ozero(X10)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).

fof(fact_nonzero__imp__inverse__nonzero,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X9 != c_Groups_Ozero__class_Ozero(X10)
       => c_Rings_Oinverse__class_Oinverse(X10,X9) != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).

fof(fact_inverse__zero__imp__zero,axiom,
    ! [X9,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( c_Rings_Oinverse__class_Oinverse(X10,X9) = c_Groups_Ozero__class_Ozero(X10)
       => X9 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).

fof(fact_nat__mult__1__right,axiom,
    ! [X28] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X28),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X28,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_zmult__1__right,axiom,
    ! [X5] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X77,X78] :
      ( class_Groups_Ouminus(X78)
     => class_Groups_Ouminus(tc_fun(X77,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X77,X78] :
      ( class_Lattices_Oboolean__algebra(X78)
     => class_Lattices_Oboolean__algebra(tc_fun(X77,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X77,X78] :
      ( class_Orderings_Oord(X78)
     => class_Orderings_Oord(tc_fun(X77,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X77,X78] :
      ( class_Orderings_Oorder(X78)
     => class_Orderings_Oorder(tc_fun(X77,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X77,X78] :
      ( class_Orderings_Opreorder(X78)
     => class_Orderings_Opreorder(tc_fun(X77,X78)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(fact_zminus__zminus,axiom,
    ! [X5] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5)) = X5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_neg__equal__zero,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Groups_Ouminus__class_Ouminus(X10,X17) = X17
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_equal__neg__zero,axiom,
    ! [X17,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X10,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_iszero__def,axiom,
    ! [X22,X10] :
      ( class_Rings_Osemiring__1(X10)
     => ( c_Int_Oiszero(X10,X22)
      <=> X22 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).

fof(fact_exp__eq__one__iff,axiom,
    ! [X21] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X21) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__eq__one__iff) ).

fof(fact_mult__Pls,axiom,
    ! [X4] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),X4) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).

fof(fact_abs__one,axiom,
    ! [X10] :
      ( class_Rings_Olinordered__idom(X10)
     => c_Groups_Oabs__class_Oabs(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_minus__zero,axiom,
    ! [X10] :
      ( class_Groups_Ogroup__add(X10)
     => c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_sgn__one,axiom,
    ! [X10] :
      ( class_RealVector_Oreal__normed__algebra__1(X10)
     => c_Groups_Osgn__class_Osgn(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).

fof(fact_sgn0,axiom,
    ! [X10] :
      ( class_Groups_Osgn__if(X10)
     => c_Groups_Osgn__class_Osgn(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

fof(fact_sgn__zero,axiom,
    ! [X10] :
      ( class_RealVector_Oreal__normed__vector(X10)
     => c_Groups_Osgn__class_Osgn(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).

fof(fact_inverse__1,axiom,
    ! [X10] :
      ( class_Rings_Odivision__ring(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).

fof(fact_inverse__zero,axiom,
    ! [X10] :
      ( class_Rings_Odivision__ring__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).

fof(fact_field__inverse__zero,axiom,
    ! [X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).

fof(fact_real__sqrt__eq__1__iff,axiom,
    ! [X21] :
      ( hAPP(c_NthRoot_Osqrt,X21) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    <=> X21 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).

fof(fact_real__sqrt__eq__0__iff,axiom,
    ! [X21] :
      ( hAPP(c_NthRoot_Osqrt,X21) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__0__iff) ).

fof(fact_iszero__0,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => c_Int_Oiszero(X10,c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).

fof(fact_number__of__Pls,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => c_Groups_Ozero__class_Ozero(X10) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_zero__neq__one,axiom,
    ! [X10] :
      ( class_Rings_Ozero__neq__one(X10)
     => c_Groups_Ozero__class_Ozero(X10) != c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_one__neq__zero,axiom,
    ! [X10] :
      ( class_Rings_Ozero__neq__one(X10)
     => c_Groups_Oone__class_Oone(X10) != c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_number__of__is__id,axiom,
    ! [X31] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X31) = X31,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

fof(fact_em0,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_em0) ).

fof(fact_d_I3_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I3_J) ).

fof(fact_H_I3_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I3_J) ).

fof(fact_dm_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dm_I1_J) ).

fof(fact_dm_I2_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dm_I2_J) ).

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/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_int__0__less__1,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(fact_one0,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one0) ).

fof(fact_d1_I2_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d1_I2_J) ).

fof(fact_d_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I1_J) ).

fof(fact_assms,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).

fof(fact_H_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I1_J) ).

fof(fact_m_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).

fof(fact_d_I2_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I2_J) ).

fof(fact_H_I2_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I2_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/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_zminus__0,axiom,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

fof(fact_INVERSE__ZERO,axiom,
    c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).

fof(fact_arctan__zero__zero,axiom,
    hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__zero__zero) ).

fof(fact_real__sqrt__one,axiom,
    hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).

fof(fact_real__sqrt__zero,axiom,
    hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).

fof(fact_ln__one,axiom,
    hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__one) ).

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/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_zero__code__numeral__code,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).

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/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).

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/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_minus__Pls,axiom,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).

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/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

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/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

fof(arity_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

fof(arity_Int__Oint__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).

fof(arity_Complex__Ocomplex__Power_Opower,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_RealDef__Oreal__Power_Opower,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).

fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).

fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
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fof(arity_HOL__Obool__Groups_Ouminus,axiom,
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fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__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/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__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/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).

fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).

fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(arity_Int__Oint__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).

fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).

fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
    class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
    class_Rings_Odivision__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
    class_Fields_Ofield(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
    class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
    class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

fof(i_0_1237,plain,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,c_Power_Opower__class_Opower(X10,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X10,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(i_0_1238,plain,
    ! [X9,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Power_Opower__class_Opower(X10,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).

fof(i_0_1239,plain,
    ! [X4,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ~ c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(X4))) ),
    inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(i_0_1240,plain,
    ! [X10] :
      ( class_Int_Onumber__ring(X10)
     => ~ c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(i_0_1241,plain,
    ! [X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X37)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(i_0_1242,plain,
    ! [X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X37)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(i_0_1243,plain,
    ! [X4841,X4842,X4843,X4844] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4844,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,X4843,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,X4842,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,X4841,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)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4844,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,X4843,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,X4842,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,X4841,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_1244,plain,
    ! [X4599] : c_Int_Osucc(c_Int_OBit0(X4599)) = c_Int_OBit1(X4599),
    inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).

fof(i_0_1245,plain,
    ! [X4611] : c_Int_OBit0(X4611) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4611,X4611),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_1246,plain,
    ! [X4058] : c_Int_Osucc(X4058) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4058,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_succ__def]) ).

fof(i_0_1247,plain,
    ! [X4725,X4726,X4727,X4728] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4728,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,X4727,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,X4726,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,X4725,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_1248,plain,
    ! [X4833,X4834,X4835,X4836] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,X4836,X4835),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,X4834,X4833),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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4836,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,X4834,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4835,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,X4833,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_1249,plain,
    ! [X4990] : hAPP(c_Transcendental_Oarctan,X4990) = hAPP(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)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4990,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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,X4990,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_1250,plain,
    ! [X4997,X4998] : 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,X4998,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4998,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,X4997,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_1251,plain,
    ! [X4999,X5000,X5001] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5001),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X5000,hAPP(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,X4999),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X5000,hAPP(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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X5001,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,X4999,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X5000) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__less])]) ).

fof(i_0_1252,plain,
    ! [X4813,X4814,X4815] :
      ( ~ class_Int_Onumber__ring(X4815)
      | c_Power_Opower__class_Opower(X4815,c_Groups_Oplus__class_Oplus(X4815,X4814,X4813),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X4815,c_Groups_Oplus__class_Oplus(X4815,c_Power_Opower__class_Opower(X4815,X4814,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4815,X4813,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(X4815,hAPP(c_Groups_Otimes__class_Otimes(X4815,c_Int_Onumber__class_Onumber__of(X4815,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4814)),X4813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).

fof(i_0_1253,plain,
    ! [X4848,X4849] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4849,X4848),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,X4849,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,X4848,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(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)))),X4849)),X4848)),
    inference(variable_rename,[status(thm)],[fact_real__sum__squared__expand]) ).

fof(i_0_1254,plain,
    ! [X4722,X4723,X4724] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4724)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4723,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4724,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,X4722,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4724,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),X4723)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4722)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4723,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,X4722,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X4724) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__sqrt__hcomplex__capprox])]) ).

fof(i_0_1255,plain,
    ! [X4845,X4846] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4846,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,X4845,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_1256,plain,
    ! [X4829,X4830] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4830,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4830,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,X4829,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_1257,plain,
    ! [X4831,X4832] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4832,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4831,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,X4832,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_1258,plain,
    ! [X4794] : hAPP(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,X4794,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,hAPP(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)))),X4794),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_1259,plain,
    ! [X4810,X4811,X4812] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4812,c_Groups_Ozero__class_Ozero(X4812),c_Groups_Oplus__class_Oplus(X4812,c_Power_Opower__class_Opower(X4812,X4811,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4812,X4810,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X4811 != c_Groups_Ozero__class_Ozero(X4812)
        | X4810 != c_Groups_Ozero__class_Ozero(X4812)
        | ~ class_Rings_Olinordered__idom(X4812) )
      & ( X4811 = c_Groups_Ozero__class_Ozero(X4812)
        | c_Orderings_Oord__class_Oless(X4812,c_Groups_Ozero__class_Ozero(X4812),c_Groups_Oplus__class_Oplus(X4812,c_Power_Opower__class_Opower(X4812,X4811,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4812,X4810,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X4812) )
      & ( X4810 = c_Groups_Ozero__class_Ozero(X4812)
        | c_Orderings_Oord__class_Oless(X4812,c_Groups_Ozero__class_Ozero(X4812),c_Groups_Oplus__class_Oplus(X4812,c_Power_Opower__class_Opower(X4812,X4811,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4812,X4810,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X4812) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).

fof(i_0_1260,plain,
    ! [X4804,X4805,X4806] :
      ( ( X4805 = c_Groups_Ozero__class_Ozero(X4806)
        | ~ c_Orderings_Oord__class_Oless__eq(X4806,c_Groups_Oplus__class_Oplus(X4806,c_Power_Opower__class_Opower(X4806,X4805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4806,X4804,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4806))
        | ~ class_Rings_Olinordered__idom(X4806) )
      & ( X4804 = c_Groups_Ozero__class_Ozero(X4806)
        | ~ c_Orderings_Oord__class_Oless__eq(X4806,c_Groups_Oplus__class_Oplus(X4806,c_Power_Opower__class_Opower(X4806,X4805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4806,X4804,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4806))
        | ~ class_Rings_Olinordered__idom(X4806) )
      & ( X4805 != c_Groups_Ozero__class_Ozero(X4806)
        | X4804 != c_Groups_Ozero__class_Ozero(X4806)
        | c_Orderings_Oord__class_Oless__eq(X4806,c_Groups_Oplus__class_Oplus(X4806,c_Power_Opower__class_Opower(X4806,X4805,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4806,X4804,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4806))
        | ~ class_Rings_Olinordered__idom(X4806) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).

fof(i_0_1261,plain,
    ! [X4807,X4808,X4809] :
      ( ~ class_Rings_Olinordered__idom(X4809)
      | ~ c_Orderings_Oord__class_Oless(X4809,c_Groups_Oplus__class_Oplus(X4809,c_Power_Opower__class_Opower(X4809,X4808,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4809,X4807,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1237])]) ).

fof(i_0_1262,plain,
    ! [X4839,X4840] :
      ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4840,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,X4839,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != X4839
      | X4840 = 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_1263,plain,
    ! [X4837,X4838] :
      ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4838,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,X4837,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != X4838
      | X4837 = 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_1264,plain,
    ! [X4816,X4817,X4818] :
      ( ~ class_Rings_Olinordered__idom(X4818)
      | ~ c_Orderings_Oord__class_Oless__eq(X4818,c_Power_Opower__class_Opower(X4818,X4817,hAPP(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)))),X4816)),c_Groups_Ozero__class_Ozero(X4818))
      | X4817 = c_Groups_Ozero__class_Ozero(X4818) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power__le__0__imp__0])]) ).

fof(i_0_1265,plain,
    ! [X4657,X4658,X4659] :
      ( ( X4659 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4658,hAPP(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)))),X4657))
        | hAPP(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)))),X4659) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4658,X4657) )
      & ( hAPP(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)))),X4659) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4658,X4657)
        | X4659 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4658,hAPP(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)))),X4657)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__2__times__iff])]) ).

fof(i_0_1266,plain,
    ! [X4996] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,X4996,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4996,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(variable_rename,[status(thm)],[fact_DERIV__arctan]) ).

fof(i_0_1267,plain,
    ! [X4801,X4802,X4803] :
      ( ~ class_Rings_Olinordered__idom(X4803)
      | c_Orderings_Oord__class_Oless__eq(X4803,c_Groups_Ozero__class_Ozero(X4803),c_Groups_Oplus__class_Oplus(X4803,c_Power_Opower__class_Opower(X4803,X4802,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4803,X4801,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_1268,plain,
    ! [X4819,X4820,X4821] :
      ( ~ class_Rings_Olinordered__idom(X4821)
      | c_Orderings_Oord__class_Oless__eq(X4821,c_Groups_Ozero__class_Ozero(X4821),c_Power_Opower__class_Opower(X4821,X4820,hAPP(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)))),X4819))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).

fof(i_0_1269,plain,
    ! [X4789,X4790,X4791] :
      ( ~ class_Rings_Oring__1(X4791)
      | c_Power_Opower__class_Opower(X4791,c_Groups_Ouminus__class_Ouminus(X4791,X4790),hAPP(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)))),X4789)) = c_Power_Opower__class_Opower(X4791,X4790,hAPP(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)))),X4789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ring__1__class_Opower__minus__even])]) ).

fof(i_0_1270,plain,
    ! [X4769,X4770,X4771] :
      ( ~ class_Rings_Olinordered__semidom(X4771)
      | ~ c_Orderings_Oord__class_Oless__eq(X4771,c_Power_Opower__class_Opower(X4771,X4770,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4771,X4769,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ c_Orderings_Oord__class_Oless__eq(X4771,c_Groups_Ozero__class_Ozero(X4771),X4769)
      | c_Orderings_Oord__class_Oless__eq(X4771,X4770,X4769) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).

fof(i_0_1271,plain,
    ! [X4798,X4799,X4800] :
      ( ~ class_Rings_Olinordered__semidom(X4800)
      | ~ c_Orderings_Oord__class_Oless(X4800,c_Power_Opower__class_Opower(X4800,X4799,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4800,X4798,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ c_Orderings_Oord__class_Oless__eq(X4800,c_Groups_Ozero__class_Ozero(X4800),X4798)
      | c_Orderings_Oord__class_Oless(X4800,X4799,X4798) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).

fof(i_0_1272,plain,
    ! [X4779,X4780,X4781] :
      ( ( X4780 = c_Groups_Ozero__class_Ozero(X4781)
        | c_Groups_Oplus__class_Oplus(X4781,c_Power_Opower__class_Opower(X4781,X4780,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4781,X4779,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X4781)
        | ~ class_Rings_Olinordered__idom(X4781) )
      & ( X4779 = c_Groups_Ozero__class_Ozero(X4781)
        | c_Groups_Oplus__class_Oplus(X4781,c_Power_Opower__class_Opower(X4781,X4780,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4781,X4779,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X4781)
        | ~ class_Rings_Olinordered__idom(X4781) )
      & ( X4780 != c_Groups_Ozero__class_Ozero(X4781)
        | X4779 != c_Groups_Ozero__class_Ozero(X4781)
        | c_Groups_Oplus__class_Oplus(X4781,c_Power_Opower__class_Opower(X4781,X4780,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4781,X4779,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X4781)
        | ~ class_Rings_Olinordered__idom(X4781) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).

fof(i_0_1273,plain,
    ! [X4792,X4793] :
      ( ( X4793 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4793,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,X4792,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) )
      & ( X4792 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4793,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,X4792,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) )
      & ( X4793 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X4792 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4793,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,X4792,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_1274,plain,
    ! [X4796,X4797] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4797,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,X4796,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(variable_rename,[status(thm)],[fact_realpow__square__minus__le]) ).

fof(i_0_1275,plain,
    ! [X4764,X4765,X4766] :
      ( ~ class_Groups_Omonoid__mult(X4766)
      | c_Power_Opower__class_Opower(X4766,X4765,hAPP(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)))),X4764)) = c_Power_Opower__class_Opower(X4766,c_Power_Opower__class_Opower(X4766,X4765,X4764),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_1276,plain,
    ! [X4786,X4787,X4788] :
      ( ~ class_Rings_Ocomm__semiring__1(X4788)
      | c_Power_Opower__class_Opower(X4788,X4787,hAPP(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)))),X4786)) = hAPP(c_Groups_Otimes__class_Otimes(X4788,c_Power_Opower__class_Opower(X4788,X4787,X4786)),c_Power_Opower__class_Opower(X4788,X4787,X4786)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).

fof(i_0_1277,plain,
    ! [X4720] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4720)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4720,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),X4720) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__real__divide__sqrt__less])]) ).

fof(i_0_1278,plain,
    ! [X4676] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4676,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,X4676,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X4676,
    inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).

fof(i_0_1279,plain,
    ! [X4822,X4823] :
      ( ~ class_Rings_Oring__1(X4823)
      | c_Power_Opower__class_Opower(X4823,c_Groups_Ouminus__class_Ouminus(X4823,c_Groups_Oone__class_Oone(X4823)),hAPP(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)))),X4822)) = c_Groups_Oone__class_Oone(X4823) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).

fof(i_0_1280,plain,
    ! [X4679,X4680,X4681,X4682] :
      ( X4682 = X4681
      | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4680,esk12_4(X4679,X4680,X4681,X4682),X4679)
      | hAPP(X4680,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4682,X4681),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(X4680,X4682),hAPP(X4680,X4681)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__const__average])])]) ).

fof(i_0_1281,plain,
    ! [X4677,X4678] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4678,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X4678,X4677)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4678)
        | X4678 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4677 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4678))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
        | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X4678,X4677)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4678)
        | X4678 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4678,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X4678,X4677)
        | X4677 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4678)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
        | X4678 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4677 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4678))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
        | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X4678,X4677)
        | X4677 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4678)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
        | X4678 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__real__sqrt__generic])])]) ).

fof(i_0_1282,plain,
    ! [X4772,X4773,X4774] :
      ( ~ class_Rings_Olinordered__semidom(X4774)
      | c_Power_Opower__class_Opower(X4774,X4773,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X4774,X4772,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ c_Orderings_Oord__class_Oless__eq(X4774,c_Groups_Ozero__class_Ozero(X4774),X4773)
      | ~ c_Orderings_Oord__class_Oless__eq(X4774,c_Groups_Ozero__class_Ozero(X4774),X4772)
      | X4773 = X4772 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).

fof(i_0_1283,plain,
    ! [X4673,X4674] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4674,c_Groups_Ozero__class_Ozero(X4674),c_Rings_Oinverse__class_Odivide(X4674,X4673,c_Int_Onumber__class_Onumber__of(X4674,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | c_Orderings_Oord__class_Oless(X4674,c_Groups_Ozero__class_Ozero(X4674),X4673)
        | ~ class_Fields_Olinordered__field__inverse__zero(X4674)
        | ~ class_Int_Onumber__ring(X4674) )
      & ( ~ c_Orderings_Oord__class_Oless(X4674,c_Groups_Ozero__class_Ozero(X4674),X4673)
        | c_Orderings_Oord__class_Oless(X4674,c_Groups_Ozero__class_Ozero(X4674),c_Rings_Oinverse__class_Odivide(X4674,X4673,c_Int_Onumber__class_Onumber__of(X4674,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4674)
        | ~ class_Int_Onumber__ring(X4674) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_1284,plain,
    ! [X4775,X4776] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4776,c_Groups_Ozero__class_Ozero(X4776),c_Power_Opower__class_Opower(X4776,X4775,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X4775 != c_Groups_Ozero__class_Ozero(X4776)
        | ~ class_Rings_Olinordered__idom(X4776) )
      & ( X4775 = c_Groups_Ozero__class_Ozero(X4776)
        | c_Orderings_Oord__class_Oless(X4776,c_Groups_Ozero__class_Ozero(X4776),c_Power_Opower__class_Opower(X4776,X4775,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Rings_Olinordered__idom(X4776) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).

fof(i_0_1285,plain,
    ! [X4777,X4778] :
      ( ~ class_Rings_Olinordered__idom(X4778)
      | ~ c_Orderings_Oord__class_Oless(X4778,c_Power_Opower__class_Opower(X4778,X4777,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X4778)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1238])]) ).

fof(i_0_1286,plain,
    ! [X4721] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4721)
      | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X4721,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4721)),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_DERIV__real__sqrt])]) ).

fof(i_0_1287,plain,
    ! [X4752,X4753] :
      ( ~ class_Groups_Omonoid__mult(X4753)
      | c_Power_Opower__class_Opower(X4753,X4752,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X4753,hAPP(c_Groups_Otimes__class_Otimes(X4753,X4752),X4752)),X4752) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).

fof(i_0_1288,plain,
    ! [X4669,X4670] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4670,X4669)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4670,X4669),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__gt__half__sum])]) ).

fof(i_0_1289,plain,
    ! [X4667,X4668] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4668,X4667)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4668,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4668,X4667),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_1290,plain,
    ! [X4828] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4828)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4828),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_1291,plain,
    ! [X4671,X4672] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X4672)
      | ~ class_Int_Onumber__ring(X4672)
      | ~ c_Orderings_Oord__class_Oless(X4672,c_Groups_Ozero__class_Ozero(X4672),X4671)
      | c_Orderings_Oord__class_Oless(X4672,c_Groups_Ozero__class_Ozero(X4672),c_Rings_Oinverse__class_Odivide(X4672,X4671,c_Int_Onumber__class_Onumber__of(X4672,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_1292,plain,
    ! [X4589] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X4589)
      | ~ class_Int_Onumber__ring(X4589)
      | c_Orderings_Oord__class_Oless(X4589,c_Groups_Ozero__class_Ozero(X4589),c_Rings_Oinverse__class_Odivide(X4589,c_Groups_Oone__class_Oone(X4589),c_Int_Onumber__class_Onumber__of(X4589,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half])]) ).

fof(i_0_1293,plain,
    ! [X4767,X4768] :
      ( ~ class_Rings_Olinordered__idom(X4768)
      | c_Orderings_Oord__class_Oless__eq(X4768,c_Groups_Ozero__class_Ozero(X4768),c_Power_Opower__class_Opower(X4768,X4767,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_1294,plain,
    ! [X4795] : 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))),X4795)),
    inference(variable_rename,[status(thm)],[fact_two__realpow__ge__one]) ).

fof(i_0_1295,plain,
    ! [X4762,X4763] :
      ( ~ class_Rings_Oring__1(X4763)
      | c_Power_Opower__class_Opower(X4763,c_Groups_Ouminus__class_Ouminus(X4763,X4762),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X4763,X4762,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__minus])]) ).

fof(i_0_1296,plain,
    ! [X4662,X4663] :
      ( ~ class_Int_Onumber__ring(X4663)
      | hAPP(c_Groups_Otimes__class_Otimes(X4663,c_Int_Onumber__class_Onumber__of(X4663,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4662) = c_Groups_Oplus__class_Oplus(X4663,X4662,X4662) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).

fof(i_0_1297,plain,
    ! [X4666] : hAPP(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)))),X4666) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4666,X4666),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).

fof(i_0_1298,plain,
    ! [X4314,X4315] :
      ( ( c_Int_Onumber__class_Onumber__of(X4315,X4314) != c_Groups_Oone__class_Oone(X4315)
        | c_Int_Oiszero(X4315,c_Int_Onumber__class_Onumber__of(X4315,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4314,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Int_Onumber__ring(X4315) )
      & ( ~ c_Int_Oiszero(X4315,c_Int_Onumber__class_Onumber__of(X4315,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4314,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
        | c_Int_Onumber__class_Onumber__of(X4315,X4314) = c_Groups_Oone__class_Oone(X4315)
        | ~ class_Int_Onumber__ring(X4315) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).

fof(i_0_1299,plain,
    ! [X4824,X4825] :
      ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4825,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X4824
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4825)
      | hAPP(c_NthRoot_Osqrt,X4824) = X4825 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__unique])]) ).

fof(i_0_1300,plain,
    ! [X4675] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4675)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4675,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | X4675 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X4675 = 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_1301,plain,
    ! [X4827] :
      ( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X4827
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4827) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4827)
        | c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4827 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__iff])]) ).

fof(i_0_1302,plain,
    ! [X4784,X4785] :
      ( ( c_Power_Opower__class_Opower(X4785,X4784,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X4785)
        | X4784 = c_Groups_Oone__class_Oone(X4785)
        | X4784 = c_Groups_Ouminus__class_Ouminus(X4785,c_Groups_Oone__class_Oone(X4785))
        | ~ class_Rings_Oring__1__no__zero__divisors(X4785) )
      & ( X4784 != c_Groups_Oone__class_Oone(X4785)
        | c_Power_Opower__class_Opower(X4785,X4784,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4785)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4785) )
      & ( X4784 != c_Groups_Ouminus__class_Ouminus(X4785,c_Groups_Oone__class_Oone(X4785))
        | c_Power_Opower__class_Opower(X4785,X4784,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4785)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4785) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).

fof(i_0_1303,plain,
    ! [X4755,X4756] :
      ( ( c_Power_Opower__class_Opower(X4756,X4755,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X4756)
        | X4755 = c_Groups_Ozero__class_Ozero(X4756)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4756) )
      & ( X4755 != c_Groups_Ozero__class_Ozero(X4756)
        | c_Power_Opower__class_Opower(X4756,X4755,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X4756)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4756) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).

fof(i_0_1304,plain,
    ! [X4847] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4847)
      | c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4847)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4847) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__inv__sqrt__pow2])]) ).

fof(i_0_1305,plain,
    ! [X4782,X4783] :
      ( ~ class_Groups_Omonoid__mult(X4783)
      | ~ class_Int_Onumber(X4783)
      | c_Power_Opower__class_Opower(X4783,c_Int_Onumber__class_Onumber__of(X4783,X4782),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X4783,c_Int_Onumber__class_Onumber__of(X4783,X4782)),c_Int_Onumber__class_Onumber__of(X4783,X4782)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).

fof(i_0_1306,plain,
    ! [X4826] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4826)
      | c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4826),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4826 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2])]) ).

fof(i_0_1307,plain,
    ! [X4660,X4661] :
      ( ~ class_Int_Onumber__ring(X4661)
      | hAPP(c_Groups_Otimes__class_Otimes(X4661,X4660),c_Int_Onumber__class_Onumber__of(X4661,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X4661,X4660,X4660) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

fof(i_0_1308,plain,
    ! [X4759,X4760] :
      ( ~ class_Groups_Omonoid__mult(X4760)
      | c_Power_Opower__class_Opower(X4760,X4759,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(X4760,X4759),X4759) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).

fof(i_0_1309,plain,
    ! [X4757,X4758] :
      ( ~ class_Rings_Ocomm__semiring__1(X4758)
      | hAPP(c_Groups_Otimes__class_Otimes(X4758,X4757),X4757) = c_Power_Opower__class_Opower(X4758,X4757,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_1310,plain,
    ! [X4665] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4665),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,X4665,X4665),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).

fof(i_0_1311,plain,
    ! [X4761] :
      ( ~ class_Rings_Osemiring__1(X4761)
      | c_Power_Opower__class_Opower(X4761,c_Groups_Oone__class_Oone(X4761),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4761) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

fof(i_0_1312,plain,
    ! [X4754] :
      ( ~ class_Rings_Osemiring__1(X4754)
      | c_Power_Opower__class_Opower(X4754,c_Groups_Ozero__class_Ozero(X4754),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X4754) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).

fof(i_0_1313,plain,
    ! [X4989] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X4989),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4989,
    inference(variable_rename,[status(thm)],[fact_csqrt]) ).

fof(i_0_1314,plain,
    ! [X4316,X4317] :
      ( ( c_Groups_Oone__class_Oone(X4317) != c_Int_Onumber__class_Onumber__of(X4317,X4316)
        | c_Int_Oiszero(X4317,c_Int_Onumber__class_Onumber__of(X4317,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4316))))
        | ~ class_Int_Onumber__ring(X4317) )
      & ( ~ c_Int_Oiszero(X4317,c_Int_Onumber__class_Onumber__of(X4317,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4316))))
        | c_Groups_Oone__class_Oone(X4317) = c_Int_Onumber__class_Onumber__of(X4317,X4316)
        | ~ class_Int_Onumber__ring(X4317) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).

fof(i_0_1315,plain,
    ! [X4664] :
      ( ~ class_Int_Onumber__ring(X4664)
      | c_Groups_Oplus__class_Oplus(X4664,c_Groups_Oone__class_Oone(X4664),c_Groups_Oone__class_Oone(X4664)) = c_Int_Onumber__class_Onumber__of(X4664,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_1316,plain,
    ! [X4652,X4653] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X4653),c_Int_OBit1(X4652)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4653,c_Int_Osucc(X4652))),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(i_0_1317,plain,
    ! [X4339,X4340] :
      ( ~ class_Int_Onumber__ring(X4340)
      | hAPP(c_Groups_Otimes__class_Otimes(X4340,c_Int_Onumber__class_Onumber__of(X4340,c_Int_OBit1(c_Int_OPls))),X4339) = X4339 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).

fof(i_0_1318,plain,
    ! [X4322,X4323] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4323),c_Int_OBit1(X4322))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4323,X4322) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4323,X4322)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4323),c_Int_OBit1(X4322)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_1319,plain,
    ! [X4320,X4321] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4321),c_Int_OBit1(X4320))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4321,X4320) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4321,X4320)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4321),c_Int_OBit1(X4320)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_1320,plain,
    ! [X4326,X4327] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4327),c_Int_OBit1(X4326))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4327,X4326) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4327,X4326)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4327),c_Int_OBit1(X4326)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_1321,plain,
    ! [X4324,X4325] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4325),c_Int_OBit1(X4324))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4325,X4324) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4325,X4324)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4325),c_Int_OBit1(X4324)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_1322,plain,
    ! [X4650,X4651] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X4651)),X4650) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4651),X4650)),X4650),
    inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).

fof(i_0_1323,plain,
    ! [X27,X18,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(i_0_1324,plain,
    ! [X27,X18,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(i_0_1325,plain,
    ! [X18,X16,X27,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(i_0_1326,plain,
    ! [X18,X16,X27,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,c_Int_Onumber__class_Onumber__of(X10,X27)),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(i_0_1327,plain,
    ! [X4335,X4336] :
      ( ~ class_Int_Onumber__ring(X4336)
      | ~ class_Int_Oring__char__0(X4336)
      | ~ c_Int_Oiszero(X4336,c_Int_Onumber__class_Onumber__of(X4336,c_Int_OBit1(X4335))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1239])]) ).

fof(i_0_1328,plain,
    ! [X4625,X4626] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X4626),c_Int_OBit0(X4625)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4626,X4625)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_1329,plain,
    ! [X4623,X4624] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X4624),c_Int_OBit1(X4623)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4624,X4623)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_1330,plain,
    ! [X4352] :
      ( ~ class_Int_Onumber__ring(X4352)
      | ~ c_Int_Oiszero(X4352,c_Int_Onumber__class_Onumber__of(X4352,c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1240])]) ).

fof(i_0_1331,plain,
    ! [X4349] :
      ( ~ class_Fields_Ofield(X4349)
      | ~ class_Int_Onumber__ring(X4349)
      | c_Rings_Oinverse__class_Oinverse(X4349,c_Int_Onumber__class_Onumber__of(X4349,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(X4349,c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__numeral__1])]) ).

fof(i_0_1332,plain,
    ! [X17,X27,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(i_0_1333,plain,
    ! [X17,X27,X16,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(i_0_1334,plain,
    ! [X27,X16,X17,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(i_0_1335,plain,
    ! [X27,X16,X17,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,c_Int_Onumber__class_Onumber__of(X10,X27)))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27)),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X27))
           => ( ( c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),c_Int_Onumber__class_Onumber__of(X10,X27))) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(i_0_1336,plain,
    ! [X4656] :
      ( ( 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(X4656)))
        | ~ 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,X4656)) )
      & ( 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(X4656)))
        | ~ 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,X4656)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).

fof(i_0_1337,plain,
    ! [X4361,X4362] :
      ( ~ class_Int_Onumber__ring(X4362)
      | c_Groups_Oplus__class_Oplus(X4362,c_Int_Onumber__class_Onumber__of(X4362,X4361),c_Groups_Oone__class_Oone(X4362)) = c_Int_Onumber__class_Onumber__of(X4362,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4361,c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_1338,plain,
    ! [X4363,X4364] :
      ( ~ class_Int_Onumber__ring(X4364)
      | c_Groups_Oplus__class_Oplus(X4364,c_Groups_Oone__class_Oone(X4364),c_Int_Onumber__class_Onumber__of(X4364,X4363)) = c_Int_Onumber__class_Onumber__of(X4364,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4363)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_1339,plain,
    ! [X4648,X4649] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4649),c_Int_OBit0(X4648))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4649,X4648) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4649,X4648)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4649),c_Int_OBit0(X4648)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_1340,plain,
    ! [X4646,X4647] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4647),c_Int_OBit0(X4646))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4647,X4646) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4647,X4646)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4647),c_Int_OBit0(X4646)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_1341,plain,
    ! [X4632,X4633] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4633),c_Int_OBit0(X4632))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4633,X4632) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4633,X4632)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4633),c_Int_OBit0(X4632)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_1342,plain,
    ! [X4630,X4631] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4631),c_Int_OBit0(X4630))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4631,X4630) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4631,X4630)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4631),c_Int_OBit0(X4630)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_1343,plain,
    ! [X4638,X4639] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4639),c_Int_OBit1(X4638))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4639,X4638) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4639,X4638)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4639),c_Int_OBit1(X4638)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_1344,plain,
    ! [X4636,X4637] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4637),c_Int_OBit1(X4636))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4637,X4636) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4637,X4636)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4637),c_Int_OBit1(X4636)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_1345,plain,
    ! [X4644,X4645] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4645),c_Int_OBit1(X4644))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4645,X4644) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4645,X4644)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4645),c_Int_OBit1(X4644)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_1346,plain,
    ! [X4642,X4643] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4643),c_Int_OBit1(X4642))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4643,X4642) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4643,X4642)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4643),c_Int_OBit1(X4642)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_1347,plain,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X11),X11),hAPP(c_Groups_Otimes__class_Otimes(X10,X19),X19)),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(i_0_1348,plain,
    ! [X4347,X4348] :
      ( ~ class_Fields_Ofield(X4348)
      | ~ class_Int_Onumber__ring(X4348)
      | c_Rings_Oinverse__class_Odivide(X4348,X4347,c_Int_Onumber__class_Onumber__of(X4348,c_Int_OBit1(c_Int_OPls))) = X4347 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_1349,plain,
    ! [X4345,X4346] :
      ( ~ class_Fields_Ofield(X4346)
      | ~ class_Int_Onumber__ring(X4346)
      | c_Rings_Oinverse__class_Odivide(X4346,X4345,c_Int_Onumber__class_Onumber__of(X4346,c_Int_OBit1(c_Int_OPls))) = X4345 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_1350,plain,
    ! [X4334] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(X4334)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4334))),
    inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).

fof(i_0_1351,plain,
    ! [X4341,X4342] :
      ( ~ class_Int_Onumber__ring(X4342)
      | hAPP(c_Groups_Otimes__class_Otimes(X4342,X4341),c_Int_Onumber__class_Onumber__of(X4342,c_Int_OBit1(c_Int_OPls))) = X4341 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).

fof(i_0_1352,plain,
    ! [X17,X18,X16,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).

fof(i_0_1353,plain,
    ! [X17,X18,X16,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Odivide(X10,X16,X18),X17)
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X17) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

fof(i_0_1354,plain,
    ! [X18,X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless__eq(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless__eq(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).

fof(i_0_1355,plain,
    ! [X18,X16,X17,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X17,c_Rings_Oinverse__class_Odivide(X10,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18),X16) )
          & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X18)
           => ( ( c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X16,hAPP(c_Groups_Otimes__class_Otimes(X10,X17),X18)) )
              & ( ~ c_Orderings_Oord__class_Oless(X10,X18,c_Groups_Ozero__class_Ozero(X10))
               => c_Orderings_Oord__class_Oless(X10,X17,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).

fof(i_0_1356,plain,
    ! [X31,X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)),X31)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)),X31)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X65))),X31) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(i_0_1357,plain,
    ! [X4355,X4356] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4356,c_Int_Onumber__class_Onumber__of(X4356,X4355),c_Groups_Oone__class_Oone(X4356))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4355,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X4356)
        | ~ class_Rings_Olinordered__idom(X4356) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4355,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless__eq(X4356,c_Int_Onumber__class_Onumber__of(X4356,X4355),c_Groups_Oone__class_Oone(X4356))
        | ~ class_Int_Onumber__ring(X4356)
        | ~ class_Rings_Olinordered__idom(X4356) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_1358,plain,
    ! [X4359,X4360] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4360,c_Int_Onumber__class_Onumber__of(X4360,X4359),c_Groups_Oone__class_Oone(X4360))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4359,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X4360)
        | ~ class_Rings_Olinordered__idom(X4360) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4359,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless(X4360,c_Int_Onumber__class_Onumber__of(X4360,X4359),c_Groups_Oone__class_Oone(X4360))
        | ~ class_Int_Onumber__ring(X4360)
        | ~ class_Rings_Olinordered__idom(X4360) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_1359,plain,
    ! [X4353,X4354] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4354,c_Groups_Oone__class_Oone(X4354),c_Int_Onumber__class_Onumber__of(X4354,X4353))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4353)
        | ~ class_Int_Onumber__ring(X4354)
        | ~ class_Rings_Olinordered__idom(X4354) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4353)
        | c_Orderings_Oord__class_Oless__eq(X4354,c_Groups_Oone__class_Oone(X4354),c_Int_Onumber__class_Onumber__of(X4354,X4353))
        | ~ class_Int_Onumber__ring(X4354)
        | ~ class_Rings_Olinordered__idom(X4354) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_1360,plain,
    ! [X4357,X4358] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4358,c_Groups_Oone__class_Oone(X4358),c_Int_Onumber__class_Onumber__of(X4358,X4357))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4357)
        | ~ class_Int_Onumber__ring(X4358)
        | ~ class_Rings_Olinordered__idom(X4358) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4357)
        | c_Orderings_Oord__class_Oless(X4358,c_Groups_Oone__class_Oone(X4358),c_Int_Onumber__class_Onumber__of(X4358,X4357))
        | ~ class_Int_Onumber__ring(X4358)
        | ~ class_Rings_Olinordered__idom(X4358) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_1361,plain,
    ! [X4600] : c_Int_Osucc(c_Int_OBit1(X4600)) = c_Int_OBit0(c_Int_Osucc(X4600)),
    inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).

fof(i_0_1362,plain,
    ! [X4331] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4331),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4331,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4331,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4331),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_1363,plain,
    ! [X4330] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4330))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4330) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4330)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4330)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_1364,plain,
    ! [X4351] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4351))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4351) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4351)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4351)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_1365,plain,
    ! [X4350] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4350),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4350,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4350,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4350),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_1366,plain,
    ! [X4332] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4332),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4332),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_1367,plain,
    ! [X4337,X4338] :
      ( ~ class_Int_Onumber__ring(X4338)
      | c_Int_Onumber__class_Onumber__of(X4338,c_Int_OBit1(X4337)) = c_Groups_Oplus__class_Oplus(X4338,c_Groups_Oplus__class_Oplus(X4338,c_Groups_Oone__class_Oone(X4338),c_Int_Onumber__class_Onumber__of(X4338,X4337)),c_Int_Onumber__class_Onumber__of(X4338,X4337)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_1368,plain,
    ! [X4612,X4613] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X4613),c_Int_OBit0(X4612)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4613,X4612)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_1369,plain,
    ! [X4328,X4329] :
      ( ( c_Int_OBit1(X4329) != c_Int_OBit1(X4328)
        | X4329 = X4328 )
      & ( X4329 != X4328
        | c_Int_OBit1(X4329) = c_Int_OBit1(X4328) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_1370,plain,
    ! [X4603,X4604] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4604),c_Int_OBit0(X4603))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4604,X4603) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4604,X4603)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4604),c_Int_OBit0(X4603)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_1371,plain,
    ! [X4601,X4602] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4602),c_Int_OBit0(X4601))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4602,X4601) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4602,X4601)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4602),c_Int_OBit0(X4601)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_1372,plain,
    ! [X4609,X4610] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4610),c_Int_OBit0(X4609))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4610,X4609) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4610,X4609)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4610),c_Int_OBit0(X4609)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_1373,plain,
    ! [X4607,X4608] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4608),c_Int_OBit0(X4607))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4608,X4607) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4608,X4607)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4608),c_Int_OBit0(X4607)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_1374,plain,
    ! [X4654,X4655] :
      ( ~ class_Int_Onumber__ring(X4655)
      | hAPP(c_Groups_Otimes__class_Otimes(X4655,c_Groups_Oplus__class_Oplus(X4655,c_Groups_Oone__class_Oone(X4655),c_Groups_Oone__class_Oone(X4655))),c_Int_Onumber__class_Onumber__of(X4655,X4654)) = c_Int_Onumber__class_Onumber__of(X4655,c_Int_OBit0(X4654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).

fof(i_0_1375,plain,
    ! [X4595,X4596] :
      ( ( ~ c_Int_Oiszero(X4596,c_Int_Onumber__class_Onumber__of(X4596,c_Int_OBit0(X4595)))
        | c_Int_Oiszero(X4596,c_Int_Onumber__class_Onumber__of(X4596,X4595))
        | ~ class_Int_Onumber__ring(X4596)
        | ~ class_Int_Oring__char__0(X4596) )
      & ( ~ c_Int_Oiszero(X4596,c_Int_Onumber__class_Onumber__of(X4596,X4595))
        | c_Int_Oiszero(X4596,c_Int_Onumber__class_Onumber__of(X4596,c_Int_OBit0(X4595)))
        | ~ class_Int_Onumber__ring(X4596)
        | ~ class_Int_Oring__char__0(X4596) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).

fof(i_0_1376,plain,
    ! [X4605,X4606] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X4606)),X4605) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4606),X4605)),
    inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).

fof(i_0_1377,plain,
    ! [X4640,X4641] :
      ( ~ class_Int_Onumber__ring(X4641)
      | c_Int_Onumber__class_Onumber__of(X4641,c_Int_OBit0(X4640)) = c_Groups_Oplus__class_Oplus(X4641,c_Groups_Oplus__class_Oplus(X4641,c_Groups_Ozero__class_Ozero(X4641),c_Int_Onumber__class_Onumber__of(X4641,X4640)),c_Int_Onumber__class_Onumber__of(X4641,X4640)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_1378,plain,
    ! [X4597] : c_Int_Opred(c_Int_OBit1(X4597)) = c_Int_OBit0(X4597),
    inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).

fof(i_0_1379,plain,
    ! [X27,X48,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Olinorder(X10) )
     => ( c_Orderings_Oord__class_Oless__eq(X10,c_Int_Onumber__class_Onumber__of(X10,X48),c_Int_Onumber__class_Onumber__of(X10,X27))
      <=> ~ c_Orderings_Oord__class_Oless(X10,c_Int_Onumber__class_Onumber__of(X10,X27),c_Int_Onumber__class_Onumber__of(X10,X48)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_1380,plain,
    ! [X4616,X4617] : c_Int_OBit0(X4617) != c_Int_OBit1(X4616),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_1381,plain,
    ! [X4614,X4615] : c_Int_OBit1(X4615) != c_Int_OBit0(X4614),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_1382,plain,
    ! [X4343] :
      ( ~ class_Int_Onumber__ring(X4343)
      | c_Int_Onumber__class_Onumber__of(X4343,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X4343) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_1383,plain,
    ! [X4344] :
      ( ~ class_Int_Onumber__ring(X4344)
      | c_Groups_Oone__class_Oone(X4344) = c_Int_Onumber__class_Onumber__of(X4344,c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_1384,plain,
    ! [X4333] : c_Int_OBit1(X4333) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4333),X4333),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_1385,plain,
    ! [X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,X65)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_1386,plain,
    ! [X4629] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4629),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4629,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4629,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4629),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_1387,plain,
    ! [X28,X31,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X29,X31),X28)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X28)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X28) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_1388,plain,
    ! [X4635] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4635))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4635) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4635)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4635)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_1389,plain,
    ! [X4627] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4627))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4627) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4627)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4627)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_1390,plain,
    ! [X4634] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4634),c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4634,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4634,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4634),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_1391,plain,
    ! [X4628] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4628),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4628,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4628,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4628),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_1392,plain,
    ! [X1,X2,X10,X35] :
      ( class_Orderings_Oord(X35)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X10,X35),X2,X1)
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X2,X1)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X35),X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_1393,plain,
    ! [X4598] : c_Int_Opred(c_Int_OBit0(X4598)) = c_Int_OBit1(c_Int_Opred(X4598)),
    inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).

fof(i_0_1394,plain,
    ! [X64,X48] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X64)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_1395,plain,
    ! [X4301] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4301,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4301),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4301,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4301),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X4301)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1241])]) ).

fof(i_0_1396,plain,
    ! [X4300] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4300,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4300)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4300,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4300)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X4300)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1242])]) ).

fof(i_0_1397,plain,
    ! [X4319] : c_Int_OBit1(X4319) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_1398,plain,
    ! [X4318] : c_Int_OPls != c_Int_OBit1(X4318),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_1399,plain,
    ! [X32,X33] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X32),X33),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_1400,plain,
    ! [X33,X32] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X33),X33),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_1401,plain,
    ! [X65,X37] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Int_OPls)
       => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X37),X65)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).

fof(i_0_1402,plain,
    ! [X9,X10] :
      ( class_Rings_Olinordered__ring(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,hAPP(c_Groups_Otimes__class_Otimes(X10,X9),X9),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_1403,plain,
    ! [X3892,X3893] :
      ( ~ class_Int_Onumber__ring(X3893)
      | c_Int_Onumber__class_Onumber__of(X3893,c_Int_Osucc(X3892)) = c_Groups_Oplus__class_Oplus(X3893,c_Groups_Oone__class_Oone(X3893),c_Int_Onumber__class_Onumber__of(X3893,X3892)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).

fof(i_0_1404,plain,
    ! [X4618] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X4618)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4618)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_1405,plain,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21),X21))
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).

fof(i_0_1406,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
          & ~ c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_1407,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
       => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_1408,plain,
    ! [X9,X12,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X12,X9)
       => ~ c_Orderings_Oord__class_Oless(X10,X9,X12) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_1409,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
      <=> c_Orderings_Oord__class_Oless(X10,X20,X21) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_1410,plain,
    ! [X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => ~ c_Orderings_Oord__class_Oless(X10,X11,X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_1411,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> c_Orderings_Oord__class_Oless__eq(X10,X20,X21) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_1412,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
      <=> ( c_Orderings_Oord__class_Oless(X10,X20,X21)
          | X21 = X20 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_1413,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_1414,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_1415,plain,
    ! [X12,X9,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X9,X12)
       => ~ c_Orderings_Oord__class_Oless(X10,X12,X9) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_1416,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ~ c_Orderings_Oord__class_Oless(X10,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_1417,plain,
    ! [X4619,X4620] :
      ( ( c_Int_OBit0(X4620) != c_Int_OBit0(X4619)
        | X4620 = X4619 )
      & ( X4620 != X4619
        | c_Int_OBit0(X4620) = c_Int_OBit0(X4619) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_1418,plain,
    ! [X20,X21,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_1419,plain,
    ~ ! [X24] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
         => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X24,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
    inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(i_0_1420,plain,
    ! [X11] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(fof_simplification,[status(thm)],[fact_not__exp__le__zero]) ).

fof(i_0_1421,plain,
    ! [X11] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(fof_simplification,[status(thm)],[fact_not__exp__less__zero]) ).

fof(i_0_1422,plain,
    ! [X9,X10] :
      ( class_Groups_Oabs__if(X10)
     => ( ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
         => c_Groups_Oabs__class_Oabs(X10,X9) = c_Groups_Ouminus__class_Ouminus(X10,X9) )
        & ( ~ c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
         => c_Groups_Oabs__class_Oabs(X10,X9) = X9 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_1423,plain,
    ! [X11,X10] :
      ( class_Groups_Osgn__if(X10)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(X10)
         => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Ozero__class_Ozero(X10) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X10)
         => ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
             => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Oone__class_Oone(X10) )
            & ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
             => c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_1424,plain,
    ! [X21,X20,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X20,X21)
       => ( ~ c_Orderings_Oord__class_Oless(X10,X21,X20)
        <=> X21 = X20 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_1425,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( X11 != X19
       => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_1426,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
       => ( X11 != X19
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_1427,plain,
    ! [X19,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( X11 != X19
       => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
         => c_Orderings_Oord__class_Oless(X10,X19,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_1428,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_1429,plain,
    ! [X19,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless(X10,X11,X19)
       => c_Orderings_Oord__class_Oless__eq(X10,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_1430,plain,
    ! [X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X10,X19,X11)
       => c_Orderings_Oord__class_Oless(X10,X11,X19) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_1431,plain,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_1432,plain,
    ! [X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_1433,plain,
    ! [X19,X11] :
      ( X11 != X19
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_1434,plain,
    ! [X33] :
      ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X33 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X33) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_zsgn__def]) ).

fof(i_0_1435,plain,
    ! [X11] :
      ( ( X11 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X11 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_real__sgn__def]) ).

fof(i_0_1436,plain,
    ! [X9] :
      ( ( X9 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X9 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X9)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X9) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__real__def]) ).

fof(i_0_1437,plain,
    ! [X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ~ c_Orderings_Oord__class_Oless(X10,X11,X11) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_1438,plain,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_1439,plain,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_1440,plain,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_1441,plain,
    ! [X4622] :
      ( ( c_Int_OPls != c_Int_OBit0(X4622)
        | c_Int_OPls = X4622 )
      & ( c_Int_OPls != X4622
        | c_Int_OPls = c_Int_OBit0(X4622) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_1442,plain,
    ! [X4621] :
      ( ( c_Int_OBit0(X4621) != c_Int_OPls
        | X4621 = c_Int_OPls )
      & ( X4621 != c_Int_OPls
        | c_Int_OBit0(X4621) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_1443,plain,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X28),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_1444,plain,
    ! [X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X28),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_1445,plain,
    ! [X4285] : c_Int_Osucc(c_Int_Opred(X4285)) = X4285,
    inference(variable_rename,[status(thm)],[fact_succ__pred]) ).

fof(i_0_1446,plain,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => ~ c_Int_Oiszero(X10,c_Groups_Oone__class_Oone(X10)) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).

cnf(i_0_1447,plain,
    c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(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)))) = hAPP(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_1243]) ).

cnf(i_0_1448,plain,
    c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_1244]) ).

cnf(i_0_1449,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_1245]) ).

cnf(i_0_1450,plain,
    c_Int_Osucc(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[i_0_1246]) ).

cnf(i_0_1451,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(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_1247]) ).

cnf(i_0_1452,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,hAPP(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)))))),hAPP(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_1248]) ).

cnf(i_0_1453,plain,
    hAPP(c_Transcendental_Oarctan,X1) = hAPP(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)))),hAPP(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),hAPP(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_1249]) ).

cnf(i_0_1454,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,hAPP(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_1250]) ).

cnf(i_0_1455,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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,hAPP(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,hAPP(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_1251]) ).

cnf(i_0_1456,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))))),hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(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_1252]) ).

cnf(i_0_1457,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))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(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_1253]) ).

cnf(i_0_1458,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_1254]) ).

cnf(i_0_1459,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_1255]) ).

cnf(i_0_1460,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(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_1256]) ).

cnf(i_0_1461,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(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_1257]) ).

cnf(i_0_1462,plain,
    hAPP(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,hAPP(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_1258]) ).

cnf(i_0_1463,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_1259]) ).

cnf(i_0_1464,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_1260]) ).

cnf(i_0_1465,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_1260]) ).

cnf(i_0_1466,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_1261]) ).

cnf(i_0_1467,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(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_1262]) ).

cnf(i_0_1468,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(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_1263]) ).

cnf(i_0_1469,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,hAPP(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_1264]) ).

cnf(i_0_1470,plain,
    ( hAPP(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,hAPP(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_1265]) ).

cnf(i_0_1471,plain,
    c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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_1266]) ).

cnf(i_0_1472,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_1260]) ).

cnf(i_0_1473,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_1259]) ).

cnf(i_0_1474,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_1259]) ).

cnf(i_0_1475,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_1267]) ).

cnf(i_0_1476,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,hAPP(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_1268]) ).

cnf(i_0_1477,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),hAPP(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,X2,hAPP(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_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1269]) ).

cnf(i_0_1478,plain,
    ( X1 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,hAPP(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))
    | hAPP(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_1265]) ).

cnf(i_0_1479,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_1270]) ).

cnf(i_0_1480,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_1271]) ).

cnf(i_0_1481,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_1272]) ).

cnf(i_0_1482,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_1272]) ).

cnf(i_0_1483,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_1273]) ).

cnf(i_0_1484,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_1273]) ).

cnf(i_0_1485,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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_1274]) ).

cnf(i_0_1486,plain,
    ( c_Power_Opower__class_Opower(X1,X2,hAPP(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_1275]) ).

cnf(i_0_1487,plain,
    ( c_Power_Opower__class_Opower(X1,X2,hAPP(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)) = hAPP(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_1276]) ).

cnf(i_0_1488,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_1272]) ).

cnf(i_0_1489,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,hAPP(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_1277]) ).

cnf(i_0_1490,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_1273]) ).

cnf(i_0_1491,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_1278]) ).

cnf(i_0_1492,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)),hAPP(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_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1279]) ).

cnf(i_0_1493,plain,
    ( X1 = X2
    | hAPP(X3,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(X3,X1),hAPP(X3,X2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X3,esk12_4(X4,X3,X2,X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1280]) ).

cnf(i_0_1494,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X2,X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X2))),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,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X2)),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_1281]) ).

cnf(i_0_1495,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_1282]) ).

cnf(i_0_1496,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_1283]) ).

cnf(i_0_1497,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_1284]) ).

cnf(i_0_1498,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_1285]) ).

cnf(i_0_1499,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1286]) ).

cnf(i_0_1500,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)))) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2)),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1287]) ).

cnf(i_0_1501,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_1288]) ).

cnf(i_0_1502,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_1289]) ).

cnf(i_0_1503,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,hAPP(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_1290]) ).

cnf(i_0_1504,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_1283]) ).

cnf(i_0_1505,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_1291]) ).

cnf(i_0_1506,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_1507,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_1292]) ).

cnf(i_0_1508,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_1284]) ).

cnf(i_0_1509,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_1293]) ).

cnf(i_0_1510,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_1294]) ).

cnf(i_0_1511,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(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_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1295]) ).

cnf(i_0_1512,plain,
    ( hAPP(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_1296]) ).

cnf(i_0_1513,plain,
    hAPP(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_1297]) ).

cnf(i_0_1514,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_1515,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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_1516,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_1517,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X2))),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_1281]) ).

cnf(i_0_1518,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1)),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_1281]) ).

cnf(i_0_1519,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1298]) ).

cnf(i_0_1520,plain,
    ( hAPP(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_1299]) ).

cnf(i_0_1521,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_1300]) ).

cnf(i_0_1522,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,hAPP(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_1301]) ).

cnf(i_0_1523,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(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_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1302]) ).

cnf(i_0_1524,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_1303]) ).

fof(i_0_1525,plain,
    ! [X3116,X3117,X3118,X3119,X3120] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,X3119),X3117,X3116)
        | c_Orderings_Oord__class_Oless__eq(X3119,hAPP(X3117,X3120),hAPP(X3116,X3120))
        | ~ class_Orderings_Oord(X3119) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3119,hAPP(X3117,esk4_4(X3116,X3117,X3118,X3119)),hAPP(X3116,esk4_4(X3116,X3117,X3118,X3119)))
        | c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,X3119),X3117,X3116)
        | ~ class_Orderings_Oord(X3119) ) ),
    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_1526,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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_1304]) ).

cnf(i_0_1527,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)))) = hAPP(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_1305]) ).

cnf(i_0_1528,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_1301]) ).

cnf(i_0_1529,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_1306]) ).

cnf(i_0_1530,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1298]) ).

cnf(i_0_1531,plain,
    ( hAPP(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_1307]) ).

cnf(i_0_1532,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)))) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1308]) ).

cnf(i_0_1533,plain,
    ( hAPP(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_1309]) ).

cnf(i_0_1534,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_Oone__class_Oone(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1302]) ).

cnf(i_0_1535,plain,
    hAPP(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_1310]) ).

cnf(i_0_1536,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_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1302]) ).

cnf(i_0_1537,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_1303]) ).

cnf(i_0_1538,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_1311]) ).

cnf(i_0_1539,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_1312]) ).

cnf(i_0_1540,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_1313]) ).

cnf(i_0_1541,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_1542,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_1543,plain,
    ( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1314]) ).

fof(i_0_1544,plain,
    ! [X4590,X4591,X4592,X4594] :
      ( ( hBOOL(hAPP(X4591,esk11_3(X4590,X4591,X4592)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4590)
        | ~ hBOOL(hAPP(X4591,X4594))
        | hBOOL(hAPP(X4591,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4594,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4590),X4592))))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4592) )
      & ( ~ hBOOL(hAPP(X4591,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk11_3(X4590,X4591,X4592),X4592)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4590)
        | ~ hBOOL(hAPP(X4591,X4594))
        | hBOOL(hAPP(X4591,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4594,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4590),X4592))))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4592) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma])])])])]) ).

cnf(i_0_1545,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))))
    | c_Groups_Oone__class_Oone(X1) != c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1314]) ).

cnf(i_0_1546,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_1315]) ).

cnf(i_0_1547,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]) ).

cnf(i_0_1548,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_Osucc(X2))),
    inference(split_conjunct,[status(thm)],[i_0_1316]) ).

cnf(i_0_1549,plain,
    ( hAPP(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_1317]) ).

fof(i_0_1550,plain,
    ! [X3376,X3377,X3378] :
      ( ~ class_Fields_Ofield(X3378)
      | X3377 = c_Groups_Ozero__class_Ozero(X3378)
      | X3376 = c_Groups_Ozero__class_Ozero(X3378)
      | c_Groups_Oplus__class_Oplus(X3378,c_Rings_Oinverse__class_Oinverse(X3378,X3377),c_Rings_Oinverse__class_Oinverse(X3378,X3376)) = hAPP(c_Groups_Otimes__class_Otimes(X3378,hAPP(c_Groups_Otimes__class_Otimes(X3378,c_Groups_Oplus__class_Oplus(X3378,X3377,X3376)),c_Rings_Oinverse__class_Oinverse(X3378,X3377))),c_Rings_Oinverse__class_Oinverse(X3378,X3376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).

fof(i_0_1551,plain,
    ! [X4205,X4206,X4207,X4208,X4209,X4210] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4210),X4209),X4208) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4207),X4206),X4205)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4207),X4206),X4205),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4208,X4210)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4205)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4207)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4207,X4210)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4206,X4209) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).

fof(i_0_1552,plain,
    ! [X4216,X4217,X4218,X4219,X4220,X4221] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4221),X4220),X4219) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4218),X4217),X4216)
      | ~ 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4218),X4217),X4216))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4216,X4218)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4219)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4218)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4218,X4221)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4220,X4217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).

fof(i_0_1553,plain,
    ! [X4222,X4223,X4224,X4225,X4226] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4226),X4225),X4224),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4226),X4223),X4222))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4224)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4224,X4226)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4222,X4226)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4225,X4223) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).

fof(i_0_1554,plain,
    ! [X4211,X4212,X4213,X4214,X4215] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4215),X4214),X4213),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4215),X4212),X4211))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4211,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4215,X4211)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4215,X4213)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4212,X4214) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).

cnf(i_0_1555,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_1318]) ).

cnf(i_0_1556,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_1319]) ).

cnf(i_0_1557,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_1320]) ).

cnf(i_0_1558,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_1321]) ).

fof(i_0_1559,plain,
    ! [X4260,X4261,X4262,X4264] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_3(X4260,X4261,X4262))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4260,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4262,X4261,X4260) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4264)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4264,esk8_3(X4260,X4261,X4262))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X4262,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4261,X4264)),hAPP(X4262,X4261))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4260,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4262,X4261,X4260) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__neg__dec__right])])])])]) ).

fof(i_0_1560,plain,
    ! [X4255,X4256,X4257,X4259] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_3(X4255,X4256,X4257))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4255)
        | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4257,X4256,X4255) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4259)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4259,esk7_3(X4255,X4256,X4257))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X4257,X4256),hAPP(X4257,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4256,X4259)))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4255)
        | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4257,X4256,X4255) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__pos__inc__right])])])])]) ).

cnf(i_0_1561,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_1322]) ).

fof(i_0_1562,plain,
    ! [X3798,X3799,X3800,X3801] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless__eq(X3801,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799),X3800)
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Ozero__class_Ozero(X3801),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Ozero__class_Ozero(X3801),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799),X3800)
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Ozero__class_Ozero(X3801),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799),X3800)
        | c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,c_Groups_Ozero__class_Ozero(X3801),X3799)
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Ozero__class_Ozero(X3801),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless(X3801,X3799,c_Groups_Ozero__class_Ozero(X3801))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799),X3800)
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Ozero__class_Ozero(X3801),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799),X3800)
        | ~ c_Orderings_Oord__class_Oless__eq(X3801,X3800,hAPP(c_Groups_Otimes__class_Otimes(X3801,c_Int_Onumber__class_Onumber__of(X3801,X3798)),X3799))
        | c_Orderings_Oord__class_Oless__eq(X3801,c_Rings_Oinverse__class_Odivide(X3801,X3800,X3799),c_Int_Onumber__class_Onumber__of(X3801,X3798))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3801)
        | ~ class_Int_Onumber(X3801) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])])]) ).

fof(i_0_1563,plain,
    ! [X3876,X3877,X3878,X3879] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | ~ c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | c_Orderings_Oord__class_Oless(X3879,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877),X3878)
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | ~ c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | ~ c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,X3877,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_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | ~ c_Orderings_Oord__class_Oless(X3879,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877),X3878)
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ c_Orderings_Oord__class_Oless(X3879,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877),X3878)
        | c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),X3877)
        | ~ c_Orderings_Oord__class_Oless(X3879,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,X3877,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,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | ~ c_Orderings_Oord__class_Oless(X3879,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
        | ~ c_Orderings_Oord__class_Oless(X3879,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877),X3878)
        | ~ c_Orderings_Oord__class_Oless(X3879,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) )
      & ( ~ c_Orderings_Oord__class_Oless(X3879,c_Groups_Ozero__class_Ozero(X3879),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ c_Orderings_Oord__class_Oless(X3879,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877),X3878)
        | ~ c_Orderings_Oord__class_Oless(X3879,X3878,hAPP(c_Groups_Otimes__class_Otimes(X3879,c_Int_Onumber__class_Onumber__of(X3879,X3876)),X3877))
        | c_Orderings_Oord__class_Oless(X3879,c_Rings_Oinverse__class_Odivide(X3879,X3878,X3877),c_Int_Onumber__class_Onumber__of(X3879,X3876))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3879)
        | ~ class_Int_Onumber(X3879) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1324])])]) ).

fof(i_0_1564,plain,
    ! [X3802,X3803,X3804,X3805] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless__eq(X3805,X3803,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,X3803,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,X3803,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802))
        | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),X3802)
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Groups_Ozero__class_Ozero(X3805))
        | c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless(X3805,X3802,c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,X3803,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Groups_Ozero__class_Ozero(X3805))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,X3803,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802))
        | ~ c_Orderings_Oord__class_Oless__eq(X3805,hAPP(c_Groups_Otimes__class_Otimes(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804)),X3802),X3803)
        | c_Orderings_Oord__class_Oless__eq(X3805,c_Int_Onumber__class_Onumber__of(X3805,X3804),c_Rings_Oinverse__class_Odivide(X3805,X3803,X3802))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3805)
        | ~ class_Int_Onumber(X3805) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])])]) ).

fof(i_0_1565,plain,
    ! [X3880,X3881,X3882,X3883] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,X3881,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,X3881,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,X3881,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880))
        | c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Groups_Ozero__class_Ozero(X3883),X3880)
        | ~ c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Groups_Ozero__class_Ozero(X3883))
        | c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,X3880,c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,X3881,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880))
        | ~ c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) )
      & ( ~ c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Groups_Ozero__class_Ozero(X3883))
        | ~ c_Orderings_Oord__class_Oless(X3883,X3881,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880))
        | ~ c_Orderings_Oord__class_Oless(X3883,hAPP(c_Groups_Otimes__class_Otimes(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882)),X3880),X3881)
        | c_Orderings_Oord__class_Oless(X3883,c_Int_Onumber__class_Onumber__of(X3883,X3882),c_Rings_Oinverse__class_Odivide(X3883,X3881,X3880))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3883)
        | ~ class_Int_Onumber(X3883) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1326])])]) ).

cnf(i_0_1566,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1327]) ).

cnf(i_0_1567,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_1328]) ).

cnf(i_0_1568,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_1329]) ).

cnf(i_0_1569,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) ),
    inference(split_conjunct,[status(thm)],[i_0_1330]) ).

cnf(i_0_1570,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1331]) ).

fof(i_0_1571,plain,
    ! [X3379,X3380,X3381] :
      ( ~ class_Rings_Odivision__ring(X3381)
      | X3380 = c_Groups_Ozero__class_Ozero(X3381)
      | X3379 = c_Groups_Ozero__class_Ozero(X3381)
      | c_Groups_Oplus__class_Oplus(X3381,c_Rings_Oinverse__class_Oinverse(X3381,X3380),c_Rings_Oinverse__class_Oinverse(X3381,X3379)) = hAPP(c_Groups_Otimes__class_Otimes(X3381,hAPP(c_Groups_Otimes__class_Otimes(X3381,c_Rings_Oinverse__class_Oinverse(X3381,X3380)),c_Groups_Oplus__class_Oplus(X3381,X3380,X3379))),c_Rings_Oinverse__class_Oinverse(X3381,X3379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).

fof(i_0_1572,plain,
    ! [X3521,X3522,X3523,X3524,X3525] :
      ( ~ class_Rings_Osemiring(X3525)
      | c_Groups_Oplus__class_Oplus(X3525,hAPP(c_Groups_Otimes__class_Otimes(X3525,X3524),X3523),c_Groups_Oplus__class_Oplus(X3525,hAPP(c_Groups_Otimes__class_Otimes(X3525,X3522),X3523),X3521)) = c_Groups_Oplus__class_Oplus(X3525,hAPP(c_Groups_Otimes__class_Otimes(X3525,c_Groups_Oplus__class_Oplus(X3525,X3524,X3522)),X3523),X3521) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_1573,plain,
    ! [X3794,X3795,X3796,X3797] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless__eq(X3797,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3796)
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Ozero__class_Ozero(X3797),X3794)
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Ozero__class_Ozero(X3797),X3794)
        | c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3796)
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Ozero__class_Ozero(X3797),X3794)
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3796)
        | c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Groups_Ozero__class_Ozero(X3797),c_Int_Onumber__class_Onumber__of(X3797,X3795))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Ozero__class_Ozero(X3797),X3794)
        | c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless(X3797,c_Int_Onumber__class_Onumber__of(X3797,X3795),c_Groups_Ozero__class_Ozero(X3797))
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3796)
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Ozero__class_Ozero(X3797),X3794)
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3796)
        | ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,hAPP(c_Groups_Otimes__class_Otimes(X3797,X3794),c_Int_Onumber__class_Onumber__of(X3797,X3795)))
        | c_Orderings_Oord__class_Oless__eq(X3797,c_Rings_Oinverse__class_Odivide(X3797,X3796,c_Int_Onumber__class_Onumber__of(X3797,X3795)),X3794)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3797)
        | ~ class_Int_Onumber(X3797) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1332])])]) ).

fof(i_0_1574,plain,
    ! [X3872,X3873,X3874,X3875] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | ~ c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3874)
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | ~ c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),X3872)
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | ~ c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),X3872)
        | c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | ~ c_Orderings_Oord__class_Oless(X3875,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3874)
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),X3872)
        | ~ c_Orderings_Oord__class_Oless(X3875,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3874)
        | c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),c_Int_Onumber__class_Onumber__of(X3875,X3873))
        | ~ c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | ~ c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),X3872)
        | c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | ~ c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Int_Onumber__class_Onumber__of(X3875,X3873),c_Groups_Ozero__class_Ozero(X3875))
        | ~ c_Orderings_Oord__class_Oless(X3875,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3874)
        | ~ c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) )
      & ( ~ c_Orderings_Oord__class_Oless(X3875,c_Groups_Ozero__class_Ozero(X3875),X3872)
        | ~ c_Orderings_Oord__class_Oless(X3875,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3874)
        | ~ c_Orderings_Oord__class_Oless(X3875,X3874,hAPP(c_Groups_Otimes__class_Otimes(X3875,X3872),c_Int_Onumber__class_Onumber__of(X3875,X3873)))
        | c_Orderings_Oord__class_Oless(X3875,c_Rings_Oinverse__class_Odivide(X3875,X3874,c_Int_Onumber__class_Onumber__of(X3875,X3873)),X3872)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3875)
        | ~ class_Int_Onumber(X3875) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1333])])]) ).

fof(i_0_1575,plain,
    ! [X3806,X3807,X3808,X3809] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3807,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3807,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3807,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Groups_Ozero__class_Ozero(X3809),c_Int_Onumber__class_Onumber__of(X3809,X3806))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Groups_Ozero__class_Ozero(X3809))
        | c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless(X3809,c_Int_Onumber__class_Onumber__of(X3809,X3806),c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3807,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Groups_Ozero__class_Ozero(X3809))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,X3807,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ c_Orderings_Oord__class_Oless__eq(X3809,hAPP(c_Groups_Otimes__class_Otimes(X3809,X3808),c_Int_Onumber__class_Onumber__of(X3809,X3806)),X3807)
        | c_Orderings_Oord__class_Oless__eq(X3809,X3808,c_Rings_Oinverse__class_Odivide(X3809,X3807,c_Int_Onumber__class_Onumber__of(X3809,X3806)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3809)
        | ~ class_Int_Onumber(X3809) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1334])])]) ).

fof(i_0_1576,plain,
    ! [X3884,X3885,X3886,X3887] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,X3885,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3885,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3885,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Groups_Ozero__class_Ozero(X3887),c_Int_Onumber__class_Onumber__of(X3887,X3884))
        | ~ c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Groups_Ozero__class_Ozero(X3887))
        | c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,c_Int_Onumber__class_Onumber__of(X3887,X3884),c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3885,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) )
      & ( ~ c_Orderings_Oord__class_Oless(X3887,X3886,c_Groups_Ozero__class_Ozero(X3887))
        | ~ c_Orderings_Oord__class_Oless(X3887,X3885,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ c_Orderings_Oord__class_Oless(X3887,hAPP(c_Groups_Otimes__class_Otimes(X3887,X3886),c_Int_Onumber__class_Onumber__of(X3887,X3884)),X3885)
        | c_Orderings_Oord__class_Oless(X3887,X3886,c_Rings_Oinverse__class_Odivide(X3887,X3885,c_Int_Onumber__class_Onumber__of(X3887,X3884)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3887)
        | ~ class_Int_Onumber(X3887) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1335])])]) ).

fof(i_0_1577,plain,
    ! [X3288,X3289,X3290] :
      ( ( c_Orderings_Oord__class_Oless(X3290,c_Groups_Ozero__class_Ozero(X3290),esk5_3(X3288,X3289,X3290))
        | c_Orderings_Oord__class_Oless__eq(X3290,X3289,X3288)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3290) )
      & ( c_Orderings_Oord__class_Oless(X3290,esk5_3(X3288,X3289,X3290),c_Groups_Oone__class_Oone(X3290))
        | c_Orderings_Oord__class_Oless__eq(X3290,X3289,X3288)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3290) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3290,hAPP(c_Groups_Otimes__class_Otimes(X3290,esk5_3(X3288,X3289,X3290)),X3289),X3288)
        | c_Orderings_Oord__class_Oless__eq(X3290,X3289,X3288)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3290) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval])])])]) ).

fof(i_0_1578,plain,
    ! [X3298,X3299,X3300,X3301,X3302,X3303] :
      ( ~ class_Rings_Olinordered__semiring__1(X3303)
      | ~ c_Orderings_Oord__class_Oless__eq(X3303,X3302,X3301)
      | ~ c_Orderings_Oord__class_Oless__eq(X3303,X3300,X3301)
      | ~ c_Orderings_Oord__class_Oless__eq(X3303,c_Groups_Ozero__class_Ozero(X3303),X3299)
      | ~ c_Orderings_Oord__class_Oless__eq(X3303,c_Groups_Ozero__class_Ozero(X3303),X3298)
      | c_Groups_Oplus__class_Oplus(X3303,X3299,X3298) != c_Groups_Oone__class_Oone(X3303)
      | c_Orderings_Oord__class_Oless__eq(X3303,c_Groups_Oplus__class_Oplus(X3303,hAPP(c_Groups_Otimes__class_Otimes(X3303,X3299),X3302),hAPP(c_Groups_Otimes__class_Otimes(X3303,X3298),X3300)),X3301) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).

fof(i_0_1579,plain,
    ! [X3292,X3293,X3294,X3295,X3296,X3297] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X3297)
      | ~ c_Orderings_Oord__class_Oless(X3297,X3296,X3295)
      | ~ c_Orderings_Oord__class_Oless(X3297,X3294,X3295)
      | ~ c_Orderings_Oord__class_Oless__eq(X3297,c_Groups_Ozero__class_Ozero(X3297),X3293)
      | ~ c_Orderings_Oord__class_Oless__eq(X3297,c_Groups_Ozero__class_Ozero(X3297),X3292)
      | c_Groups_Oplus__class_Oplus(X3297,X3293,X3292) != c_Groups_Oone__class_Oone(X3297)
      | c_Orderings_Oord__class_Oless(X3297,c_Groups_Oplus__class_Oplus(X3297,hAPP(c_Groups_Otimes__class_Otimes(X3297,X3293),X3296),hAPP(c_Groups_Otimes__class_Otimes(X3297,X3292),X3294)),X3295) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).

fof(i_0_1580,plain,
    ! [X4565,X4566,X4567,X4568] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4568),X4567),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4566),X4567),X4565)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4568,X4566)),X4567),X4565),
    inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(i_0_1581,plain,
    ! [X3760,X3761,X3762,X3763] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3763)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3762)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3762),X3761),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3763),X3760))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3763)),X3761),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3762)),X3760)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel])]) ).

fof(i_0_1582,plain,
    ! [X4717,X4718] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4718),X4718),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4717),X4717)))),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__mult__self__sum__ge__zero]) ).

fof(i_0_1583,plain,
    ! [X4715,X4716] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4716,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4716),X4716),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4715),X4715)))),
    inference(variable_rename,[status(thm)],[fact_le__real__sqrt__sumsq]) ).

cnf(i_0_1584,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_1336]) ).

fof(i_0_1585,plain,
    ! [X3715,X3716,X3717,X3718,X3719] :
      ( ~ class_Fields_Ofield(X3719)
      | X3718 = c_Groups_Ozero__class_Ozero(X3719)
      | X3717 = c_Groups_Ozero__class_Ozero(X3719)
      | c_Groups_Oplus__class_Oplus(X3719,c_Rings_Oinverse__class_Odivide(X3719,X3716,X3718),c_Rings_Oinverse__class_Odivide(X3719,X3715,X3717)) = c_Rings_Oinverse__class_Odivide(X3719,c_Groups_Oplus__class_Oplus(X3719,hAPP(c_Groups_Otimes__class_Otimes(X3719,X3716),X3717),hAPP(c_Groups_Otimes__class_Otimes(X3719,X3715),X3718)),hAPP(c_Groups_Otimes__class_Otimes(X3719,X3718),X3717)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).

cnf(i_0_1586,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_1337]) ).

cnf(i_0_1587,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_1338]) ).

cnf(i_0_1588,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_1339]) ).

cnf(i_0_1589,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_1340]) ).

cnf(i_0_1590,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_1341]) ).

cnf(i_0_1591,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_1342]) ).

cnf(i_0_1592,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_1343]) ).

cnf(i_0_1593,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_1344]) ).

cnf(i_0_1594,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_1345]) ).

cnf(i_0_1595,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_1346]) ).

fof(i_0_1596,plain,
    ! [X4183,X4184,X4185,X4186,X4187] :
      ( ~ class_RealVector_Oreal__normed__field(X4187)
      | ~ c_Deriv_Oderiv(X4187,X4186,X4185,X4184)
      | ~ c_Deriv_Oderiv(X4187,X4186,X4185,X4183)
      | X4184 = X4183 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__unique])]) ).

fof(i_0_1597,plain,
    ! [X3747,X3748,X3749] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3749,c_Groups_Ozero__class_Ozero(X3749),c_Groups_Oplus__class_Oplus(X3749,hAPP(c_Groups_Otimes__class_Otimes(X3749,X3748),X3748),hAPP(c_Groups_Otimes__class_Otimes(X3749,X3747),X3747)))
        | X3748 != c_Groups_Ozero__class_Ozero(X3749)
        | X3747 != c_Groups_Ozero__class_Ozero(X3749)
        | ~ class_Rings_Olinordered__ring__strict(X3749) )
      & ( X3748 = c_Groups_Ozero__class_Ozero(X3749)
        | c_Orderings_Oord__class_Oless(X3749,c_Groups_Ozero__class_Ozero(X3749),c_Groups_Oplus__class_Oplus(X3749,hAPP(c_Groups_Otimes__class_Otimes(X3749,X3748),X3748),hAPP(c_Groups_Otimes__class_Otimes(X3749,X3747),X3747)))
        | ~ class_Rings_Olinordered__ring__strict(X3749) )
      & ( X3747 = c_Groups_Ozero__class_Ozero(X3749)
        | c_Orderings_Oord__class_Oless(X3749,c_Groups_Ozero__class_Ozero(X3749),c_Groups_Oplus__class_Oplus(X3749,hAPP(c_Groups_Otimes__class_Otimes(X3749,X3748),X3748),hAPP(c_Groups_Otimes__class_Otimes(X3749,X3747),X3747)))
        | ~ class_Rings_Olinordered__ring__strict(X3749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).

fof(i_0_1598,plain,
    ! [X3756,X3757,X3758,X3759] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3759)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3758)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3758),X3757),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3759),X3756))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3757),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3759)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3756),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3758))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel2])]) ).

cnf(i_0_1599,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_1318]) ).

cnf(i_0_1600,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_1319]) ).

cnf(i_0_1601,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_1320]) ).

cnf(i_0_1602,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_1321]) ).

fof(i_0_1603,plain,
    ! [X3750,X3751,X3752] :
      ( ( X3751 = c_Groups_Ozero__class_Ozero(X3752)
        | ~ c_Orderings_Oord__class_Oless__eq(X3752,c_Groups_Oplus__class_Oplus(X3752,hAPP(c_Groups_Otimes__class_Otimes(X3752,X3751),X3751),hAPP(c_Groups_Otimes__class_Otimes(X3752,X3750),X3750)),c_Groups_Ozero__class_Ozero(X3752))
        | ~ class_Rings_Olinordered__ring__strict(X3752) )
      & ( X3750 = c_Groups_Ozero__class_Ozero(X3752)
        | ~ c_Orderings_Oord__class_Oless__eq(X3752,c_Groups_Oplus__class_Oplus(X3752,hAPP(c_Groups_Otimes__class_Otimes(X3752,X3751),X3751),hAPP(c_Groups_Otimes__class_Otimes(X3752,X3750),X3750)),c_Groups_Ozero__class_Ozero(X3752))
        | ~ class_Rings_Olinordered__ring__strict(X3752) )
      & ( X3751 != c_Groups_Ozero__class_Ozero(X3752)
        | X3750 != c_Groups_Ozero__class_Ozero(X3752)
        | c_Orderings_Oord__class_Oless__eq(X3752,c_Groups_Oplus__class_Oplus(X3752,hAPP(c_Groups_Otimes__class_Otimes(X3752,X3751),X3751),hAPP(c_Groups_Otimes__class_Otimes(X3752,X3750),X3750)),c_Groups_Ozero__class_Ozero(X3752))
        | ~ class_Rings_Olinordered__ring__strict(X3752) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).

fof(i_0_1604,plain,
    ! [X3744,X3745,X3746] :
      ( ~ class_Rings_Olinordered__ring(X3746)
      | ~ c_Orderings_Oord__class_Oless(X3746,c_Groups_Oplus__class_Oplus(X3746,hAPP(c_Groups_Otimes__class_Otimes(X3746,X3745),X3745),hAPP(c_Groups_Otimes__class_Otimes(X3746,X3744),X3744)),c_Groups_Ozero__class_Ozero(X3746)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1347])]) ).

fof(i_0_1605,plain,
    ! [X3737,X3738,X3739] :
      ( ~ class_Fields_Olinordered__field(X3739)
      | ~ c_Orderings_Oord__class_Oless(X3739,X3738,X3737)
      | c_Orderings_Oord__class_Oless(X3739,c_Rings_Oinverse__class_Odivide(X3739,c_Groups_Oplus__class_Oplus(X3739,X3738,X3737),c_Groups_Oplus__class_Oplus(X3739,c_Groups_Oone__class_Oone(X3739),c_Groups_Oone__class_Oone(X3739))),X3737) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_1606,plain,
    ! [X3740,X3741,X3742] :
      ( ~ class_Fields_Olinordered__field(X3742)
      | ~ c_Orderings_Oord__class_Oless(X3742,X3741,X3740)
      | c_Orderings_Oord__class_Oless(X3742,X3741,c_Rings_Oinverse__class_Odivide(X3742,c_Groups_Oplus__class_Oplus(X3742,X3741,X3740),c_Groups_Oplus__class_Oplus(X3742,c_Groups_Oone__class_Oone(X3742),c_Groups_Oone__class_Oone(X3742)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

fof(i_0_1607,plain,
    ! [X4245,X4246,X4247] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4247),X4246),X4245),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),X4245)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4247)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4246,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).

fof(i_0_1608,plain,
    ! [X2610,X2611,X2612,X2613,X2614] :
      ( ~ class_Rings_Ocomm__semiring__1(X2614)
      | hAPP(c_Groups_Otimes__class_Otimes(X2614,hAPP(c_Groups_Otimes__class_Otimes(X2614,X2613),X2612)),hAPP(c_Groups_Otimes__class_Otimes(X2614,X2611),X2610)) = hAPP(c_Groups_Otimes__class_Otimes(X2614,X2611),hAPP(c_Groups_Otimes__class_Otimes(X2614,hAPP(c_Groups_Otimes__class_Otimes(X2614,X2613),X2612)),X2610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).

cnf(i_0_1609,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_1348]) ).

cnf(i_0_1610,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_1349]) ).

fof(i_0_1611,plain,
    ! [X4242,X4243,X4244] :
      ( ~ 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4244),X4243),X4242))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4242,X4244)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4244)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4243) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).

cnf(i_0_1612,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(X1)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1350]) ).

cnf(i_0_1613,plain,
    ( hAPP(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_1351]) ).

fof(i_0_1614,plain,
    ! [X3054,X3055,X3056,X3057] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless__eq(X3057,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055),X3056)
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Groups_Ozero__class_Ozero(X3057),X3054)
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Groups_Ozero__class_Ozero(X3057),X3054)
        | c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055),X3056)
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Groups_Ozero__class_Ozero(X3057),X3054)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055),X3056)
        | c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,c_Groups_Ozero__class_Ozero(X3057),X3055)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Groups_Ozero__class_Ozero(X3057),X3054)
        | c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless(X3057,X3055,c_Groups_Ozero__class_Ozero(X3057))
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055),X3056)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3057,c_Groups_Ozero__class_Ozero(X3057),X3054)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055),X3056)
        | ~ c_Orderings_Oord__class_Oless__eq(X3057,X3056,hAPP(c_Groups_Otimes__class_Otimes(X3057,X3054),X3055))
        | c_Orderings_Oord__class_Oless__eq(X3057,c_Rings_Oinverse__class_Odivide(X3057,X3056,X3055),X3054)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3057) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1352])])]) ).

fof(i_0_1615,plain,
    ! [X2666,X2667,X2668,X2669] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | ~ c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667),X2668)
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | ~ c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2666)
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | ~ c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2666)
        | c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | ~ c_Orderings_Oord__class_Oless(X2669,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667),X2668)
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2666)
        | ~ c_Orderings_Oord__class_Oless(X2669,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667),X2668)
        | c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2667)
        | ~ c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | ~ c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2666)
        | c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | ~ c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,X2667,c_Groups_Ozero__class_Ozero(X2669))
        | ~ c_Orderings_Oord__class_Oless(X2669,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667),X2668)
        | ~ c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) )
      & ( ~ c_Orderings_Oord__class_Oless(X2669,c_Groups_Ozero__class_Ozero(X2669),X2666)
        | ~ c_Orderings_Oord__class_Oless(X2669,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667),X2668)
        | ~ c_Orderings_Oord__class_Oless(X2669,X2668,hAPP(c_Groups_Otimes__class_Otimes(X2669,X2666),X2667))
        | c_Orderings_Oord__class_Oless(X2669,c_Rings_Oinverse__class_Odivide(X2669,X2668,X2667),X2666)
        | ~ class_Fields_Olinordered__field__inverse__zero(X2669) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1353])])]) ).

fof(i_0_1616,plain,
    ! [X3050,X3051,X3052,X3053] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless__eq(X3053,X3051,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3051,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3051,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050))
        | c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3050)
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Groups_Ozero__class_Ozero(X3053))
        | c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless(X3053,X3050,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3051,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Groups_Ozero__class_Ozero(X3053))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3051,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050))
        | ~ c_Orderings_Oord__class_Oless__eq(X3053,hAPP(c_Groups_Otimes__class_Otimes(X3053,X3052),X3050),X3051)
        | c_Orderings_Oord__class_Oless__eq(X3053,X3052,c_Rings_Oinverse__class_Odivide(X3053,X3051,X3050))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3053) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1354])])]) ).

fof(i_0_1617,plain,
    ! [X2670,X2671,X2672,X2673] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2671,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,X2671,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,X2671,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670))
        | c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,c_Groups_Ozero__class_Ozero(X2673),X2670)
        | ~ c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Groups_Ozero__class_Ozero(X2673))
        | c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2670,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,X2671,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670))
        | ~ c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) )
      & ( ~ c_Orderings_Oord__class_Oless(X2673,X2672,c_Groups_Ozero__class_Ozero(X2673))
        | ~ c_Orderings_Oord__class_Oless(X2673,X2671,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670))
        | ~ c_Orderings_Oord__class_Oless(X2673,hAPP(c_Groups_Otimes__class_Otimes(X2673,X2672),X2670),X2671)
        | c_Orderings_Oord__class_Oless(X2673,X2672,c_Rings_Oinverse__class_Odivide(X2673,X2671,X2670))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2673) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1355])])]) ).

fof(i_0_1618,plain,
    ! [X3082,X3083,X3084,X3085] :
      ( ~ class_Fields_Olinordered__field(X3085)
      | ~ c_Orderings_Oord__class_Oless__eq(X3085,X3084,X3083)
      | ~ c_Orderings_Oord__class_Oless__eq(X3085,c_Groups_Ozero__class_Ozero(X3085),X3082)
      | ~ c_Orderings_Oord__class_Oless(X3085,c_Groups_Ozero__class_Ozero(X3085),hAPP(c_Groups_Otimes__class_Otimes(X3085,X3083),X3084))
      | c_Orderings_Oord__class_Oless__eq(X3085,c_Rings_Oinverse__class_Odivide(X3085,X3082,X3083),c_Rings_Oinverse__class_Odivide(X3085,X3082,X3084)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).

fof(i_0_1619,plain,
    ! [X2638,X2639,X2640,X2641] :
      ( ~ class_Fields_Olinordered__field(X2641)
      | ~ c_Orderings_Oord__class_Oless(X2641,X2640,X2639)
      | ~ c_Orderings_Oord__class_Oless(X2641,c_Groups_Ozero__class_Ozero(X2641),X2638)
      | ~ c_Orderings_Oord__class_Oless(X2641,c_Groups_Ozero__class_Ozero(X2641),hAPP(c_Groups_Otimes__class_Otimes(X2641,X2639),X2640))
      | c_Orderings_Oord__class_Oless(X2641,c_Rings_Oinverse__class_Odivide(X2641,X2638,X2639),c_Rings_Oinverse__class_Odivide(X2641,X2638,X2640)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).

fof(i_0_1620,plain,
    ! [X3086,X3087,X3088,X3089] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X3089)
      | ~ c_Orderings_Oord__class_Oless__eq(X3089,X3088,X3087)
      | ~ c_Orderings_Oord__class_Oless__eq(X3089,X3086,c_Groups_Ozero__class_Ozero(X3089))
      | ~ c_Orderings_Oord__class_Oless(X3089,c_Groups_Ozero__class_Ozero(X3089),hAPP(c_Groups_Otimes__class_Otimes(X3089,X3088),X3087))
      | c_Orderings_Oord__class_Oless__eq(X3089,c_Rings_Oinverse__class_Odivide(X3089,X3086,X3088),c_Rings_Oinverse__class_Odivide(X3089,X3086,X3087)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).

fof(i_0_1621,plain,
    ! [X2634,X2635,X2636,X2637] :
      ( ~ class_Fields_Olinordered__field(X2637)
      | ~ c_Orderings_Oord__class_Oless(X2637,X2636,X2635)
      | ~ c_Orderings_Oord__class_Oless(X2637,X2634,c_Groups_Ozero__class_Ozero(X2637))
      | ~ c_Orderings_Oord__class_Oless(X2637,c_Groups_Ozero__class_Ozero(X2637),hAPP(c_Groups_Otimes__class_Otimes(X2637,X2636),X2635))
      | c_Orderings_Oord__class_Oless(X2637,c_Rings_Oinverse__class_Odivide(X2637,X2634,X2636),c_Rings_Oinverse__class_Odivide(X2637,X2634,X2635)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).

fof(i_0_1622,plain,
    ! [X3499,X3500,X3501,X3502,X3503] :
      ( ( X3502 = X3501
        | X3500 = X3499
        | c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3500),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3499)) != c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3499),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3500))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3503) )
      & ( X3502 != X3501
        | c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3500),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3499)) = c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3499),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3500))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3503) )
      & ( X3500 != X3499
        | c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3500),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3499)) = c_Groups_Oplus__class_Oplus(X3503,hAPP(c_Groups_Otimes__class_Otimes(X3503,X3502),X3499),hAPP(c_Groups_Otimes__class_Otimes(X3503,X3501),X3500))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3503) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_1623,plain,
    ! [X3512,X3513,X3514,X3515,X3516] :
      ( ( c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3514),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3512)) != c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3512),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3514))
        | X3515 = X3513
        | X3514 = X3512
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3516) )
      & ( X3515 != X3513
        | c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3514),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3512)) = c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3512),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3514))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3516) )
      & ( X3514 != X3512
        | c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3514),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3512)) = c_Groups_Oplus__class_Oplus(X3516,hAPP(c_Groups_Otimes__class_Otimes(X3516,X3515),X3512),hAPP(c_Groups_Otimes__class_Otimes(X3516,X3513),X3514))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3516) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

fof(i_0_1624,plain,
    ! [X4294,X4295,X4296] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4296,c_Int_OPls)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4296)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4295)),X4294)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4296,c_Int_OPls)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4296)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4295)),X4294)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4296),X4295))),X4294) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1356])]) ).

cnf(i_0_1625,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_1357]) ).

cnf(i_0_1626,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_1358]) ).

cnf(i_0_1627,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_1359]) ).

cnf(i_0_1628,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_1360]) ).

fof(i_0_1629,plain,
    ! [X3830,X3831,X3832,X3833] :
      ( ~ class_Int_Onumber__ring(X3833)
      | hAPP(c_Groups_Otimes__class_Otimes(X3833,c_Int_Onumber__class_Onumber__of(X3833,X3832)),hAPP(c_Groups_Otimes__class_Otimes(X3833,c_Int_Onumber__class_Onumber__of(X3833,X3831)),X3830)) = hAPP(c_Groups_Otimes__class_Otimes(X3833,c_Int_Onumber__class_Onumber__of(X3833,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3832),X3831))),X3830) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_1630,plain,
    ! [X4063] :
      ( ( ~ 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),X4063),X4063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4063,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4063,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),X4063),X4063),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).

fof(i_0_1631,plain,
    ! [X4963,X4964,X4965] :
      ( ~ class_Rings_Olinordered__semidom(X4965)
      | ~ c_Orderings_Oord__class_Oless(X4965,c_Groups_Ozero__class_Ozero(X4965),X4964)
      | ~ c_Orderings_Oord__class_Oless(X4965,X4964,c_Groups_Oone__class_Oone(X4965))
      | c_Orderings_Oord__class_Oless(X4965,hAPP(c_Groups_Otimes__class_Otimes(X4965,X4964),c_Power_Opower__class_Opower(X4965,X4964,X4963)),c_Power_Opower__class_Opower(X4965,X4964,X4963)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).

fof(i_0_1632,plain,
    ! [X3771,X3772,X3773] :
      ( ( c_Orderings_Oord__class_Oless(X3773,c_Groups_Ozero__class_Ozero(X3773),esk6_3(X3771,X3772,X3773))
        | c_Orderings_Oord__class_Oless__eq(X3773,X3772,X3771)
        | ~ class_Fields_Olinordered__field(X3773) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3773,X3772,c_Groups_Oplus__class_Oplus(X3773,X3771,esk6_3(X3771,X3772,X3773)))
        | c_Orderings_Oord__class_Oless__eq(X3773,X3772,X3771)
        | ~ class_Fields_Olinordered__field(X3773) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__le__epsilon])])])]) ).

cnf(i_0_1633,plain,
    c_Int_Osucc(c_Int_OBit1(X1)) = c_Int_OBit0(c_Int_Osucc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

cnf(i_0_1634,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_1362]) ).

fof(i_0_1635,plain,
    ! [X3015,X3016,X3017,X3018,X3019] :
      ( ~ class_Fields_Olinordered__field(X3019)
      | ~ c_Orderings_Oord__class_Oless__eq(X3019,c_Groups_Ozero__class_Ozero(X3019),X3018)
      | ~ c_Orderings_Oord__class_Oless__eq(X3019,X3018,X3017)
      | ~ c_Orderings_Oord__class_Oless(X3019,c_Groups_Ozero__class_Ozero(X3019),X3016)
      | ~ c_Orderings_Oord__class_Oless__eq(X3019,X3016,X3015)
      | c_Orderings_Oord__class_Oless__eq(X3019,c_Rings_Oinverse__class_Odivide(X3019,X3018,X3015),c_Rings_Oinverse__class_Odivide(X3019,X3017,X3016)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_1636,plain,
    ! [X3020,X3021,X3022,X3023,X3024] :
      ( ~ class_Fields_Olinordered__field(X3024)
      | ~ c_Orderings_Oord__class_Oless__eq(X3024,c_Groups_Ozero__class_Ozero(X3024),X3023)
      | ~ c_Orderings_Oord__class_Oless(X3024,X3023,X3022)
      | ~ c_Orderings_Oord__class_Oless(X3024,c_Groups_Ozero__class_Ozero(X3024),X3021)
      | ~ c_Orderings_Oord__class_Oless__eq(X3024,X3021,X3020)
      | c_Orderings_Oord__class_Oless(X3024,c_Rings_Oinverse__class_Odivide(X3024,X3023,X3020),c_Rings_Oinverse__class_Odivide(X3024,X3022,X3021)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_1637,plain,
    ! [X3025,X3026,X3027,X3028,X3029] :
      ( ~ class_Fields_Olinordered__field(X3029)
      | ~ c_Orderings_Oord__class_Oless(X3029,c_Groups_Ozero__class_Ozero(X3029),X3028)
      | ~ c_Orderings_Oord__class_Oless__eq(X3029,X3028,X3027)
      | ~ c_Orderings_Oord__class_Oless(X3029,c_Groups_Ozero__class_Ozero(X3029),X3026)
      | ~ c_Orderings_Oord__class_Oless(X3029,X3026,X3025)
      | c_Orderings_Oord__class_Oless(X3029,c_Rings_Oinverse__class_Odivide(X3029,X3028,X3025),c_Rings_Oinverse__class_Odivide(X3029,X3027,X3026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

cnf(i_0_1638,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_1363]) ).

cnf(i_0_1639,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_1364]) ).

cnf(i_0_1640,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_1365]) ).

cnf(i_0_1641,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_1366]) ).

fof(i_0_1642,plain,
    ! [X3850,X3851,X3852,X3853] :
      ( ~ class_Int_Onumber(X3853)
      | ~ class_Rings_Osemiring(X3853)
      | hAPP(c_Groups_Otimes__class_Otimes(X3853,c_Int_Onumber__class_Onumber__of(X3853,X3852)),c_Groups_Oplus__class_Oplus(X3853,X3851,X3850)) = c_Groups_Oplus__class_Oplus(X3853,hAPP(c_Groups_Otimes__class_Otimes(X3853,c_Int_Onumber__class_Onumber__of(X3853,X3852)),X3851),hAPP(c_Groups_Otimes__class_Otimes(X3853,c_Int_Onumber__class_Onumber__of(X3853,X3852)),X3850)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

fof(i_0_1643,plain,
    ! [X5033,X5034,X5035,X5036,X5037] :
      ( ~ class_Rings_Olinordered__idom(X5037)
      | ~ c_Orderings_Oord__class_Oless(X5037,c_Groups_Oabs__class_Oabs(X5037,X5036),X5035)
      | ~ c_Orderings_Oord__class_Oless(X5037,c_Groups_Oabs__class_Oabs(X5037,X5034),X5033)
      | c_Orderings_Oord__class_Oless(X5037,hAPP(c_Groups_Otimes__class_Otimes(X5037,c_Groups_Oabs__class_Oabs(X5037,X5036)),c_Groups_Oabs__class_Oabs(X5037,X5034)),hAPP(c_Groups_Otimes__class_Otimes(X5037,X5035),X5033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).

fof(i_0_1644,plain,
    ! [X3846,X3847,X3848,X3849] :
      ( ~ class_Int_Onumber(X3849)
      | ~ class_Rings_Osemiring(X3849)
      | hAPP(c_Groups_Otimes__class_Otimes(X3849,c_Groups_Oplus__class_Oplus(X3849,X3848,X3847)),c_Int_Onumber__class_Onumber__of(X3849,X3846)) = c_Groups_Oplus__class_Oplus(X3849,hAPP(c_Groups_Otimes__class_Otimes(X3849,X3848),c_Int_Onumber__class_Onumber__of(X3849,X3846)),hAPP(c_Groups_Otimes__class_Otimes(X3849,X3847),c_Int_Onumber__class_Onumber__of(X3849,X3846))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_1645,plain,
    ! [X4944,X4945,X4946] :
      ( ~ class_Rings_Oring__1(X4946)
      | c_Power_Opower__class_Opower(X4946,c_Groups_Ouminus__class_Ouminus(X4946,X4945),X4944) = hAPP(c_Groups_Otimes__class_Otimes(X4946,c_Power_Opower__class_Opower(X4946,c_Groups_Ouminus__class_Ouminus(X4946,c_Groups_Oone__class_Oone(X4946)),X4944)),c_Power_Opower__class_Opower(X4946,X4945,X4944)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).

cnf(i_0_1646,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_1367]) ).

fof(i_0_1647,plain,
    ! [X2885,X2886,X2887,X2888,X2889] :
      ( ~ class_Rings_Oordered__semiring(X2889)
      | ~ c_Orderings_Oord__class_Oless__eq(X2889,X2888,X2887)
      | ~ c_Orderings_Oord__class_Oless__eq(X2889,X2886,X2885)
      | ~ c_Orderings_Oord__class_Oless__eq(X2889,c_Groups_Ozero__class_Ozero(X2889),X2888)
      | ~ c_Orderings_Oord__class_Oless__eq(X2889,c_Groups_Ozero__class_Ozero(X2889),X2886)
      | c_Orderings_Oord__class_Oless__eq(X2889,hAPP(c_Groups_Otimes__class_Otimes(X2889,X2888),X2886),hAPP(c_Groups_Otimes__class_Otimes(X2889,X2887),X2885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_1648,plain,
    ! [X2880,X2881,X2882,X2883,X2884] :
      ( ~ class_Rings_Oordered__semiring(X2884)
      | ~ c_Orderings_Oord__class_Oless__eq(X2884,X2883,X2882)
      | ~ c_Orderings_Oord__class_Oless__eq(X2884,X2881,X2880)
      | ~ c_Orderings_Oord__class_Oless__eq(X2884,c_Groups_Ozero__class_Ozero(X2884),X2882)
      | ~ c_Orderings_Oord__class_Oless__eq(X2884,c_Groups_Ozero__class_Ozero(X2884),X2881)
      | c_Orderings_Oord__class_Oless__eq(X2884,hAPP(c_Groups_Otimes__class_Otimes(X2884,X2883),X2881),hAPP(c_Groups_Otimes__class_Otimes(X2884,X2882),X2880)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

fof(i_0_1649,plain,
    ! [X2969,X2970,X2971,X2972,X2973] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2973)
      | ~ c_Orderings_Oord__class_Oless(X2973,X2972,X2971)
      | ~ c_Orderings_Oord__class_Oless__eq(X2973,X2970,X2969)
      | ~ c_Orderings_Oord__class_Oless__eq(X2973,c_Groups_Ozero__class_Ozero(X2973),X2972)
      | ~ c_Orderings_Oord__class_Oless(X2973,c_Groups_Ozero__class_Ozero(X2973),X2970)
      | c_Orderings_Oord__class_Oless(X2973,hAPP(c_Groups_Otimes__class_Otimes(X2973,X2972),X2970),hAPP(c_Groups_Otimes__class_Otimes(X2973,X2971),X2969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).

fof(i_0_1650,plain,
    ! [X2974,X2975,X2976,X2977,X2978] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2978)
      | ~ c_Orderings_Oord__class_Oless__eq(X2978,X2977,X2976)
      | ~ c_Orderings_Oord__class_Oless(X2978,X2975,X2974)
      | ~ c_Orderings_Oord__class_Oless(X2978,c_Groups_Ozero__class_Ozero(X2978),X2977)
      | ~ c_Orderings_Oord__class_Oless__eq(X2978,c_Groups_Ozero__class_Ozero(X2978),X2975)
      | c_Orderings_Oord__class_Oless(X2978,hAPP(c_Groups_Otimes__class_Otimes(X2978,X2977),X2975),hAPP(c_Groups_Otimes__class_Otimes(X2978,X2976),X2974)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).

fof(i_0_1651,plain,
    ! [X2964,X2965,X2966,X2967,X2968] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2968)
      | ~ c_Orderings_Oord__class_Oless(X2968,X2967,X2966)
      | ~ c_Orderings_Oord__class_Oless(X2968,X2965,X2964)
      | ~ c_Orderings_Oord__class_Oless__eq(X2968,c_Groups_Ozero__class_Ozero(X2968),X2967)
      | ~ c_Orderings_Oord__class_Oless__eq(X2968,c_Groups_Ozero__class_Ozero(X2968),X2965)
      | c_Orderings_Oord__class_Oless(X2968,hAPP(c_Groups_Otimes__class_Otimes(X2968,X2967),X2965),hAPP(c_Groups_Otimes__class_Otimes(X2968,X2966),X2964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).

fof(i_0_1652,plain,
    ! [X2959,X2960,X2961,X2962,X2963] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2963)
      | ~ c_Orderings_Oord__class_Oless(X2963,X2962,X2961)
      | ~ c_Orderings_Oord__class_Oless(X2963,X2960,X2959)
      | ~ c_Orderings_Oord__class_Oless(X2963,c_Groups_Ozero__class_Ozero(X2963),X2961)
      | ~ c_Orderings_Oord__class_Oless__eq(X2963,c_Groups_Ozero__class_Ozero(X2963),X2960)
      | c_Orderings_Oord__class_Oless(X2963,hAPP(c_Groups_Otimes__class_Otimes(X2963,X2962),X2960),hAPP(c_Groups_Otimes__class_Otimes(X2963,X2961),X2959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).

fof(i_0_1653,plain,
    ! [X4932,X4933,X4934,X4935] :
      ( ~ class_Rings_Olinordered__semidom(X4935)
      | ~ c_Orderings_Oord__class_Oless(X4935,c_Power_Opower__class_Opower(X4935,X4934,X4933),c_Power_Opower__class_Opower(X4935,X4932,X4933))
      | ~ c_Orderings_Oord__class_Oless__eq(X4935,c_Groups_Ozero__class_Ozero(X4935),X4932)
      | c_Orderings_Oord__class_Oless(X4935,X4934,X4932) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).

fof(i_0_1654,plain,
    ! [X4982,X4983,X4984,X4985] :
      ( ~ class_Rings_Olinordered__semidom(X4985)
      | ~ c_Orderings_Oord__class_Oless(X4985,c_Groups_Oone__class_Oone(X4985),X4984)
      | ~ c_Orderings_Oord__class_Oless__eq(X4985,c_Power_Opower__class_Opower(X4985,X4984,X4983),c_Power_Opower__class_Opower(X4985,X4984,X4982))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4983,X4982) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).

fof(i_0_1655,plain,
    ! [X4978,X4979,X4980,X4981] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4981,c_Power_Opower__class_Opower(X4981,X4980,X4979),c_Power_Opower__class_Opower(X4981,X4980,X4978))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4979,X4978)
        | ~ c_Orderings_Oord__class_Oless(X4981,c_Groups_Oone__class_Oone(X4981),X4980)
        | ~ class_Rings_Olinordered__semidom(X4981) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4979,X4978)
        | c_Orderings_Oord__class_Oless__eq(X4981,c_Power_Opower__class_Opower(X4981,X4980,X4979),c_Power_Opower__class_Opower(X4981,X4980,X4978))
        | ~ c_Orderings_Oord__class_Oless(X4981,c_Groups_Oone__class_Oone(X4981),X4980)
        | ~ class_Rings_Olinordered__semidom(X4981) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).

fof(i_0_1656,plain,
    ! [X4951,X4952,X4953,X4954] :
      ( ~ class_Rings_Olinordered__semidom(X4954)
      | ~ c_Orderings_Oord__class_Oless(X4954,c_Groups_Oone__class_Oone(X4954),X4953)
      | ~ c_Orderings_Oord__class_Oless(X4954,c_Power_Opower__class_Opower(X4954,X4953,X4952),c_Power_Opower__class_Opower(X4954,X4953,X4951))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4952,X4951) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).

fof(i_0_1657,plain,
    ! [X4947,X4948,X4949,X4950] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4950,c_Power_Opower__class_Opower(X4950,X4949,X4948),c_Power_Opower__class_Opower(X4950,X4949,X4947))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4948,X4947)
        | ~ c_Orderings_Oord__class_Oless(X4950,c_Groups_Oone__class_Oone(X4950),X4949)
        | ~ class_Rings_Olinordered__semidom(X4950) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4948,X4947)
        | c_Orderings_Oord__class_Oless(X4950,c_Power_Opower__class_Opower(X4950,X4949,X4948),c_Power_Opower__class_Opower(X4950,X4949,X4947))
        | ~ c_Orderings_Oord__class_Oless(X4950,c_Groups_Oone__class_Oone(X4950),X4949)
        | ~ class_Rings_Olinordered__semidom(X4950) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).

fof(i_0_1658,plain,
    ! [X2674,X2675,X2676,X2677,X2678] :
      ( ~ class_Fields_Ofield__inverse__zero(X2678)
      | hAPP(c_Groups_Otimes__class_Otimes(X2678,c_Rings_Oinverse__class_Odivide(X2678,X2677,X2676)),c_Rings_Oinverse__class_Odivide(X2678,X2675,X2674)) = c_Rings_Oinverse__class_Odivide(X2678,hAPP(c_Groups_Otimes__class_Otimes(X2678,X2677),X2675),hAPP(c_Groups_Otimes__class_Otimes(X2678,X2676),X2674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).

fof(i_0_1659,plain,
    ! [X4252,X4253,X4254] :
      ( ( c_Int_Onumber__class_Onumber__of(X4254,X4253) != c_Int_Onumber__class_Onumber__of(X4254,X4252)
        | c_Int_Oiszero(X4254,c_Int_Onumber__class_Onumber__of(X4254,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4253,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4252))))
        | ~ class_Int_Onumber__ring(X4254) )
      & ( ~ c_Int_Oiszero(X4254,c_Int_Onumber__class_Onumber__of(X4254,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4253,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4252))))
        | c_Int_Onumber__class_Onumber__of(X4254,X4253) = c_Int_Onumber__class_Onumber__of(X4254,X4252)
        | ~ class_Int_Onumber__ring(X4254) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).

cnf(i_0_1660,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_1339]) ).

cnf(i_0_1661,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_1340]) ).

cnf(i_0_1662,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_1341]) ).

cnf(i_0_1663,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_1342]) ).

cnf(i_0_1664,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_1343]) ).

cnf(i_0_1665,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_1344]) ).

cnf(i_0_1666,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_1345]) ).

cnf(i_0_1667,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_1346]) ).

fof(i_0_1668,plain,
    ! [X4939,X4940,X4941] :
      ( ~ class_Rings_Olinordered__semidom(X4941)
      | ~ c_Orderings_Oord__class_Oless(X4941,c_Groups_Oone__class_Oone(X4941),X4940)
      | c_Orderings_Oord__class_Oless(X4941,c_Power_Opower__class_Opower(X4941,X4940,X4939),hAPP(c_Groups_Otimes__class_Otimes(X4941,X4940),c_Power_Opower__class_Opower(X4941,X4940,X4939))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).

fof(i_0_1669,plain,
    ! [X2605,X2606,X2607,X2608,X2609] :
      ( ~ class_Rings_Ocomm__semiring__1(X2609)
      | hAPP(c_Groups_Otimes__class_Otimes(X2609,hAPP(c_Groups_Otimes__class_Otimes(X2609,X2608),X2607)),hAPP(c_Groups_Otimes__class_Otimes(X2609,X2606),X2605)) = hAPP(c_Groups_Otimes__class_Otimes(X2609,hAPP(c_Groups_Otimes__class_Otimes(X2609,X2608),X2606)),hAPP(c_Groups_Otimes__class_Otimes(X2609,X2607),X2605)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).

fof(i_0_1670,plain,
    ! [X2615,X2616,X2617,X2618,X2619] :
      ( ~ class_Rings_Ocomm__semiring__1(X2619)
      | hAPP(c_Groups_Otimes__class_Otimes(X2619,hAPP(c_Groups_Otimes__class_Otimes(X2619,X2618),X2617)),hAPP(c_Groups_Otimes__class_Otimes(X2619,X2616),X2615)) = hAPP(c_Groups_Otimes__class_Otimes(X2619,X2618),hAPP(c_Groups_Otimes__class_Otimes(X2619,X2617),hAPP(c_Groups_Otimes__class_Otimes(X2619,X2616),X2615))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).

fof(i_0_1671,plain,
    ! [X4854,X4855,X4856] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4856)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X4856,X4855),c_Power_Opower__class_Opower(tc_Nat_Onat,X4856,X4854))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4855,X4854) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).

fof(i_0_1672,plain,
    ! [X4974,X4975,X4976,X4977] :
      ( ~ class_Rings_Olinordered__semidom(X4977)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4976,X4975)
      | ~ c_Orderings_Oord__class_Oless__eq(X4977,c_Groups_Ozero__class_Ozero(X4977),X4974)
      | ~ c_Orderings_Oord__class_Oless__eq(X4977,X4974,c_Groups_Oone__class_Oone(X4977))
      | c_Orderings_Oord__class_Oless__eq(X4977,c_Power_Opower__class_Opower(X4977,X4974,X4975),c_Power_Opower__class_Opower(X4977,X4974,X4976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).

fof(i_0_1673,plain,
    ! [X4966,X4967,X4968,X4969] :
      ( ~ class_Rings_Olinordered__semidom(X4969)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4968,X4967)
      | ~ c_Orderings_Oord__class_Oless(X4969,c_Groups_Ozero__class_Ozero(X4969),X4966)
      | ~ c_Orderings_Oord__class_Oless(X4969,X4966,c_Groups_Oone__class_Oone(X4969))
      | c_Orderings_Oord__class_Oless(X4969,c_Power_Opower__class_Opower(X4969,X4966,X4967),c_Power_Opower__class_Opower(X4969,X4966,X4968)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).

fof(i_0_1674,plain,
    ! [X4271,X4272] :
      ( ( c_Groups_Ozero__class_Ozero(X4272) != c_Int_Onumber__class_Onumber__of(X4272,X4271)
        | c_Int_Oiszero(X4272,c_Int_Onumber__class_Onumber__of(X4272,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4271))))
        | ~ class_Int_Onumber__ring(X4272) )
      & ( ~ c_Int_Oiszero(X4272,c_Int_Onumber__class_Onumber__of(X4272,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4271))))
        | c_Groups_Ozero__class_Ozero(X4272) = c_Int_Onumber__class_Onumber__of(X4272,X4271)
        | ~ class_Int_Onumber__ring(X4272) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).

fof(i_0_1675,plain,
    ! [X4850,X4851,X4852,X4853] :
      ( ~ class_Rings_Olinordered__semidom(X4853)
      | ~ c_Orderings_Oord__class_Oless(X4853,X4852,X4851)
      | ~ c_Orderings_Oord__class_Oless__eq(X4853,c_Groups_Ozero__class_Ozero(X4853),X4852)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4850)
      | c_Orderings_Oord__class_Oless(X4853,c_Power_Opower__class_Opower(X4853,X4852,X4850),c_Power_Opower__class_Opower(X4853,X4851,X4850)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).

fof(i_0_1676,plain,
    ! [X3347,X3348,X3349,X3350,X3351] :
      ( ~ class_Rings_Ocomm__semiring__1(X3351)
      | c_Groups_Oplus__class_Oplus(X3351,c_Groups_Oplus__class_Oplus(X3351,X3350,X3349),c_Groups_Oplus__class_Oplus(X3351,X3348,X3347)) = c_Groups_Oplus__class_Oplus(X3351,c_Groups_Oplus__class_Oplus(X3351,X3350,X3348),c_Groups_Oplus__class_Oplus(X3351,X3349,X3347)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_1677,plain,
    ! [X4269,X4270] :
      ( ( c_Int_Onumber__class_Onumber__of(X4270,X4269) != c_Groups_Ozero__class_Ozero(X4270)
        | c_Int_Oiszero(X4270,c_Int_Onumber__class_Onumber__of(X4270,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4269,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
        | ~ class_Int_Onumber__ring(X4270) )
      & ( ~ c_Int_Oiszero(X4270,c_Int_Onumber__class_Onumber__of(X4270,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4269,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
        | c_Int_Onumber__class_Onumber__of(X4270,X4269) = c_Groups_Ozero__class_Ozero(X4270)
        | ~ class_Int_Onumber__ring(X4270) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).

fof(i_0_1678,plain,
    ! [X3811,X3812,X3813,X3814] :
      ( ~ class_Int_Onumber__ring(X3814)
      | c_Groups_Oplus__class_Oplus(X3814,c_Int_Onumber__class_Onumber__of(X3814,X3813),c_Groups_Oplus__class_Oplus(X3814,c_Int_Onumber__class_Onumber__of(X3814,X3812),X3811)) = c_Groups_Oplus__class_Oplus(X3814,c_Int_Onumber__class_Onumber__of(X3814,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3813,X3812)),X3811) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_1679,plain,
    ! [X4733,X4734,X4735,X4736] :
      ( ~ class_Rings_Ocomm__semiring__1(X4736)
      | hAPP(c_Groups_Otimes__class_Otimes(X4736,c_Power_Opower__class_Opower(X4736,X4735,X4734)),c_Power_Opower__class_Opower(X4736,X4735,X4733)) = c_Power_Opower__class_Opower(X4736,X4735,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4734,X4733)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).

fof(i_0_1680,plain,
    ! [X4922,X4923,X4924,X4925] :
      ( ~ class_Groups_Omonoid__mult(X4925)
      | c_Power_Opower__class_Opower(X4925,X4924,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4923,X4922)) = hAPP(c_Groups_Otimes__class_Otimes(X4925,c_Power_Opower__class_Opower(X4925,X4924,X4923)),c_Power_Opower__class_Opower(X4925,X4924,X4922)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).

cnf(i_0_1681,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_1368]) ).

cnf(i_0_1682,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_1359]) ).

cnf(i_0_1683,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_1360]) ).

cnf(i_0_1684,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_1357]) ).

cnf(i_0_1685,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_1358]) ).

fof(i_0_1686,plain,
    ! [X4861,X4862,X4863] : c_Power_Opower__class_Opower(tc_Int_Oint,X4863,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4862,X4861)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4863,X4862)),c_Power_Opower__class_Opower(tc_Int_Oint,X4863,X4861)),
    inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).

cnf(i_0_1687,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1369]) ).

fof(i_0_1688,plain,
    ! [X4874,X4875,X4876,X4877] :
      ( ~ class_Groups_Ocomm__monoid__mult(X4877)
      | c_Power_Opower__class_Opower(X4877,hAPP(c_Groups_Otimes__class_Otimes(X4877,X4876),X4875),X4874) = hAPP(c_Groups_Otimes__class_Otimes(X4877,c_Power_Opower__class_Opower(X4877,X4876,X4874)),c_Power_Opower__class_Opower(X4877,X4875,X4874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).

fof(i_0_1689,plain,
    ! [X4741,X4742,X4743,X4744] :
      ( ~ class_Rings_Ocomm__semiring__1(X4744)
      | c_Power_Opower__class_Opower(X4744,hAPP(c_Groups_Otimes__class_Otimes(X4744,X4743),X4742),X4741) = hAPP(c_Groups_Otimes__class_Otimes(X4744,c_Power_Opower__class_Opower(X4744,X4743,X4741)),c_Power_Opower__class_Opower(X4744,X4742,X4741)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).

fof(i_0_1690,plain,
    ! [X3720,X3721,X3722,X3723] :
      ( ~ class_Fields_Ofield(X3723)
      | X3722 = c_Groups_Ozero__class_Ozero(X3723)
      | c_Groups_Oplus__class_Oplus(X3723,c_Rings_Oinverse__class_Odivide(X3723,X3721,X3722),X3720) = c_Rings_Oinverse__class_Odivide(X3723,c_Groups_Oplus__class_Oplus(X3723,X3721,hAPP(c_Groups_Otimes__class_Otimes(X3723,X3722),X3720)),X3722) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).

fof(i_0_1691,plain,
    ! [X3724,X3725,X3726,X3727] :
      ( ~ class_Fields_Ofield__inverse__zero(X3727)
      | X3726 = c_Groups_Ozero__class_Ozero(X3727)
      | c_Groups_Oplus__class_Oplus(X3727,c_Rings_Oinverse__class_Odivide(X3727,X3725,X3726),X3724) = c_Rings_Oinverse__class_Odivide(X3727,c_Groups_Oplus__class_Oplus(X3727,X3725,hAPP(c_Groups_Otimes__class_Otimes(X3727,X3724),X3726)),X3726) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).

fof(i_0_1692,plain,
    ! [X3728,X3729,X3730,X3731] :
      ( ~ class_Fields_Ofield(X3731)
      | X3730 = c_Groups_Ozero__class_Ozero(X3731)
      | c_Groups_Oplus__class_Oplus(X3731,X3729,c_Rings_Oinverse__class_Odivide(X3731,X3728,X3730)) = c_Rings_Oinverse__class_Odivide(X3731,c_Groups_Oplus__class_Oplus(X3731,hAPP(c_Groups_Otimes__class_Otimes(X3731,X3730),X3729),X3728),X3730) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).

fof(i_0_1693,plain,
    ! [X3732,X3733,X3734,X3735] :
      ( ~ class_Fields_Ofield__inverse__zero(X3735)
      | X3734 = c_Groups_Ozero__class_Ozero(X3735)
      | c_Groups_Oplus__class_Oplus(X3735,X3733,c_Rings_Oinverse__class_Odivide(X3735,X3732,X3734)) = c_Rings_Oinverse__class_Odivide(X3735,c_Groups_Oplus__class_Oplus(X3735,X3732,hAPP(c_Groups_Otimes__class_Otimes(X3735,X3733),X3734)),X3734) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).

fof(i_0_1694,plain,
    ! [X3058,X3059,X3060,X3061] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3061,X3059,c_Rings_Oinverse__class_Odivide(X3061,X3058,X3060))
        | c_Orderings_Oord__class_Oless__eq(X3061,hAPP(c_Groups_Otimes__class_Otimes(X3061,X3059),X3060),X3058)
        | ~ c_Orderings_Oord__class_Oless(X3061,c_Groups_Ozero__class_Ozero(X3061),X3060)
        | ~ class_Fields_Olinordered__field(X3061) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3061,hAPP(c_Groups_Otimes__class_Otimes(X3061,X3059),X3060),X3058)
        | c_Orderings_Oord__class_Oless__eq(X3061,X3059,c_Rings_Oinverse__class_Odivide(X3061,X3058,X3060))
        | ~ c_Orderings_Oord__class_Oless(X3061,c_Groups_Ozero__class_Ozero(X3061),X3060)
        | ~ class_Fields_Olinordered__field(X3061) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).

fof(i_0_1695,plain,
    ! [X2662,X2663,X2664,X2665] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2665,X2663,c_Rings_Oinverse__class_Odivide(X2665,X2662,X2664))
        | c_Orderings_Oord__class_Oless(X2665,hAPP(c_Groups_Otimes__class_Otimes(X2665,X2663),X2664),X2662)
        | ~ c_Orderings_Oord__class_Oless(X2665,c_Groups_Ozero__class_Ozero(X2665),X2664)
        | ~ class_Fields_Olinordered__field(X2665) )
      & ( ~ c_Orderings_Oord__class_Oless(X2665,hAPP(c_Groups_Otimes__class_Otimes(X2665,X2663),X2664),X2662)
        | c_Orderings_Oord__class_Oless(X2665,X2663,c_Rings_Oinverse__class_Odivide(X2665,X2662,X2664))
        | ~ c_Orderings_Oord__class_Oless(X2665,c_Groups_Ozero__class_Ozero(X2665),X2664)
        | ~ class_Fields_Olinordered__field(X2665) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).

fof(i_0_1696,plain,
    ! [X3078,X3079,X3080,X3081] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3081,c_Rings_Oinverse__class_Odivide(X3081,X3079,X3080),X3078)
        | c_Orderings_Oord__class_Oless__eq(X3081,hAPP(c_Groups_Otimes__class_Otimes(X3081,X3078),X3080),X3079)
        | ~ c_Orderings_Oord__class_Oless(X3081,X3080,c_Groups_Ozero__class_Ozero(X3081))
        | ~ class_Fields_Olinordered__field(X3081) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3081,hAPP(c_Groups_Otimes__class_Otimes(X3081,X3078),X3080),X3079)
        | c_Orderings_Oord__class_Oless__eq(X3081,c_Rings_Oinverse__class_Odivide(X3081,X3079,X3080),X3078)
        | ~ c_Orderings_Oord__class_Oless(X3081,X3080,c_Groups_Ozero__class_Ozero(X3081))
        | ~ class_Fields_Olinordered__field(X3081) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).

fof(i_0_1697,plain,
    ! [X2642,X2643,X2644,X2645] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2645,c_Rings_Oinverse__class_Odivide(X2645,X2643,X2644),X2642)
        | c_Orderings_Oord__class_Oless(X2645,hAPP(c_Groups_Otimes__class_Otimes(X2645,X2642),X2644),X2643)
        | ~ c_Orderings_Oord__class_Oless(X2645,X2644,c_Groups_Ozero__class_Ozero(X2645))
        | ~ class_Fields_Olinordered__field(X2645) )
      & ( ~ c_Orderings_Oord__class_Oless(X2645,hAPP(c_Groups_Otimes__class_Otimes(X2645,X2642),X2644),X2643)
        | c_Orderings_Oord__class_Oless(X2645,c_Rings_Oinverse__class_Odivide(X2645,X2643,X2644),X2642)
        | ~ c_Orderings_Oord__class_Oless(X2645,X2644,c_Groups_Ozero__class_Ozero(X2645))
        | ~ class_Fields_Olinordered__field(X2645) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).

fof(i_0_1698,plain,
    ! [X3062,X3063,X3064,X3065] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3065,c_Rings_Oinverse__class_Odivide(X3065,X3063,X3064),X3062)
        | c_Orderings_Oord__class_Oless__eq(X3065,X3063,hAPP(c_Groups_Otimes__class_Otimes(X3065,X3062),X3064))
        | ~ c_Orderings_Oord__class_Oless(X3065,c_Groups_Ozero__class_Ozero(X3065),X3064)
        | ~ class_Fields_Olinordered__field(X3065) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3065,X3063,hAPP(c_Groups_Otimes__class_Otimes(X3065,X3062),X3064))
        | c_Orderings_Oord__class_Oless__eq(X3065,c_Rings_Oinverse__class_Odivide(X3065,X3063,X3064),X3062)
        | ~ c_Orderings_Oord__class_Oless(X3065,c_Groups_Ozero__class_Ozero(X3065),X3064)
        | ~ class_Fields_Olinordered__field(X3065) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).

fof(i_0_1699,plain,
    ! [X2658,X2659,X2660,X2661] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2661,c_Rings_Oinverse__class_Odivide(X2661,X2659,X2660),X2658)
        | c_Orderings_Oord__class_Oless(X2661,X2659,hAPP(c_Groups_Otimes__class_Otimes(X2661,X2658),X2660))
        | ~ c_Orderings_Oord__class_Oless(X2661,c_Groups_Ozero__class_Ozero(X2661),X2660)
        | ~ class_Fields_Olinordered__field(X2661) )
      & ( ~ c_Orderings_Oord__class_Oless(X2661,X2659,hAPP(c_Groups_Otimes__class_Otimes(X2661,X2658),X2660))
        | c_Orderings_Oord__class_Oless(X2661,c_Rings_Oinverse__class_Odivide(X2661,X2659,X2660),X2658)
        | ~ c_Orderings_Oord__class_Oless(X2661,c_Groups_Ozero__class_Ozero(X2661),X2660)
        | ~ class_Fields_Olinordered__field(X2661) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).

fof(i_0_1700,plain,
    ! [X3074,X3075,X3076,X3077] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3077,X3075,c_Rings_Oinverse__class_Odivide(X3077,X3074,X3076))
        | c_Orderings_Oord__class_Oless__eq(X3077,X3074,hAPP(c_Groups_Otimes__class_Otimes(X3077,X3075),X3076))
        | ~ c_Orderings_Oord__class_Oless(X3077,X3076,c_Groups_Ozero__class_Ozero(X3077))
        | ~ class_Fields_Olinordered__field(X3077) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3077,X3074,hAPP(c_Groups_Otimes__class_Otimes(X3077,X3075),X3076))
        | c_Orderings_Oord__class_Oless__eq(X3077,X3075,c_Rings_Oinverse__class_Odivide(X3077,X3074,X3076))
        | ~ c_Orderings_Oord__class_Oless(X3077,X3076,c_Groups_Ozero__class_Ozero(X3077))
        | ~ class_Fields_Olinordered__field(X3077) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).

fof(i_0_1701,plain,
    ! [X2646,X2647,X2648,X2649] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2649,X2647,c_Rings_Oinverse__class_Odivide(X2649,X2646,X2648))
        | c_Orderings_Oord__class_Oless(X2649,X2646,hAPP(c_Groups_Otimes__class_Otimes(X2649,X2647),X2648))
        | ~ c_Orderings_Oord__class_Oless(X2649,X2648,c_Groups_Ozero__class_Ozero(X2649))
        | ~ class_Fields_Olinordered__field(X2649) )
      & ( ~ c_Orderings_Oord__class_Oless(X2649,X2646,hAPP(c_Groups_Otimes__class_Otimes(X2649,X2647),X2648))
        | c_Orderings_Oord__class_Oless(X2649,X2647,c_Rings_Oinverse__class_Odivide(X2649,X2646,X2648))
        | ~ c_Orderings_Oord__class_Oless(X2649,X2648,c_Groups_Ozero__class_Ozero(X2649))
        | ~ class_Fields_Olinordered__field(X2649) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).

fof(i_0_1702,plain,
    ! [X2995,X2996,X2997,X2998] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2998)
      | ~ c_Orderings_Oord__class_Oless__eq(X2998,hAPP(c_Groups_Otimes__class_Otimes(X2998,X2997),X2996),hAPP(c_Groups_Otimes__class_Otimes(X2998,X2995),X2996))
      | ~ c_Orderings_Oord__class_Oless(X2998,c_Groups_Ozero__class_Ozero(X2998),X2996)
      | c_Orderings_Oord__class_Oless__eq(X2998,X2997,X2995) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).

fof(i_0_1703,plain,
    ! [X2999,X3000,X3001,X3002] :
      ( ~ class_Rings_Olinordered__semiring__strict(X3002)
      | ~ c_Orderings_Oord__class_Oless__eq(X3002,hAPP(c_Groups_Otimes__class_Otimes(X3002,X3001),X3000),hAPP(c_Groups_Otimes__class_Otimes(X3002,X3001),X2999))
      | ~ c_Orderings_Oord__class_Oless(X3002,c_Groups_Ozero__class_Ozero(X3002),X3001)
      | c_Orderings_Oord__class_Oless__eq(X3002,X3000,X2999) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).

fof(i_0_1704,plain,
    ! [X2951,X2952,X2953,X2954] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2954,hAPP(c_Groups_Otimes__class_Otimes(X2954,X2953),X2952),hAPP(c_Groups_Otimes__class_Otimes(X2954,X2953),X2951))
        | c_Orderings_Oord__class_Oless__eq(X2954,X2952,X2951)
        | ~ c_Orderings_Oord__class_Oless(X2954,c_Groups_Ozero__class_Ozero(X2954),X2953)
        | ~ class_Rings_Olinordered__ring__strict(X2954) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2954,X2952,X2951)
        | c_Orderings_Oord__class_Oless__eq(X2954,hAPP(c_Groups_Otimes__class_Otimes(X2954,X2953),X2952),hAPP(c_Groups_Otimes__class_Otimes(X2954,X2953),X2951))
        | ~ c_Orderings_Oord__class_Oless(X2954,c_Groups_Ozero__class_Ozero(X2954),X2953)
        | ~ class_Rings_Olinordered__ring__strict(X2954) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).

fof(i_0_1705,plain,
    ! [X2979,X2980,X2981,X2982] :
      ( ~ class_Rings_Olinordered__semiring(X2982)
      | ~ c_Orderings_Oord__class_Oless(X2982,hAPP(c_Groups_Otimes__class_Otimes(X2982,X2981),X2980),hAPP(c_Groups_Otimes__class_Otimes(X2982,X2979),X2980))
      | ~ c_Orderings_Oord__class_Oless__eq(X2982,c_Groups_Ozero__class_Ozero(X2982),X2980)
      | c_Orderings_Oord__class_Oless(X2982,X2981,X2979) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).

fof(i_0_1706,plain,
    ! [X2983,X2984,X2985,X2986] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2986)
      | ~ c_Orderings_Oord__class_Oless(X2986,hAPP(c_Groups_Otimes__class_Otimes(X2986,X2985),X2984),hAPP(c_Groups_Otimes__class_Otimes(X2986,X2983),X2984))
      | ~ c_Orderings_Oord__class_Oless__eq(X2986,c_Groups_Ozero__class_Ozero(X2986),X2984)
      | c_Orderings_Oord__class_Oless(X2986,X2985,X2983) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).

fof(i_0_1707,plain,
    ! [X2987,X2988,X2989,X2990] :
      ( ~ class_Rings_Olinordered__semiring(X2990)
      | ~ c_Orderings_Oord__class_Oless(X2990,hAPP(c_Groups_Otimes__class_Otimes(X2990,X2989),X2988),hAPP(c_Groups_Otimes__class_Otimes(X2990,X2989),X2987))
      | ~ c_Orderings_Oord__class_Oless__eq(X2990,c_Groups_Ozero__class_Ozero(X2990),X2989)
      | c_Orderings_Oord__class_Oless(X2990,X2988,X2987) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).

fof(i_0_1708,plain,
    ! [X2991,X2992,X2993,X2994] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2994)
      | ~ c_Orderings_Oord__class_Oless(X2994,hAPP(c_Groups_Otimes__class_Otimes(X2994,X2993),X2992),hAPP(c_Groups_Otimes__class_Otimes(X2994,X2993),X2991))
      | ~ c_Orderings_Oord__class_Oless__eq(X2994,c_Groups_Ozero__class_Ozero(X2994),X2993)
      | c_Orderings_Oord__class_Oless(X2994,X2992,X2991) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).

fof(i_0_1709,plain,
    ! [X2830,X2831,X2832,X2833] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2833,hAPP(c_Groups_Otimes__class_Otimes(X2833,X2832),X2831),hAPP(c_Groups_Otimes__class_Otimes(X2833,X2832),X2830))
        | c_Orderings_Oord__class_Oless(X2833,X2831,X2830)
        | ~ c_Orderings_Oord__class_Oless(X2833,c_Groups_Ozero__class_Ozero(X2833),X2832)
        | ~ class_Rings_Olinordered__ring__strict(X2833) )
      & ( ~ c_Orderings_Oord__class_Oless(X2833,X2831,X2830)
        | c_Orderings_Oord__class_Oless(X2833,hAPP(c_Groups_Otimes__class_Otimes(X2833,X2832),X2831),hAPP(c_Groups_Otimes__class_Otimes(X2833,X2832),X2830))
        | ~ c_Orderings_Oord__class_Oless(X2833,c_Groups_Ozero__class_Ozero(X2833),X2832)
        | ~ class_Rings_Olinordered__ring__strict(X2833) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

fof(i_0_1710,plain,
    ! [X2955,X2956,X2957,X2958] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2958,hAPP(c_Groups_Otimes__class_Otimes(X2958,X2957),X2956),hAPP(c_Groups_Otimes__class_Otimes(X2958,X2957),X2955))
        | c_Orderings_Oord__class_Oless__eq(X2958,X2955,X2956)
        | ~ c_Orderings_Oord__class_Oless(X2958,X2957,c_Groups_Ozero__class_Ozero(X2958))
        | ~ class_Rings_Olinordered__ring__strict(X2958) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2958,X2955,X2956)
        | c_Orderings_Oord__class_Oless__eq(X2958,hAPP(c_Groups_Otimes__class_Otimes(X2958,X2957),X2956),hAPP(c_Groups_Otimes__class_Otimes(X2958,X2957),X2955))
        | ~ c_Orderings_Oord__class_Oless(X2958,X2957,c_Groups_Ozero__class_Ozero(X2958))
        | ~ class_Rings_Olinordered__ring__strict(X2958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).

fof(i_0_1711,plain,
    ! [X2811,X2812,X2813,X2814] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2814,hAPP(c_Groups_Otimes__class_Otimes(X2814,X2813),X2812),hAPP(c_Groups_Otimes__class_Otimes(X2814,X2813),X2811))
        | c_Orderings_Oord__class_Oless(X2814,X2811,X2812)
        | ~ c_Orderings_Oord__class_Oless(X2814,X2813,c_Groups_Ozero__class_Ozero(X2814))
        | ~ class_Rings_Olinordered__ring__strict(X2814) )
      & ( ~ c_Orderings_Oord__class_Oless(X2814,X2811,X2812)
        | c_Orderings_Oord__class_Oless(X2814,hAPP(c_Groups_Otimes__class_Otimes(X2814,X2813),X2812),hAPP(c_Groups_Otimes__class_Otimes(X2814,X2813),X2811))
        | ~ c_Orderings_Oord__class_Oless(X2814,X2813,c_Groups_Ozero__class_Ozero(X2814))
        | ~ class_Rings_Olinordered__ring__strict(X2814) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_1712,plain,
    ! [X3753,X3754,X3755] :
      ( ~ class_Rings_Olinordered__ring(X3755)
      | c_Orderings_Oord__class_Oless__eq(X3755,c_Groups_Ozero__class_Ozero(X3755),c_Groups_Oplus__class_Oplus(X3755,hAPP(c_Groups_Otimes__class_Otimes(X3755,X3754),X3754),hAPP(c_Groups_Otimes__class_Otimes(X3755,X3753),X3753))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).

fof(i_0_1713,plain,
    ! [X3446,X3447,X3448,X3449] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3449,c_Groups_Oplus__class_Oplus(X3449,X3448,X3447),c_Groups_Oplus__class_Oplus(X3449,X3446,X3447))
        | c_Orderings_Oord__class_Oless__eq(X3449,X3448,X3446)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3449) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3449,X3448,X3446)
        | c_Orderings_Oord__class_Oless__eq(X3449,c_Groups_Oplus__class_Oplus(X3449,X3448,X3447),c_Groups_Oplus__class_Oplus(X3449,X3446,X3447))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3449) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_1714,plain,
    ! [X3425,X3426,X3427,X3428] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3428)
      | ~ c_Orderings_Oord__class_Oless__eq(X3428,c_Groups_Oplus__class_Oplus(X3428,X3427,X3426),c_Groups_Oplus__class_Oplus(X3428,X3425,X3426))
      | c_Orderings_Oord__class_Oless__eq(X3428,X3427,X3425) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_1715,plain,
    ! [X3442,X3443,X3444,X3445] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3445,c_Groups_Oplus__class_Oplus(X3445,X3444,X3443),c_Groups_Oplus__class_Oplus(X3445,X3444,X3442))
        | c_Orderings_Oord__class_Oless__eq(X3445,X3443,X3442)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3445) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3445,X3443,X3442)
        | c_Orderings_Oord__class_Oless__eq(X3445,c_Groups_Oplus__class_Oplus(X3445,X3444,X3443),c_Groups_Oplus__class_Oplus(X3445,X3444,X3442))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3445) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_1716,plain,
    ! [X3421,X3422,X3423,X3424] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3424)
      | ~ c_Orderings_Oord__class_Oless__eq(X3424,c_Groups_Oplus__class_Oplus(X3424,X3423,X3422),c_Groups_Oplus__class_Oplus(X3424,X3423,X3421))
      | c_Orderings_Oord__class_Oless__eq(X3424,X3422,X3421) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_1717,plain,
    ! [X3471,X3472,X3473,X3474] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3474)
      | ~ c_Orderings_Oord__class_Oless(X3474,c_Groups_Oplus__class_Oplus(X3474,X3473,X3472),c_Groups_Oplus__class_Oplus(X3474,X3471,X3472))
      | c_Orderings_Oord__class_Oless(X3474,X3473,X3471) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_1718,plain,
    ! [X3450,X3451,X3452,X3453] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3453,c_Groups_Oplus__class_Oplus(X3453,X3452,X3451),c_Groups_Oplus__class_Oplus(X3453,X3450,X3451))
        | c_Orderings_Oord__class_Oless(X3453,X3452,X3450)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3453) )
      & ( ~ c_Orderings_Oord__class_Oless(X3453,X3452,X3450)
        | c_Orderings_Oord__class_Oless(X3453,c_Groups_Oplus__class_Oplus(X3453,X3452,X3451),c_Groups_Oplus__class_Oplus(X3453,X3450,X3451))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3453) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_1719,plain,
    ! [X3475,X3476,X3477,X3478] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3478)
      | ~ c_Orderings_Oord__class_Oless(X3478,c_Groups_Oplus__class_Oplus(X3478,X3477,X3476),c_Groups_Oplus__class_Oplus(X3478,X3477,X3475))
      | c_Orderings_Oord__class_Oless(X3478,X3476,X3475) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_1720,plain,
    ! [X3454,X3455,X3456,X3457] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3457,c_Groups_Oplus__class_Oplus(X3457,X3456,X3455),c_Groups_Oplus__class_Oplus(X3457,X3456,X3454))
        | c_Orderings_Oord__class_Oless(X3457,X3455,X3454)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3457) )
      & ( ~ c_Orderings_Oord__class_Oless(X3457,X3455,X3454)
        | c_Orderings_Oord__class_Oless(X3457,c_Groups_Oplus__class_Oplus(X3457,X3456,X3455),c_Groups_Oplus__class_Oplus(X3457,X3456,X3454))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3457) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_1721,plain,
    ! [X3066,X3067,X3068,X3069] :
      ( ~ class_Fields_Olinordered__field(X3069)
      | ~ c_Orderings_Oord__class_Oless(X3069,c_Groups_Ozero__class_Ozero(X3069),X3068)
      | ~ c_Orderings_Oord__class_Oless__eq(X3069,X3067,hAPP(c_Groups_Otimes__class_Otimes(X3069,X3066),X3068))
      | c_Orderings_Oord__class_Oless__eq(X3069,c_Rings_Oinverse__class_Odivide(X3069,X3067,X3068),X3066) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).

fof(i_0_1722,plain,
    ! [X2654,X2655,X2656,X2657] :
      ( ~ class_Fields_Olinordered__field(X2657)
      | ~ c_Orderings_Oord__class_Oless(X2657,c_Groups_Ozero__class_Ozero(X2657),X2656)
      | ~ c_Orderings_Oord__class_Oless(X2657,X2655,hAPP(c_Groups_Otimes__class_Otimes(X2657,X2654),X2656))
      | c_Orderings_Oord__class_Oless(X2657,c_Rings_Oinverse__class_Odivide(X2657,X2655,X2656),X2654) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).

fof(i_0_1723,plain,
    ! [X3070,X3071,X3072,X3073] :
      ( ~ class_Fields_Olinordered__field(X3073)
      | ~ c_Orderings_Oord__class_Oless(X3073,c_Groups_Ozero__class_Ozero(X3073),X3072)
      | ~ c_Orderings_Oord__class_Oless__eq(X3073,hAPP(c_Groups_Otimes__class_Otimes(X3073,X3071),X3072),X3070)
      | c_Orderings_Oord__class_Oless__eq(X3073,X3071,c_Rings_Oinverse__class_Odivide(X3073,X3070,X3072)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).

fof(i_0_1724,plain,
    ! [X2650,X2651,X2652,X2653] :
      ( ~ class_Fields_Olinordered__field(X2653)
      | ~ c_Orderings_Oord__class_Oless(X2653,c_Groups_Ozero__class_Ozero(X2653),X2652)
      | ~ c_Orderings_Oord__class_Oless(X2653,hAPP(c_Groups_Otimes__class_Otimes(X2653,X2651),X2652),X2650)
      | c_Orderings_Oord__class_Oless(X2653,X2651,c_Rings_Oinverse__class_Odivide(X2653,X2650,X2652)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).

fof(i_0_1725,plain,
    ! [X3508,X3509,X3510,X3511] :
      ( ~ class_Rings_Ocomm__semiring__1(X3511)
      | c_Groups_Oplus__class_Oplus(X3511,hAPP(c_Groups_Otimes__class_Otimes(X3511,X3510),X3509),hAPP(c_Groups_Otimes__class_Otimes(X3511,X3508),X3509)) = hAPP(c_Groups_Otimes__class_Otimes(X3511,c_Groups_Oplus__class_Oplus(X3511,X3510,X3508)),X3509) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_1726,plain,
    ! [X3517,X3518,X3519,X3520] :
      ( ~ class_Rings_Ocomm__semiring(X3520)
      | hAPP(c_Groups_Otimes__class_Otimes(X3520,c_Groups_Oplus__class_Oplus(X3520,X3519,X3518)),X3517) = c_Groups_Oplus__class_Oplus(X3520,hAPP(c_Groups_Otimes__class_Otimes(X3520,X3519),X3517),hAPP(c_Groups_Otimes__class_Otimes(X3520,X3518),X3517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_1727,plain,
    ! [X3491,X3492,X3493,X3494] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3494)
      | hAPP(c_Groups_Otimes__class_Otimes(X3494,c_Groups_Oplus__class_Oplus(X3494,X3493,X3492)),X3491) = c_Groups_Oplus__class_Oplus(X3494,hAPP(c_Groups_Otimes__class_Otimes(X3494,X3493),X3491),hAPP(c_Groups_Otimes__class_Otimes(X3494,X3492),X3491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).

fof(i_0_1728,plain,
    ! [X3487,X3488,X3489,X3490] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3490)
      | hAPP(c_Groups_Otimes__class_Otimes(X3490,c_Groups_Oplus__class_Oplus(X3490,X3489,X3488)),X3487) = c_Groups_Oplus__class_Oplus(X3490,hAPP(c_Groups_Otimes__class_Otimes(X3490,X3489),X3487),hAPP(c_Groups_Otimes__class_Otimes(X3490,X3488),X3487)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).

fof(i_0_1729,plain,
    ! [X3504,X3505,X3506,X3507] :
      ( ~ class_Rings_Ocomm__semiring__1(X3507)
      | hAPP(c_Groups_Otimes__class_Otimes(X3507,c_Groups_Oplus__class_Oplus(X3507,X3506,X3505)),X3504) = c_Groups_Oplus__class_Oplus(X3507,hAPP(c_Groups_Otimes__class_Otimes(X3507,X3506),X3504),hAPP(c_Groups_Otimes__class_Otimes(X3507,X3505),X3504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_1730,plain,
    ! [X4483,X4484,X4485] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4485,X4484),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4485,X4483))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4484,X4483) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4484,X4483)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4485,X4484),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4485,X4483)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

cnf(i_0_1731,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_1370]) ).

cnf(i_0_1732,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_1371]) ).

fof(i_0_1733,plain,
    ! [X4456,X4457,X4458] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4458,X4457),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4458,X4456))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4457,X4456) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4457,X4456)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4458,X4457),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4458,X4456)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

cnf(i_0_1734,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_1372]) ).

cnf(i_0_1735,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_1373]) ).

cnf(i_0_1736,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_1362]) ).

fof(i_0_1737,plain,
    ! [X4970,X4971,X4972,X4973] :
      ( ~ class_Rings_Olinordered__semidom(X4973)
      | c_Power_Opower__class_Opower(X4973,X4972,X4971) != c_Power_Opower__class_Opower(X4973,X4970,X4971)
      | ~ c_Orderings_Oord__class_Oless__eq(X4973,c_Groups_Ozero__class_Ozero(X4973),X4972)
      | ~ c_Orderings_Oord__class_Oless__eq(X4973,c_Groups_Ozero__class_Ozero(X4973),X4970)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4971)
      | X4972 = X4970 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).

fof(i_0_1738,plain,
    ! [X2834,X2835,X2836,X2837] :
      ( ( c_Orderings_Oord__class_Oless(X2837,X2836,c_Groups_Ozero__class_Ozero(X2837))
        | c_Orderings_Oord__class_Oless(X2837,c_Groups_Ozero__class_Ozero(X2837),X2836)
        | ~ c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) )
      & ( c_Orderings_Oord__class_Oless(X2837,X2834,X2835)
        | c_Orderings_Oord__class_Oless(X2837,c_Groups_Ozero__class_Ozero(X2837),X2836)
        | ~ c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) )
      & ( c_Orderings_Oord__class_Oless(X2837,X2836,c_Groups_Ozero__class_Ozero(X2837))
        | c_Orderings_Oord__class_Oless(X2837,X2835,X2834)
        | ~ c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) )
      & ( c_Orderings_Oord__class_Oless(X2837,X2834,X2835)
        | c_Orderings_Oord__class_Oless(X2837,X2835,X2834)
        | ~ c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) )
      & ( ~ c_Orderings_Oord__class_Oless(X2837,c_Groups_Ozero__class_Ozero(X2837),X2836)
        | ~ c_Orderings_Oord__class_Oless(X2837,X2835,X2834)
        | c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) )
      & ( ~ c_Orderings_Oord__class_Oless(X2837,X2836,c_Groups_Ozero__class_Ozero(X2837))
        | ~ c_Orderings_Oord__class_Oless(X2837,X2834,X2835)
        | c_Orderings_Oord__class_Oless(X2837,hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2835),hAPP(c_Groups_Otimes__class_Otimes(X2837,X2836),X2834))
        | ~ class_Rings_Olinordered__ring__strict(X2837) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_1739,plain,
    ! [X2838,X2839,X2840,X2841] :
      ( ( c_Orderings_Oord__class_Oless(X2841,X2839,c_Groups_Ozero__class_Ozero(X2841))
        | c_Orderings_Oord__class_Oless(X2841,c_Groups_Ozero__class_Ozero(X2841),X2839)
        | ~ c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) )
      & ( c_Orderings_Oord__class_Oless(X2841,X2838,X2840)
        | c_Orderings_Oord__class_Oless(X2841,c_Groups_Ozero__class_Ozero(X2841),X2839)
        | ~ c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) )
      & ( c_Orderings_Oord__class_Oless(X2841,X2839,c_Groups_Ozero__class_Ozero(X2841))
        | c_Orderings_Oord__class_Oless(X2841,X2840,X2838)
        | ~ c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) )
      & ( c_Orderings_Oord__class_Oless(X2841,X2838,X2840)
        | c_Orderings_Oord__class_Oless(X2841,X2840,X2838)
        | ~ c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) )
      & ( ~ c_Orderings_Oord__class_Oless(X2841,c_Groups_Ozero__class_Ozero(X2841),X2839)
        | ~ c_Orderings_Oord__class_Oless(X2841,X2840,X2838)
        | c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) )
      & ( ~ c_Orderings_Oord__class_Oless(X2841,X2839,c_Groups_Ozero__class_Ozero(X2841))
        | ~ c_Orderings_Oord__class_Oless(X2841,X2838,X2840)
        | c_Orderings_Oord__class_Oless(X2841,hAPP(c_Groups_Otimes__class_Otimes(X2841,X2840),X2839),hAPP(c_Groups_Otimes__class_Otimes(X2841,X2838),X2839))
        | ~ class_Rings_Olinordered__ring__strict(X2841) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_1740,plain,
    ! [X4899,X4900,X4901,X4902] :
      ( ~ class_Rings_Olinordered__semidom(X4902)
      | ~ c_Orderings_Oord__class_Oless__eq(X4902,X4901,X4900)
      | ~ c_Orderings_Oord__class_Oless__eq(X4902,c_Groups_Ozero__class_Ozero(X4902),X4901)
      | c_Orderings_Oord__class_Oless__eq(X4902,c_Power_Opower__class_Opower(X4902,X4901,X4899),c_Power_Opower__class_Opower(X4902,X4900,X4899)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).

fof(i_0_1741,plain,
    ! [X2939,X2940,X2941,X2942] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X2942)
      | ~ c_Orderings_Oord__class_Oless__eq(X2942,X2941,X2940)
      | ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2939)
      | c_Orderings_Oord__class_Oless__eq(X2942,c_Rings_Oinverse__class_Odivide(X2942,X2941,X2939),c_Rings_Oinverse__class_Odivide(X2942,X2940,X2939)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_1742,plain,
    ! [X2683,X2684,X2685,X2686] :
      ( ~ class_Fields_Olinordered__field(X2686)
      | ~ c_Orderings_Oord__class_Oless(X2686,X2685,X2684)
      | ~ c_Orderings_Oord__class_Oless(X2686,c_Groups_Ozero__class_Ozero(X2686),X2683)
      | c_Orderings_Oord__class_Oless(X2686,c_Rings_Oinverse__class_Odivide(X2686,X2685,X2683),c_Rings_Oinverse__class_Odivide(X2686,X2684,X2683)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_1743,plain,
    ! [X2935,X2936,X2937,X2938] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X2938)
      | ~ c_Orderings_Oord__class_Oless__eq(X2938,X2937,X2936)
      | ~ c_Orderings_Oord__class_Oless__eq(X2938,X2935,c_Groups_Ozero__class_Ozero(X2938))
      | c_Orderings_Oord__class_Oless__eq(X2938,c_Rings_Oinverse__class_Odivide(X2938,X2936,X2935),c_Rings_Oinverse__class_Odivide(X2938,X2937,X2935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

fof(i_0_1744,plain,
    ! [X2679,X2680,X2681,X2682] :
      ( ~ class_Fields_Olinordered__field(X2682)
      | ~ c_Orderings_Oord__class_Oless(X2682,X2681,X2680)
      | ~ c_Orderings_Oord__class_Oless(X2682,X2679,c_Groups_Ozero__class_Ozero(X2682))
      | c_Orderings_Oord__class_Oless(X2682,c_Rings_Oinverse__class_Odivide(X2682,X2680,X2679),c_Rings_Oinverse__class_Odivide(X2682,X2681,X2679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_1745,plain,
    ! [X4959,X4960,X4961,X4962] :
      ( ~ class_Rings_Olinordered__semidom(X4962)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4961,X4960)
      | ~ c_Orderings_Oord__class_Oless__eq(X4962,c_Groups_Oone__class_Oone(X4962),X4959)
      | c_Orderings_Oord__class_Oless__eq(X4962,c_Power_Opower__class_Opower(X4962,X4959,X4961),c_Power_Opower__class_Opower(X4962,X4959,X4960)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).

fof(i_0_1746,plain,
    ! [X4955,X4956,X4957,X4958] :
      ( ~ class_Rings_Olinordered__semidom(X4958)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4957,X4956)
      | ~ c_Orderings_Oord__class_Oless(X4958,c_Groups_Oone__class_Oone(X4958),X4955)
      | c_Orderings_Oord__class_Oless(X4958,c_Power_Opower__class_Opower(X4958,X4955,X4957),c_Power_Opower__class_Opower(X4958,X4955,X4956)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).

fof(i_0_1747,plain,
    ! [X4936,X4937,X4938] :
      ( ~ class_Rings_Olinordered__semidom(X4938)
      | ~ c_Orderings_Oord__class_Oless(X4938,c_Groups_Oone__class_Oone(X4938),X4937)
      | c_Orderings_Oord__class_Oless(X4938,c_Groups_Oone__class_Oone(X4938),hAPP(c_Groups_Otimes__class_Otimes(X4938,X4937),c_Power_Opower__class_Opower(X4938,X4937,X4936))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).

cnf(i_0_1748,plain,
    ( hAPP(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_1374]) ).

fof(i_0_1749,plain,
    ! [X4550,X4551,X4552] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4552),X4551),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4550),X4551))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4551)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4552,X4550) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4551)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4552),X4551),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4550),X4551)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4552,X4550)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4552),X4551),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4550),X4551)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).

fof(i_0_1750,plain,
    ! [X4553,X4554,X4555] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4555),X4554),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4555),X4553))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4554,X4553)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4555) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4554,X4553)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4555),X4554),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4555),X4553))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4555) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).

fof(i_0_1751,plain,
    ! [X4367,X4368,X4369] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4368),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4367))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4369)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4368,X4367) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4369)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4368),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4367)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4368,X4367)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4368),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4369),X4367)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).

fof(i_0_1752,plain,
    ! [X3038,X3039,X3040] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3039),X3040),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3038),X3040))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3039,X3038)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3040) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3039,X3038)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3039),X3040),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3038),X3040))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3040) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).

fof(i_0_1753,plain,
    ! [X3041,X3042,X3043] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3043),X3042),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3043),X3041))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3042,X3041)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3043) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3042,X3041)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3043),X3042),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3043),X3041))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3043) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).

fof(i_0_1754,plain,
    ! [X4559,X4560,X4561] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4561),X4560),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4561),X4559))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4560,X4559)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4561) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4560,X4559)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4561),X4560),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4561),X4559))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4561) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).

fof(i_0_1755,plain,
    ! [X2602,X2603,X2604] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2603),X2604),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2602),X2604))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2603,X2602)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2604) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2603,X2602)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2603),X2604),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2602),X2604))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2604) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).

cnf(i_0_1756,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_1365]) ).

cnf(i_0_1757,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_1366]) ).

cnf(i_0_1758,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_1363]) ).

cnf(i_0_1759,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_1364]) ).

fof(i_0_1760,plain,
    ! [X3429,X3430,X3431,X3432,X3433] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X3433)
      | ~ c_Orderings_Oord__class_Oless__eq(X3433,X3432,X3431)
      | ~ c_Orderings_Oord__class_Oless__eq(X3433,X3430,X3429)
      | c_Orderings_Oord__class_Oless__eq(X3433,c_Groups_Oplus__class_Oplus(X3433,X3432,X3430),c_Groups_Oplus__class_Oplus(X3433,X3431,X3429)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_1761,plain,
    ! [X3632,X3633,X3634,X3635,X3636] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3636)
      | ~ c_Orderings_Oord__class_Oless(X3636,X3635,X3634)
      | ~ c_Orderings_Oord__class_Oless__eq(X3636,X3633,X3632)
      | c_Orderings_Oord__class_Oless(X3636,c_Groups_Oplus__class_Oplus(X3636,X3635,X3633),c_Groups_Oplus__class_Oplus(X3636,X3634,X3632)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_1762,plain,
    ! [X3637,X3638,X3639,X3640,X3641] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3641)
      | ~ c_Orderings_Oord__class_Oless__eq(X3641,X3640,X3639)
      | ~ c_Orderings_Oord__class_Oless(X3641,X3638,X3637)
      | c_Orderings_Oord__class_Oless(X3641,c_Groups_Oplus__class_Oplus(X3641,X3640,X3638),c_Groups_Oplus__class_Oplus(X3641,X3639,X3637)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_1763,plain,
    ! [X3466,X3467,X3468,X3469,X3470] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3470)
      | ~ c_Orderings_Oord__class_Oless(X3470,X3469,X3468)
      | ~ c_Orderings_Oord__class_Oless(X3470,X3467,X3466)
      | c_Orderings_Oord__class_Oless(X3470,c_Groups_Oplus__class_Oplus(X3470,X3469,X3467),c_Groups_Oplus__class_Oplus(X3470,X3468,X3466)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

cnf(i_0_1764,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1375]) ).

fof(i_0_1765,plain,
    ! [X3810] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3810)
      | c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X3810,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3810)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__ln__divide])]) ).

fof(i_0_1766,plain,
    ! [X4916,X4917,X4918,X4919] :
      ( ~ class_Fields_Ofield(X4919)
      | X4918 = c_Groups_Ozero__class_Ozero(X4919)
      | c_Power_Opower__class_Opower(X4919,c_Rings_Oinverse__class_Odivide(X4919,X4917,X4918),X4916) = c_Rings_Oinverse__class_Odivide(X4919,c_Power_Opower__class_Opower(X4919,X4917,X4916),c_Power_Opower__class_Opower(X4919,X4918,X4916)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).

fof(i_0_1767,plain,
    ! [X4508,X4509,X4510] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4510,X4509)),X4508) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4510),X4508),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4509),X4508)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

cnf(i_0_1768,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X1)),X2) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1376]) ).

fof(i_0_1769,plain,
    ! [X4075,X4076,X4077] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4077,X4076)),X4075) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4077),X4075),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4076),X4075)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(i_0_1770,plain,
    ! [X3537,X3538,X3539] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3539,X3538)),X3537) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3539),X3537),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3538),X3537)),
    inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).

fof(i_0_1771,plain,
    ! [X4883,X4884,X4885,X4886] :
      ( ~ class_Fields_Ofield__inverse__zero(X4886)
      | c_Power_Opower__class_Opower(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883) = c_Rings_Oinverse__class_Odivide(X4886,c_Power_Opower__class_Opower(X4886,X4885,X4883),c_Power_Opower__class_Opower(X4886,X4884,X4883)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).

fof(i_0_1772,plain,
    ! [X3526,X3527,X3528,X3529] :
      ( ~ class_RealVector_Oreal__normed__field(X3529)
      | c_Rings_Oinverse__class_Odivide(X3529,c_Groups_Oplus__class_Oplus(X3529,X3528,X3527),X3526) = c_Groups_Oplus__class_Oplus(X3529,c_Rings_Oinverse__class_Odivide(X3529,X3528,X3526),c_Rings_Oinverse__class_Odivide(X3529,X3527,X3526)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Oadd])]) ).

fof(i_0_1773,plain,
    ! [X3530,X3531,X3532,X3533] :
      ( ~ class_Rings_Odivision__ring(X3533)
      | c_Rings_Oinverse__class_Odivide(X3533,c_Groups_Oplus__class_Oplus(X3533,X3532,X3531),X3530) = c_Groups_Oplus__class_Oplus(X3533,c_Rings_Oinverse__class_Odivide(X3533,X3532,X3530),c_Rings_Oinverse__class_Odivide(X3533,X3531,X3530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_1774,plain,
    ! [X3642,X3643,X3644,X3645,X3646,X3647] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3647)
      | X3646 = c_Groups_Ozero__class_Ozero(X3647)
      | X3645 != X3644
      | X3643 = X3642
      | c_Groups_Oplus__class_Oplus(X3647,X3645,hAPP(c_Groups_Otimes__class_Otimes(X3647,X3646),X3643)) != c_Groups_Oplus__class_Oplus(X3647,X3644,hAPP(c_Groups_Otimes__class_Otimes(X3647,X3646),X3642)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_1775,plain,
    ! [X4236,X4237,X4238] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4238)
      | X4238 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4237,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4238),X4236))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4237)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4236,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_1776,plain,
    ! [X4495,X4496,X4497,X4498] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4498,X4497)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4496,X4495)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4498,X4496),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4497,X4495)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_1777,plain,
    ! [X4443,X4444,X4445,X4446] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4446,X4445)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4444,X4443)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4446,X4444),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4445,X4443)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_1778,plain,
    ! [X4089,X4090,X4091,X4092] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4092,X4091)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4090,X4089)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4092,X4090),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4091,X4089)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_1779,plain,
    ! [X3006,X3007,X3008] :
      ( ~ class_Rings_Olinordered__idom(X3008)
      | ~ c_Orderings_Oord__class_Oless__eq(X3008,c_Groups_Ozero__class_Ozero(X3008),X3007)
      | ~ c_Orderings_Oord__class_Oless__eq(X3008,c_Groups_Ozero__class_Ozero(X3008),X3006)
      | ~ c_Orderings_Oord__class_Oless__eq(X3008,X3006,c_Groups_Oone__class_Oone(X3008))
      | c_Orderings_Oord__class_Oless__eq(X3008,hAPP(c_Groups_Otimes__class_Otimes(X3008,X3007),X3006),X3007) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).

fof(i_0_1780,plain,
    ! [X3003,X3004,X3005] :
      ( ~ class_Rings_Olinordered__idom(X3005)
      | ~ c_Orderings_Oord__class_Oless__eq(X3005,c_Groups_Ozero__class_Ozero(X3005),X3004)
      | ~ c_Orderings_Oord__class_Oless__eq(X3005,c_Groups_Ozero__class_Ozero(X3005),X3003)
      | ~ c_Orderings_Oord__class_Oless__eq(X3005,X3003,c_Groups_Oone__class_Oone(X3005))
      | c_Orderings_Oord__class_Oless__eq(X3005,hAPP(c_Groups_Otimes__class_Otimes(X3005,X3003),X3004),X3004) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).

fof(i_0_1781,plain,
    ! [X4239,X4240,X4241] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4241)
      | X4241 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4240,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4241),X4239))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4240,X4241)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4239) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).

fof(i_0_1782,plain,
    ! [X3650,X3651,X3652] :
      ( ~ class_Rings_Ocomm__semiring__1(X3652)
      | c_Groups_Oplus__class_Oplus(X3652,hAPP(c_Groups_Otimes__class_Otimes(X3652,X3651),X3650),X3650) = hAPP(c_Groups_Otimes__class_Otimes(X3652,c_Groups_Oplus__class_Oplus(X3652,X3651,c_Groups_Oone__class_Oone(X3652))),X3650) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_1783,plain,
    ! [X3653,X3654,X3655] :
      ( ~ class_Rings_Ocomm__semiring__1(X3655)
      | c_Groups_Oplus__class_Oplus(X3655,X3654,hAPP(c_Groups_Otimes__class_Otimes(X3655,X3653),X3654)) = hAPP(c_Groups_Otimes__class_Otimes(X3655,c_Groups_Oplus__class_Oplus(X3655,X3653,c_Groups_Oone__class_Oone(X3655))),X3654) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

cnf(i_0_1784,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_1336]) ).

fof(i_0_1785,plain,
    ! [X5017,X5018,X5019] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X5019,c_Groups_Ozero__class_Ozero(X5019),X5017)
        | ~ c_Orderings_Oord__class_Oless__eq(X5019,c_Groups_Ozero__class_Ozero(X5019),X5018)
        | c_Groups_Oabs__class_Oabs(X5019,hAPP(c_Groups_Otimes__class_Otimes(X5019,X5018),X5017)) = hAPP(c_Groups_Otimes__class_Otimes(X5019,c_Groups_Oabs__class_Oabs(X5019,X5018)),c_Groups_Oabs__class_Oabs(X5019,X5017))
        | ~ class_Rings_Oordered__ring__abs(X5019) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X5019,X5017,c_Groups_Ozero__class_Ozero(X5019))
        | ~ c_Orderings_Oord__class_Oless__eq(X5019,c_Groups_Ozero__class_Ozero(X5019),X5018)
        | c_Groups_Oabs__class_Oabs(X5019,hAPP(c_Groups_Otimes__class_Otimes(X5019,X5018),X5017)) = hAPP(c_Groups_Otimes__class_Otimes(X5019,c_Groups_Oabs__class_Oabs(X5019,X5018)),c_Groups_Oabs__class_Oabs(X5019,X5017))
        | ~ class_Rings_Oordered__ring__abs(X5019) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X5019,c_Groups_Ozero__class_Ozero(X5019),X5017)
        | ~ c_Orderings_Oord__class_Oless__eq(X5019,X5018,c_Groups_Ozero__class_Ozero(X5019))
        | c_Groups_Oabs__class_Oabs(X5019,hAPP(c_Groups_Otimes__class_Otimes(X5019,X5018),X5017)) = hAPP(c_Groups_Otimes__class_Otimes(X5019,c_Groups_Oabs__class_Oabs(X5019,X5018)),c_Groups_Oabs__class_Oabs(X5019,X5017))
        | ~ class_Rings_Oordered__ring__abs(X5019) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X5019,X5017,c_Groups_Ozero__class_Ozero(X5019))
        | ~ c_Orderings_Oord__class_Oless__eq(X5019,X5018,c_Groups_Ozero__class_Ozero(X5019))
        | c_Groups_Oabs__class_Oabs(X5019,hAPP(c_Groups_Otimes__class_Otimes(X5019,X5018),X5017)) = hAPP(c_Groups_Otimes__class_Otimes(X5019,c_Groups_Oabs__class_Oabs(X5019,X5018)),c_Groups_Oabs__class_Oabs(X5019,X5017))
        | ~ class_Rings_Oordered__ring__abs(X5019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).

fof(i_0_1786,plain,
    ! [X4878,X4879,X4880] :
      ( ~ class_Groups_Omonoid__mult(X4880)
      | hAPP(c_Groups_Otimes__class_Otimes(X4880,c_Power_Opower__class_Opower(X4880,X4879,X4878)),X4879) = hAPP(c_Groups_Otimes__class_Otimes(X4880,X4879),c_Power_Opower__class_Opower(X4880,X4879,X4878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).

fof(i_0_1787,plain,
    ! [X2906,X2907,X2908,X2909] :
      ( ~ class_Rings_Oordered__semiring(X2909)
      | ~ c_Orderings_Oord__class_Oless__eq(X2909,X2908,X2907)
      | ~ c_Orderings_Oord__class_Oless__eq(X2909,c_Groups_Ozero__class_Ozero(X2909),X2906)
      | c_Orderings_Oord__class_Oless__eq(X2909,hAPP(c_Groups_Otimes__class_Otimes(X2909,X2908),X2906),hAPP(c_Groups_Otimes__class_Otimes(X2909,X2907),X2906)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_1788,plain,
    ! [X2898,X2899,X2900,X2901] :
      ( ~ class_Rings_Oordered__comm__semiring(X2901)
      | ~ c_Orderings_Oord__class_Oless__eq(X2901,X2900,X2899)
      | ~ c_Orderings_Oord__class_Oless__eq(X2901,c_Groups_Ozero__class_Ozero(X2901),X2898)
      | c_Orderings_Oord__class_Oless__eq(X2901,hAPP(c_Groups_Otimes__class_Otimes(X2901,X2898),X2900),hAPP(c_Groups_Otimes__class_Otimes(X2901,X2898),X2899)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_1789,plain,
    ! [X2902,X2903,X2904,X2905] :
      ( ~ class_Rings_Oordered__semiring(X2905)
      | ~ c_Orderings_Oord__class_Oless__eq(X2905,X2904,X2903)
      | ~ c_Orderings_Oord__class_Oless__eq(X2905,c_Groups_Ozero__class_Ozero(X2905),X2902)
      | c_Orderings_Oord__class_Oless__eq(X2905,hAPP(c_Groups_Otimes__class_Otimes(X2905,X2902),X2904),hAPP(c_Groups_Otimes__class_Otimes(X2905,X2902),X2903)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_1790,plain,
    ! [X2801,X2802,X2803,X2804] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2804)
      | ~ c_Orderings_Oord__class_Oless(X2804,X2803,X2802)
      | ~ c_Orderings_Oord__class_Oless(X2804,c_Groups_Ozero__class_Ozero(X2804),X2801)
      | c_Orderings_Oord__class_Oless(X2804,hAPP(c_Groups_Otimes__class_Otimes(X2804,X2803),X2801),hAPP(c_Groups_Otimes__class_Otimes(X2804,X2802),X2801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_1791,plain,
    ! [X2797,X2798,X2799,X2800] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2800)
      | ~ c_Orderings_Oord__class_Oless(X2800,X2799,X2798)
      | ~ c_Orderings_Oord__class_Oless(X2800,c_Groups_Ozero__class_Ozero(X2800),X2797)
      | c_Orderings_Oord__class_Oless(X2800,hAPP(c_Groups_Otimes__class_Otimes(X2800,X2797),X2799),hAPP(c_Groups_Otimes__class_Otimes(X2800,X2797),X2798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_1792,plain,
    ! [X2793,X2794,X2795,X2796] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X2796)
      | ~ c_Orderings_Oord__class_Oless(X2796,X2795,X2794)
      | ~ c_Orderings_Oord__class_Oless(X2796,c_Groups_Ozero__class_Ozero(X2796),X2793)
      | c_Orderings_Oord__class_Oless(X2796,hAPP(c_Groups_Otimes__class_Otimes(X2796,X2793),X2795),hAPP(c_Groups_Otimes__class_Otimes(X2796,X2793),X2794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_1793,plain,
    ! [X2894,X2895,X2896,X2897] :
      ( ~ class_Rings_Oordered__ring(X2897)
      | ~ c_Orderings_Oord__class_Oless__eq(X2897,X2896,X2895)
      | ~ c_Orderings_Oord__class_Oless__eq(X2897,X2894,c_Groups_Ozero__class_Ozero(X2897))
      | c_Orderings_Oord__class_Oless__eq(X2897,hAPP(c_Groups_Otimes__class_Otimes(X2897,X2895),X2894),hAPP(c_Groups_Otimes__class_Otimes(X2897,X2896),X2894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_1794,plain,
    ! [X2890,X2891,X2892,X2893] :
      ( ~ class_Rings_Oordered__ring(X2893)
      | ~ c_Orderings_Oord__class_Oless__eq(X2893,X2892,X2891)
      | ~ c_Orderings_Oord__class_Oless__eq(X2893,X2890,c_Groups_Ozero__class_Ozero(X2893))
      | c_Orderings_Oord__class_Oless__eq(X2893,hAPP(c_Groups_Otimes__class_Otimes(X2893,X2890),X2891),hAPP(c_Groups_Otimes__class_Otimes(X2893,X2890),X2892)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

fof(i_0_1795,plain,
    ! [X2789,X2790,X2791,X2792] :
      ( ~ class_Rings_Olinordered__ring__strict(X2792)
      | ~ c_Orderings_Oord__class_Oless(X2792,X2791,X2790)
      | ~ c_Orderings_Oord__class_Oless(X2792,X2789,c_Groups_Ozero__class_Ozero(X2792))
      | c_Orderings_Oord__class_Oless(X2792,hAPP(c_Groups_Otimes__class_Otimes(X2792,X2790),X2789),hAPP(c_Groups_Otimes__class_Otimes(X2792,X2791),X2789)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_1796,plain,
    ! [X2785,X2786,X2787,X2788] :
      ( ~ class_Rings_Olinordered__ring__strict(X2788)
      | ~ c_Orderings_Oord__class_Oless(X2788,X2787,X2786)
      | ~ c_Orderings_Oord__class_Oless(X2788,X2785,c_Groups_Ozero__class_Ozero(X2788))
      | c_Orderings_Oord__class_Oless(X2788,hAPP(c_Groups_Otimes__class_Otimes(X2788,X2785),X2786),hAPP(c_Groups_Otimes__class_Otimes(X2788,X2785),X2787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

fof(i_0_1797,plain,
    ! [X2620,X2621,X2622,X2623] :
      ( ~ class_Rings_Ocomm__semiring__1(X2623)
      | hAPP(c_Groups_Otimes__class_Otimes(X2623,hAPP(c_Groups_Otimes__class_Otimes(X2623,X2622),X2621)),X2620) = hAPP(c_Groups_Otimes__class_Otimes(X2623,hAPP(c_Groups_Otimes__class_Otimes(X2623,X2622),X2620)),X2621) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).

fof(i_0_1798,plain,
    ! [X5011,X5012,X5013] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5013,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,X5012),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5013),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5011)))
      | X5012 = 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_1799,plain,
    ! [X4869,X4870] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4870,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4869)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4869) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4870) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4869) != 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,X4870,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4869))) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4870)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4870,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4869))) ) ),
    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_1800,plain,
    ! [X2943,X2944,X2945] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2945,X2944,c_Groups_Ozero__class_Ozero(X2945))
        | c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2944)
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) )
      & ( c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2943)
        | c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2944)
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) )
      & ( c_Orderings_Oord__class_Oless__eq(X2945,X2944,c_Groups_Ozero__class_Ozero(X2945))
        | c_Orderings_Oord__class_Oless__eq(X2945,X2943,c_Groups_Ozero__class_Ozero(X2945))
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) )
      & ( c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2943)
        | c_Orderings_Oord__class_Oless__eq(X2945,X2943,c_Groups_Ozero__class_Ozero(X2945))
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2944)
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,X2943,c_Groups_Ozero__class_Ozero(X2945))
        | c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2945,X2944,c_Groups_Ozero__class_Ozero(X2945))
        | ~ c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),X2943)
        | c_Orderings_Oord__class_Oless__eq(X2945,c_Rings_Oinverse__class_Odivide(X2945,X2944,X2943),c_Groups_Ozero__class_Ozero(X2945))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2945) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_1801,plain,
    ! [X2699,X2700,X2701] :
      ( ( c_Orderings_Oord__class_Oless(X2701,X2700,c_Groups_Ozero__class_Ozero(X2701))
        | c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2700)
        | ~ c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) )
      & ( c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2699)
        | c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2700)
        | ~ c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) )
      & ( c_Orderings_Oord__class_Oless(X2701,X2700,c_Groups_Ozero__class_Ozero(X2701))
        | c_Orderings_Oord__class_Oless(X2701,X2699,c_Groups_Ozero__class_Ozero(X2701))
        | ~ c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) )
      & ( c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2699)
        | c_Orderings_Oord__class_Oless(X2701,X2699,c_Groups_Ozero__class_Ozero(X2701))
        | ~ c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) )
      & ( ~ c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2700)
        | ~ c_Orderings_Oord__class_Oless(X2701,X2699,c_Groups_Ozero__class_Ozero(X2701))
        | c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) )
      & ( ~ c_Orderings_Oord__class_Oless(X2701,X2700,c_Groups_Ozero__class_Ozero(X2701))
        | ~ c_Orderings_Oord__class_Oless(X2701,c_Groups_Ozero__class_Ozero(X2701),X2699)
        | c_Orderings_Oord__class_Oless(X2701,c_Rings_Oinverse__class_Odivide(X2701,X2700,X2699),c_Groups_Ozero__class_Ozero(X2701))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2701) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_1802,plain,
    ! [X2946,X2947,X2948] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2948,X2947,c_Groups_Ozero__class_Ozero(X2948))
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2947)
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) )
      & ( c_Orderings_Oord__class_Oless__eq(X2948,X2946,c_Groups_Ozero__class_Ozero(X2948))
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2947)
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) )
      & ( c_Orderings_Oord__class_Oless__eq(X2948,X2947,c_Groups_Ozero__class_Ozero(X2948))
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2946)
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) )
      & ( c_Orderings_Oord__class_Oless__eq(X2948,X2946,c_Groups_Ozero__class_Ozero(X2948))
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2946)
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2947)
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),X2946)
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2948,X2947,c_Groups_Ozero__class_Ozero(X2948))
        | ~ c_Orderings_Oord__class_Oless__eq(X2948,X2946,c_Groups_Ozero__class_Ozero(X2948))
        | c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Ozero__class_Ozero(X2948),c_Rings_Oinverse__class_Odivide(X2948,X2947,X2946))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2948) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_1803,plain,
    ! [X2702,X2703,X2704] :
      ( ( c_Orderings_Oord__class_Oless(X2704,X2703,c_Groups_Ozero__class_Ozero(X2704))
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2703)
        | ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) )
      & ( c_Orderings_Oord__class_Oless(X2704,X2702,c_Groups_Ozero__class_Ozero(X2704))
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2703)
        | ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) )
      & ( c_Orderings_Oord__class_Oless(X2704,X2703,c_Groups_Ozero__class_Ozero(X2704))
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2702)
        | ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) )
      & ( c_Orderings_Oord__class_Oless(X2704,X2702,c_Groups_Ozero__class_Ozero(X2704))
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2702)
        | ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) )
      & ( ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2703)
        | ~ c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),X2702)
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) )
      & ( ~ c_Orderings_Oord__class_Oless(X2704,X2703,c_Groups_Ozero__class_Ozero(X2704))
        | ~ c_Orderings_Oord__class_Oless(X2704,X2702,c_Groups_Ozero__class_Ozero(X2704))
        | c_Orderings_Oord__class_Oless(X2704,c_Groups_Ozero__class_Ozero(X2704),c_Rings_Oinverse__class_Odivide(X2704,X2703,X2702))
        | ~ class_Fields_Olinordered__field__inverse__zero(X2704) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_1804,plain,
    ! [X3783,X3784] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3784),hAPP(c_Transcendental_Oln,X3783))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3784,X3783)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3783)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3784) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3784,X3783)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3784),hAPP(c_Transcendental_Oln,X3783))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3783)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3784) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__le__cancel__iff])])]) ).

fof(i_0_1805,plain,
    ! [X3778,X3779] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3779),hAPP(c_Transcendental_Oln,X3778))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3779,X3778)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3778)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3779) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3779,X3778)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3779),hAPP(c_Transcendental_Oln,X3778))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3778)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3779) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__cancel__iff])])]) ).

fof(i_0_1806,plain,
    ! [X3905,X3906,X3907] :
      ( ~ class_Int_Onumber__ring(X3907)
      | hAPP(c_Groups_Otimes__class_Otimes(X3907,c_Groups_Ouminus__class_Ouminus(X3907,c_Int_Onumber__class_Onumber__of(X3907,X3906))),X3905) = hAPP(c_Groups_Otimes__class_Otimes(X3907,c_Int_Onumber__class_Onumber__of(X3907,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3906))),X3905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).

fof(i_0_1807,plain,
    ! [X3775] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3775)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3775)),X3775) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__add__one__self__le__self])]) ).

fof(i_0_1808,plain,
    ! [X2815,X2816,X2817] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2817)
      | ~ c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),hAPP(c_Groups_Otimes__class_Otimes(X2817,X2816),X2815))
      | ~ c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),X2815)
      | c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),X2816) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_1809,plain,
    ! [X2818,X2819,X2820] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2820)
      | ~ c_Orderings_Oord__class_Oless(X2820,c_Groups_Ozero__class_Ozero(X2820),hAPP(c_Groups_Otimes__class_Otimes(X2820,X2819),X2818))
      | ~ c_Orderings_Oord__class_Oless(X2820,c_Groups_Ozero__class_Ozero(X2820),X2819)
      | c_Orderings_Oord__class_Oless(X2820,c_Groups_Ozero__class_Ozero(X2820),X2818) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

cnf(i_0_1810,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_1377]) ).

cnf(i_0_1811,plain,
    c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_1378]) ).

fof(i_0_1812,plain,
    ! [X4536,X4537,X4538] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4538)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4537),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4536)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4537,X4536)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4537),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4536)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4538)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4537,X4536)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4537),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4538),X4536)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).

fof(i_0_1813,plain,
    ! [X4542,X4543,X4544] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4544,X4543)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4542)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4544),X4542),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4543),X4542)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).

fof(i_0_1814,plain,
    ! [X4539,X4540,X4541] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4540)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4541),X4540),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4539),X4540)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4541,X4539)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4541),X4540),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4539),X4540)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4540)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4541,X4539)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4541),X4540),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4539),X4540)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).

fof(i_0_1815,plain,
    ! [X4545,X4546,X4547] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4547,X4546)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4545)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4545),X4547),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4545),X4546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).

fof(i_0_1816,plain,
    ! [X4052,X4053,X4054] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4054,X4053)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4052)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4052),X4054),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4052),X4053)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).

fof(i_0_1817,plain,
    ! [X2597,X2598,X2599] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2599)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2598,X2597)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2599),X2598),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2599),X2597)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).

fof(i_0_1818,plain,
    ! [X3012,X3013,X3014] :
      ( ~ class_Fields_Olinordered__field(X3014)
      | ~ c_Orderings_Oord__class_Oless__eq(X3014,X3013,c_Groups_Ozero__class_Ozero(X3014))
      | ~ c_Orderings_Oord__class_Oless(X3014,c_Groups_Ozero__class_Ozero(X3014),X3012)
      | c_Orderings_Oord__class_Oless__eq(X3014,c_Rings_Oinverse__class_Odivide(X3014,X3013,X3012),c_Groups_Ozero__class_Ozero(X3014)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_1819,plain,
    ! [X3030,X3031,X3032] :
      ( ~ class_Fields_Olinordered__field(X3032)
      | ~ c_Orderings_Oord__class_Oless__eq(X3032,c_Groups_Ozero__class_Ozero(X3032),X3031)
      | ~ c_Orderings_Oord__class_Oless(X3032,X3030,c_Groups_Ozero__class_Ozero(X3032))
      | c_Orderings_Oord__class_Oless__eq(X3032,c_Rings_Oinverse__class_Odivide(X3032,X3031,X3030),c_Groups_Ozero__class_Ozero(X3032)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_1820,plain,
    ! [X2690,X2691,X2692] :
      ( ~ class_Fields_Olinordered__field(X2692)
      | ~ c_Orderings_Oord__class_Oless(X2692,X2691,c_Groups_Ozero__class_Ozero(X2692))
      | ~ c_Orderings_Oord__class_Oless(X2692,c_Groups_Ozero__class_Ozero(X2692),X2690)
      | c_Orderings_Oord__class_Oless(X2692,c_Rings_Oinverse__class_Odivide(X2692,X2691,X2690),c_Groups_Ozero__class_Ozero(X2692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_1821,plain,
    ! [X2693,X2694,X2695] :
      ( ~ class_Fields_Olinordered__field(X2695)
      | ~ c_Orderings_Oord__class_Oless(X2695,c_Groups_Ozero__class_Ozero(X2695),X2694)
      | ~ c_Orderings_Oord__class_Oless(X2695,X2693,c_Groups_Ozero__class_Ozero(X2695))
      | c_Orderings_Oord__class_Oless(X2695,c_Rings_Oinverse__class_Odivide(X2695,X2694,X2693),c_Groups_Ozero__class_Ozero(X2695)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_1822,plain,
    ! [X3597,X3598,X3599] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3599)
      | ~ c_Orderings_Oord__class_Oless__eq(X3599,X3598,c_Groups_Ozero__class_Ozero(X3599))
      | ~ c_Orderings_Oord__class_Oless__eq(X3599,X3597,c_Groups_Ozero__class_Ozero(X3599))
      | c_Orderings_Oord__class_Oless__eq(X3599,c_Groups_Oplus__class_Oplus(X3599,X3598,X3597),c_Groups_Ozero__class_Ozero(X3599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_1823,plain,
    ! [X3697,X3698,X3699] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3699)
      | ~ c_Orderings_Oord__class_Oless(X3699,X3698,c_Groups_Ozero__class_Ozero(X3699))
      | ~ c_Orderings_Oord__class_Oless__eq(X3699,X3697,c_Groups_Ozero__class_Ozero(X3699))
      | c_Orderings_Oord__class_Oless(X3699,c_Groups_Oplus__class_Oplus(X3699,X3698,X3697),c_Groups_Ozero__class_Ozero(X3699)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_1824,plain,
    ! [X3694,X3695,X3696] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3696)
      | ~ c_Orderings_Oord__class_Oless__eq(X3696,X3695,c_Groups_Ozero__class_Ozero(X3696))
      | ~ c_Orderings_Oord__class_Oless(X3696,X3694,c_Groups_Ozero__class_Ozero(X3696))
      | c_Orderings_Oord__class_Oless(X3696,c_Groups_Oplus__class_Oplus(X3696,X3695,X3694),c_Groups_Ozero__class_Ozero(X3696)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_1825,plain,
    ! [X3618,X3619,X3620] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3620)
      | ~ c_Orderings_Oord__class_Oless(X3620,X3619,c_Groups_Ozero__class_Ozero(X3620))
      | ~ c_Orderings_Oord__class_Oless(X3620,X3618,c_Groups_Ozero__class_Ozero(X3620))
      | c_Orderings_Oord__class_Oless(X3620,c_Groups_Oplus__class_Oplus(X3620,X3619,X3618),c_Groups_Ozero__class_Ozero(X3620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_1826,plain,
    ! [X3611,X3612,X3613] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3613)
      | ~ c_Orderings_Oord__class_Oless__eq(X3613,c_Groups_Ozero__class_Ozero(X3613),X3612)
      | ~ c_Orderings_Oord__class_Oless__eq(X3613,c_Groups_Ozero__class_Ozero(X3613),X3611)
      | c_Orderings_Oord__class_Oless__eq(X3613,c_Groups_Ozero__class_Ozero(X3613),c_Groups_Oplus__class_Oplus(X3613,X3612,X3611)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_1827,plain,
    ! [X3033,X3034,X3035] :
      ( ~ class_Fields_Olinordered__field(X3035)
      | ~ c_Orderings_Oord__class_Oless__eq(X3035,c_Groups_Ozero__class_Ozero(X3035),X3034)
      | ~ c_Orderings_Oord__class_Oless(X3035,c_Groups_Ozero__class_Ozero(X3035),X3033)
      | c_Orderings_Oord__class_Oless__eq(X3035,c_Groups_Ozero__class_Ozero(X3035),c_Rings_Oinverse__class_Odivide(X3035,X3034,X3033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_1828,plain,
    ! [X3711,X3712,X3713] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3713)
      | ~ c_Orderings_Oord__class_Oless(X3713,c_Groups_Ozero__class_Ozero(X3713),X3712)
      | ~ c_Orderings_Oord__class_Oless__eq(X3713,c_Groups_Ozero__class_Ozero(X3713),X3711)
      | c_Orderings_Oord__class_Oless(X3713,c_Groups_Ozero__class_Ozero(X3713),c_Groups_Oplus__class_Oplus(X3713,X3712,X3711)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_1829,plain,
    ! [X3708,X3709,X3710] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3710)
      | ~ c_Orderings_Oord__class_Oless__eq(X3710,c_Groups_Ozero__class_Ozero(X3710),X3709)
      | ~ c_Orderings_Oord__class_Oless(X3710,c_Groups_Ozero__class_Ozero(X3710),X3708)
      | c_Orderings_Oord__class_Oless(X3710,c_Groups_Ozero__class_Ozero(X3710),c_Groups_Oplus__class_Oplus(X3710,X3709,X3708)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_1830,plain,
    ! [X3621,X3622,X3623] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3623)
      | ~ c_Orderings_Oord__class_Oless(X3623,c_Groups_Ozero__class_Ozero(X3623),X3622)
      | ~ c_Orderings_Oord__class_Oless(X3623,c_Groups_Ozero__class_Ozero(X3623),X3621)
      | c_Orderings_Oord__class_Oless(X3623,c_Groups_Ozero__class_Ozero(X3623),c_Groups_Oplus__class_Oplus(X3623,X3622,X3621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_1831,plain,
    ! [X2696,X2697,X2698] :
      ( ~ class_Fields_Olinordered__field(X2698)
      | ~ c_Orderings_Oord__class_Oless(X2698,c_Groups_Ozero__class_Ozero(X2698),X2697)
      | ~ c_Orderings_Oord__class_Oless(X2698,c_Groups_Ozero__class_Ozero(X2698),X2696)
      | c_Orderings_Oord__class_Oless(X2698,c_Groups_Ozero__class_Ozero(X2698),c_Rings_Oinverse__class_Odivide(X2698,X2697,X2696)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_1832,plain,
    ! [X3009,X3010,X3011] :
      ( ~ class_Fields_Olinordered__field(X3011)
      | ~ c_Orderings_Oord__class_Oless__eq(X3011,X3010,c_Groups_Ozero__class_Ozero(X3011))
      | ~ c_Orderings_Oord__class_Oless(X3011,X3009,c_Groups_Ozero__class_Ozero(X3011))
      | c_Orderings_Oord__class_Oless__eq(X3011,c_Groups_Ozero__class_Ozero(X3011),c_Rings_Oinverse__class_Odivide(X3011,X3010,X3009)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_1833,plain,
    ! [X2687,X2688,X2689] :
      ( ~ class_Fields_Olinordered__field(X2689)
      | ~ c_Orderings_Oord__class_Oless(X2689,X2688,c_Groups_Ozero__class_Ozero(X2689))
      | ~ c_Orderings_Oord__class_Oless(X2689,X2687,c_Groups_Ozero__class_Ozero(X2689))
      | c_Orderings_Oord__class_Oless(X2689,c_Groups_Ozero__class_Ozero(X2689),c_Rings_Oinverse__class_Odivide(X2689,X2688,X2687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_1834,plain,
    ! [X4522,X4523,X4524,X4525] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4525,X4524)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4523,X4522)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4525),X4523),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4524),X4522)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).

fof(i_0_1835,plain,
    ! [X4532,X4533] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4533,X4532))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4533)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4532) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4533)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4533,X4532)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4532)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4533,X4532)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_1836,plain,
    ! [X2949,X2950] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2950,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),X2949)
        | ~ 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,X2950,X2949)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2950)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2949,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,X2950,X2949)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2950)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2950,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,X2950,X2949)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2949,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2950,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,X2950,X2949)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2950)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2949)
        | 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,X2950,X2949)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2949,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),X2949)
        | 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,X2950,X2949)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff])])]) ).

fof(i_0_1837,plain,
    ! [X3483,X3484,X3485,X3486] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3486)
      | hAPP(c_Groups_Otimes__class_Otimes(X3486,X3485),c_Groups_Oplus__class_Oplus(X3486,X3484,X3483)) = c_Groups_Oplus__class_Oplus(X3486,hAPP(c_Groups_Otimes__class_Otimes(X3486,X3485),X3484),hAPP(c_Groups_Otimes__class_Otimes(X3486,X3485),X3483)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).

fof(i_0_1838,plain,
    ! [X3479,X3480,X3481,X3482] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3482)
      | hAPP(c_Groups_Otimes__class_Otimes(X3482,X3481),c_Groups_Oplus__class_Oplus(X3482,X3480,X3479)) = c_Groups_Oplus__class_Oplus(X3482,hAPP(c_Groups_Otimes__class_Otimes(X3482,X3481),X3480),hAPP(c_Groups_Otimes__class_Otimes(X3482,X3481),X3479)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).

fof(i_0_1839,plain,
    ! [X3495,X3496,X3497,X3498] :
      ( ~ class_Rings_Ocomm__semiring__1(X3498)
      | hAPP(c_Groups_Otimes__class_Otimes(X3498,X3497),c_Groups_Oplus__class_Oplus(X3498,X3496,X3495)) = c_Groups_Oplus__class_Oplus(X3498,hAPP(c_Groups_Otimes__class_Otimes(X3498,X3497),X3496),hAPP(c_Groups_Otimes__class_Otimes(X3498,X3497),X3495)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

fof(i_0_1840,plain,
    ! [X3656,X3657] :
      ( ~ class_Rings_Ocomm__semiring__1(X3657)
      | c_Groups_Oplus__class_Oplus(X3657,X3656,X3656) = hAPP(c_Groups_Otimes__class_Otimes(X3657,c_Groups_Oplus__class_Oplus(X3657,c_Groups_Oone__class_Oone(X3657),c_Groups_Oone__class_Oone(X3657))),X3656) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_1841,plain,
    ! [X3438,X3439,X3440,X3441] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X3441)
      | ~ c_Orderings_Oord__class_Oless__eq(X3441,X3440,X3439)
      | c_Orderings_Oord__class_Oless__eq(X3441,c_Groups_Oplus__class_Oplus(X3441,X3440,X3438),c_Groups_Oplus__class_Oplus(X3441,X3439,X3438)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_1842,plain,
    ! [X3434,X3435,X3436,X3437] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X3437)
      | ~ c_Orderings_Oord__class_Oless__eq(X3437,X3436,X3435)
      | c_Orderings_Oord__class_Oless__eq(X3437,c_Groups_Oplus__class_Oplus(X3437,X3434,X3436),c_Groups_Oplus__class_Oplus(X3437,X3434,X3435)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_1843,plain,
    ! [X3458,X3459,X3460,X3461] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3461)
      | ~ c_Orderings_Oord__class_Oless(X3461,X3460,X3459)
      | c_Orderings_Oord__class_Oless(X3461,c_Groups_Oplus__class_Oplus(X3461,X3460,X3458),c_Groups_Oplus__class_Oplus(X3461,X3459,X3458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_1844,plain,
    ! [X3462,X3463,X3464,X3465] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3465)
      | ~ c_Orderings_Oord__class_Oless(X3465,X3464,X3463)
      | c_Orderings_Oord__class_Oless(X3465,c_Groups_Oplus__class_Oplus(X3465,X3462,X3464),c_Groups_Oplus__class_Oplus(X3465,X3462,X3463)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_1845,plain,
    ! [X3776,X3777] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3777)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3776)
      | hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3777),X3776)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3777),hAPP(c_Transcendental_Oln,X3776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__mult])]) ).

fof(i_0_1846,plain,
    ! [X4986,X4987,X4988] :
      ( ~ class_Rings_Olinordered__semidom(X4988)
      | ~ c_Orderings_Oord__class_Oless(X4988,c_Groups_Oone__class_Oone(X4988),X4987)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4986)
      | c_Orderings_Oord__class_Oless(X4988,c_Groups_Oone__class_Oone(X4988),c_Power_Opower__class_Opower(X4988,X4987,X4986)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).

fof(i_0_1847,plain,
    ! [X3888] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3888)
      | c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X3888,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__ln])]) ).

fof(i_0_1848,plain,
    ! [X3604,X3605,X3606,X3607] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3607)
      | ~ c_Orderings_Oord__class_Oless__eq(X3607,c_Groups_Ozero__class_Ozero(X3607),X3606)
      | ~ c_Orderings_Oord__class_Oless__eq(X3607,X3605,X3604)
      | c_Orderings_Oord__class_Oless__eq(X3607,X3605,c_Groups_Oplus__class_Oplus(X3607,X3606,X3604)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_1849,plain,
    ! [X3600,X3601,X3602,X3603] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3603)
      | ~ c_Orderings_Oord__class_Oless__eq(X3603,c_Groups_Ozero__class_Ozero(X3603),X3602)
      | ~ c_Orderings_Oord__class_Oless__eq(X3603,X3601,X3600)
      | c_Orderings_Oord__class_Oless__eq(X3603,X3601,c_Groups_Oplus__class_Oplus(X3603,X3600,X3602)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_1850,plain,
    ! [X3704,X3705,X3706,X3707] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3707)
      | ~ c_Orderings_Oord__class_Oless(X3707,c_Groups_Ozero__class_Ozero(X3707),X3706)
      | ~ c_Orderings_Oord__class_Oless__eq(X3707,X3705,X3704)
      | c_Orderings_Oord__class_Oless(X3707,X3705,c_Groups_Oplus__class_Oplus(X3707,X3706,X3704)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_1851,plain,
    ! [X3700,X3701,X3702,X3703] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3703)
      | ~ c_Orderings_Oord__class_Oless__eq(X3703,c_Groups_Ozero__class_Ozero(X3703),X3702)
      | ~ c_Orderings_Oord__class_Oless(X3703,X3701,X3700)
      | c_Orderings_Oord__class_Oless(X3703,X3701,c_Groups_Oplus__class_Oplus(X3703,X3702,X3700)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_1852,plain,
    ! [X3628,X3629,X3630,X3631] :
      ( ~ class_Rings_Olinordered__semidom(X3631)
      | ~ c_Orderings_Oord__class_Oless(X3631,c_Groups_Ozero__class_Ozero(X3631),X3630)
      | ~ c_Orderings_Oord__class_Oless(X3631,X3629,X3628)
      | c_Orderings_Oord__class_Oless(X3631,X3629,c_Groups_Oplus__class_Oplus(X3631,X3630,X3628)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_1853,plain,
    ! [X3843,X3844,X3845] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3845,c_Int_Onumber__class_Onumber__of(X3845,X3844),c_Int_Onumber__class_Onumber__of(X3845,X3843))
        | ~ c_Orderings_Oord__class_Oless(X3845,c_Int_Onumber__class_Onumber__of(X3845,X3843),c_Int_Onumber__class_Onumber__of(X3845,X3844))
        | ~ class_Int_Onumber(X3845)
        | ~ class_Orderings_Olinorder(X3845) )
      & ( c_Orderings_Oord__class_Oless(X3845,c_Int_Onumber__class_Onumber__of(X3845,X3843),c_Int_Onumber__class_Onumber__of(X3845,X3844))
        | c_Orderings_Oord__class_Oless__eq(X3845,c_Int_Onumber__class_Onumber__of(X3845,X3844),c_Int_Onumber__class_Onumber__of(X3845,X3843))
        | ~ class_Int_Onumber(X3845)
        | ~ class_Orderings_Olinorder(X3845) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1379])])]) ).

fof(i_0_1854,plain,
    ! [X3764,X3765,X3766] :
      ( ( X3765 = c_Groups_Ozero__class_Ozero(X3766)
        | c_Groups_Oplus__class_Oplus(X3766,hAPP(c_Groups_Otimes__class_Otimes(X3766,X3765),X3765),hAPP(c_Groups_Otimes__class_Otimes(X3766,X3764),X3764)) != c_Groups_Ozero__class_Ozero(X3766)
        | ~ class_Rings_Olinordered__ring__strict(X3766) )
      & ( X3764 = c_Groups_Ozero__class_Ozero(X3766)
        | c_Groups_Oplus__class_Oplus(X3766,hAPP(c_Groups_Otimes__class_Otimes(X3766,X3765),X3765),hAPP(c_Groups_Otimes__class_Otimes(X3766,X3764),X3764)) != c_Groups_Ozero__class_Ozero(X3766)
        | ~ class_Rings_Olinordered__ring__strict(X3766) )
      & ( X3765 != c_Groups_Ozero__class_Ozero(X3766)
        | X3764 != c_Groups_Ozero__class_Ozero(X3766)
        | c_Groups_Oplus__class_Oplus(X3766,hAPP(c_Groups_Otimes__class_Otimes(X3766,X3765),X3765),hAPP(c_Groups_Otimes__class_Otimes(X3766,X3764),X3764)) = c_Groups_Ozero__class_Ozero(X3766)
        | ~ class_Rings_Olinordered__ring__strict(X3766) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_1855,plain,
    ! [X4926,X4927,X4928] :
      ( ~ class_Fields_Ofield__inverse__zero(X4928)
      | c_Rings_Oinverse__class_Odivide(X4928,c_Groups_Oone__class_Oone(X4928),c_Power_Opower__class_Opower(X4928,X4927,X4926)) = c_Power_Opower__class_Opower(X4928,c_Rings_Oinverse__class_Odivide(X4928,c_Groups_Oone__class_Oone(X4928),X4927),X4926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).

fof(i_0_1856,plain,
    ! [X2925,X2926,X2927] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2927,X2926,c_Groups_Ozero__class_Ozero(X2927))
        | c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2926)
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) )
      & ( c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2925)
        | c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2926)
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) )
      & ( c_Orderings_Oord__class_Oless__eq(X2927,X2926,c_Groups_Ozero__class_Ozero(X2927))
        | c_Orderings_Oord__class_Oless__eq(X2927,X2925,c_Groups_Ozero__class_Ozero(X2927))
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) )
      & ( c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2925)
        | c_Orderings_Oord__class_Oless__eq(X2927,X2925,c_Groups_Ozero__class_Ozero(X2927))
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2926)
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,X2925,c_Groups_Ozero__class_Ozero(X2927))
        | c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2927,X2926,c_Groups_Ozero__class_Ozero(X2927))
        | ~ c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2925)
        | c_Orderings_Oord__class_Oless__eq(X2927,hAPP(c_Groups_Otimes__class_Otimes(X2927,X2926),X2925),c_Groups_Ozero__class_Ozero(X2927))
        | ~ class_Rings_Olinordered__ring__strict(X2927) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_1857,plain,
    ! [X2928,X2929,X2930] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2930,X2929,c_Groups_Ozero__class_Ozero(X2930))
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2929)
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) )
      & ( c_Orderings_Oord__class_Oless__eq(X2930,X2928,c_Groups_Ozero__class_Ozero(X2930))
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2929)
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) )
      & ( c_Orderings_Oord__class_Oless__eq(X2930,X2929,c_Groups_Ozero__class_Ozero(X2930))
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2928)
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) )
      & ( c_Orderings_Oord__class_Oless__eq(X2930,X2928,c_Groups_Ozero__class_Ozero(X2930))
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2928)
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2929)
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2928)
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2930,X2929,c_Groups_Ozero__class_Ozero(X2930))
        | ~ c_Orderings_Oord__class_Oless__eq(X2930,X2928,c_Groups_Ozero__class_Ozero(X2930))
        | c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),hAPP(c_Groups_Otimes__class_Otimes(X2930,X2929),X2928))
        | ~ class_Rings_Olinordered__ring__strict(X2930) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_1858,plain,
    ! [X4492,X4493,X4494] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4494,X4493)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4494,X4492),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4493,X4492)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

cnf(i_0_1859,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_1370]) ).

cnf(i_0_1860,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_1371]) ).

fof(i_0_1861,plain,
    ! [X4095,X4096,X4097] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4097,X4096)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4095,X4097),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4095,X4096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_1862,plain,
    ! [X3534,X3535,X3536] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3536,X3535)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3534,X3536),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3534,X3535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).

fof(i_0_1863,plain,
    ! [X4447,X4448,X4449] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4449,X4448)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4449,X4447),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4448,X4447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

cnf(i_0_1864,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_1372]) ).

cnf(i_0_1865,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_1373]) ).

fof(i_0_1866,plain,
    ! [X4064,X4065,X4066] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4066,X4065)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4066,X4064),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4065,X4064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_1867,plain,
    ! [X2913,X2914,X2915] :
      ( ~ class_Rings_Oordered__cancel__semiring(X2915)
      | ~ c_Orderings_Oord__class_Oless__eq(X2915,X2914,c_Groups_Ozero__class_Ozero(X2915))
      | ~ c_Orderings_Oord__class_Oless__eq(X2915,c_Groups_Ozero__class_Ozero(X2915),X2913)
      | c_Orderings_Oord__class_Oless__eq(X2915,hAPP(c_Groups_Otimes__class_Otimes(X2915,X2914),X2913),c_Groups_Ozero__class_Ozero(X2915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_1868,plain,
    ! [X2874,X2875,X2876] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2876,c_Groups_Ozero__class_Ozero(X2876),X2875)
        | ~ c_Orderings_Oord__class_Oless__eq(X2876,X2874,c_Groups_Ozero__class_Ozero(X2876))
        | c_Orderings_Oord__class_Oless__eq(X2876,hAPP(c_Groups_Otimes__class_Otimes(X2876,X2875),X2874),c_Groups_Ozero__class_Ozero(X2876))
        | ~ class_Rings_Oordered__cancel__semiring(X2876) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2876,X2875,c_Groups_Ozero__class_Ozero(X2876))
        | ~ c_Orderings_Oord__class_Oless__eq(X2876,c_Groups_Ozero__class_Ozero(X2876),X2874)
        | c_Orderings_Oord__class_Oless__eq(X2876,hAPP(c_Groups_Otimes__class_Otimes(X2876,X2875),X2874),c_Groups_Ozero__class_Ozero(X2876))
        | ~ class_Rings_Oordered__cancel__semiring(X2876) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_1869,plain,
    ! [X2919,X2920,X2921] :
      ( ~ class_Rings_Oordered__cancel__semiring(X2921)
      | ~ c_Orderings_Oord__class_Oless__eq(X2921,c_Groups_Ozero__class_Ozero(X2921),X2920)
      | ~ c_Orderings_Oord__class_Oless__eq(X2921,X2919,c_Groups_Ozero__class_Ozero(X2921))
      | c_Orderings_Oord__class_Oless__eq(X2921,hAPP(c_Groups_Otimes__class_Otimes(X2921,X2920),X2919),c_Groups_Ozero__class_Ozero(X2921)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_1870,plain,
    ! [X2916,X2917,X2918] :
      ( ~ class_Rings_Oordered__cancel__semiring(X2918)
      | ~ c_Orderings_Oord__class_Oless__eq(X2918,c_Groups_Ozero__class_Ozero(X2918),X2917)
      | ~ c_Orderings_Oord__class_Oless__eq(X2918,X2916,c_Groups_Ozero__class_Ozero(X2918))
      | c_Orderings_Oord__class_Oless__eq(X2918,hAPP(c_Groups_Otimes__class_Otimes(X2918,X2916),X2917),c_Groups_Ozero__class_Ozero(X2918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_1871,plain,
    ! [X2808,X2809,X2810] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2810)
      | ~ c_Orderings_Oord__class_Oless(X2810,X2809,c_Groups_Ozero__class_Ozero(X2810))
      | ~ c_Orderings_Oord__class_Oless(X2810,c_Groups_Ozero__class_Ozero(X2810),X2808)
      | c_Orderings_Oord__class_Oless(X2810,hAPP(c_Groups_Otimes__class_Otimes(X2810,X2809),X2808),c_Groups_Ozero__class_Ozero(X2810)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_1872,plain,
    ! [X2824,X2825,X2826] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2826)
      | ~ c_Orderings_Oord__class_Oless(X2826,c_Groups_Ozero__class_Ozero(X2826),X2825)
      | ~ c_Orderings_Oord__class_Oless(X2826,X2824,c_Groups_Ozero__class_Ozero(X2826))
      | c_Orderings_Oord__class_Oless(X2826,hAPP(c_Groups_Otimes__class_Otimes(X2826,X2825),X2824),c_Groups_Ozero__class_Ozero(X2826)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_1873,plain,
    ! [X2821,X2822,X2823] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2823)
      | ~ c_Orderings_Oord__class_Oless(X2823,c_Groups_Ozero__class_Ozero(X2823),X2822)
      | ~ c_Orderings_Oord__class_Oless(X2823,X2821,c_Groups_Ozero__class_Ozero(X2823))
      | c_Orderings_Oord__class_Oless(X2823,hAPP(c_Groups_Otimes__class_Otimes(X2823,X2821),X2822),c_Groups_Ozero__class_Ozero(X2823)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_1874,plain,
    ! [X2877,X2878,X2879] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2879,c_Groups_Ozero__class_Ozero(X2879),X2878)
        | ~ c_Orderings_Oord__class_Oless__eq(X2879,c_Groups_Ozero__class_Ozero(X2879),X2877)
        | c_Orderings_Oord__class_Oless__eq(X2879,c_Groups_Ozero__class_Ozero(X2879),hAPP(c_Groups_Otimes__class_Otimes(X2879,X2878),X2877))
        | ~ class_Rings_Oordered__ring(X2879) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2879,X2878,c_Groups_Ozero__class_Ozero(X2879))
        | ~ c_Orderings_Oord__class_Oless__eq(X2879,X2877,c_Groups_Ozero__class_Ozero(X2879))
        | c_Orderings_Oord__class_Oless__eq(X2879,c_Groups_Ozero__class_Ozero(X2879),hAPP(c_Groups_Otimes__class_Otimes(X2879,X2878),X2877))
        | ~ class_Rings_Oordered__ring(X2879) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_1875,plain,
    ! [X2922,X2923,X2924] :
      ( ~ class_Rings_Oordered__cancel__semiring(X2924)
      | ~ c_Orderings_Oord__class_Oless__eq(X2924,c_Groups_Ozero__class_Ozero(X2924),X2923)
      | ~ c_Orderings_Oord__class_Oless__eq(X2924,c_Groups_Ozero__class_Ozero(X2924),X2922)
      | c_Orderings_Oord__class_Oless__eq(X2924,c_Groups_Ozero__class_Ozero(X2924),hAPP(c_Groups_Otimes__class_Otimes(X2924,X2923),X2922)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_1876,plain,
    ! [X2750,X2751,X2752] :
      ( ~ class_Rings_Olinordered__semidom(X2752)
      | ~ c_Orderings_Oord__class_Oless(X2752,c_Groups_Oone__class_Oone(X2752),X2751)
      | ~ c_Orderings_Oord__class_Oless(X2752,c_Groups_Oone__class_Oone(X2752),X2750)
      | c_Orderings_Oord__class_Oless(X2752,c_Groups_Oone__class_Oone(X2752),hAPP(c_Groups_Otimes__class_Otimes(X2752,X2751),X2750)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_1877,plain,
    ! [X2827,X2828,X2829] :
      ( ~ class_Rings_Olinordered__semiring__strict(X2829)
      | ~ c_Orderings_Oord__class_Oless(X2829,c_Groups_Ozero__class_Ozero(X2829),X2828)
      | ~ c_Orderings_Oord__class_Oless(X2829,c_Groups_Ozero__class_Ozero(X2829),X2827)
      | c_Orderings_Oord__class_Oless(X2829,c_Groups_Ozero__class_Ozero(X2829),hAPP(c_Groups_Otimes__class_Otimes(X2829,X2828),X2827)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_1878,plain,
    ! [X2910,X2911,X2912] :
      ( ~ class_Rings_Oordered__ring(X2912)
      | ~ c_Orderings_Oord__class_Oless__eq(X2912,X2911,c_Groups_Ozero__class_Ozero(X2912))
      | ~ c_Orderings_Oord__class_Oless__eq(X2912,X2910,c_Groups_Ozero__class_Ozero(X2912))
      | c_Orderings_Oord__class_Oless__eq(X2912,c_Groups_Ozero__class_Ozero(X2912),hAPP(c_Groups_Otimes__class_Otimes(X2912,X2911),X2910)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_1879,plain,
    ! [X2805,X2806,X2807] :
      ( ~ class_Rings_Olinordered__ring__strict(X2807)
      | ~ c_Orderings_Oord__class_Oless(X2807,X2806,c_Groups_Ozero__class_Ozero(X2807))
      | ~ c_Orderings_Oord__class_Oless(X2807,X2805,c_Groups_Ozero__class_Ozero(X2807))
      | c_Orderings_Oord__class_Oless(X2807,c_Groups_Ozero__class_Ozero(X2807),hAPP(c_Groups_Otimes__class_Otimes(X2807,X2806),X2805)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_1880,plain,
    ! [X4250,X4251] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4251)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4250)
      | 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,X4251,X4250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_1881,plain,
    ! [X4511,X4512,X4513] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4513),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4512,X4511)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4513),X4512),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4513),X4511)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).

fof(i_0_1882,plain,
    ! [X4078,X4079,X4080] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4080),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4079,X4078)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4080),X4079),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4080),X4078)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).

cnf(i_0_1883,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_1380]) ).

cnf(i_0_1884,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_1381]) ).

fof(i_0_1885,plain,
    ! [X3616,X3617] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3617,c_Groups_Ozero__class_Ozero(X3617),c_Groups_Oplus__class_Oplus(X3617,X3616,X3616))
        | c_Orderings_Oord__class_Oless__eq(X3617,c_Groups_Ozero__class_Ozero(X3617),X3616)
        | ~ class_Groups_Olinordered__ab__group__add(X3617) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3617,c_Groups_Ozero__class_Ozero(X3617),X3616)
        | c_Orderings_Oord__class_Oless__eq(X3617,c_Groups_Ozero__class_Ozero(X3617),c_Groups_Oplus__class_Oplus(X3617,X3616,X3616))
        | ~ class_Groups_Olinordered__ab__group__add(X3617) ) ),
    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_1886,plain,
    ! [X3626,X3627] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3627,c_Groups_Ozero__class_Ozero(X3627),c_Groups_Oplus__class_Oplus(X3627,X3626,X3626))
        | c_Orderings_Oord__class_Oless(X3627,c_Groups_Ozero__class_Ozero(X3627),X3626)
        | ~ class_Groups_Olinordered__ab__group__add(X3627) )
      & ( ~ c_Orderings_Oord__class_Oless(X3627,c_Groups_Ozero__class_Ozero(X3627),X3626)
        | c_Orderings_Oord__class_Oless(X3627,c_Groups_Ozero__class_Ozero(X3627),c_Groups_Oplus__class_Oplus(X3627,X3626,X3626))
        | ~ class_Groups_Olinordered__ab__group__add(X3627) ) ),
    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_1887,plain,
    ! [X3614,X3615] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3615,c_Groups_Oplus__class_Oplus(X3615,X3614,X3614),c_Groups_Ozero__class_Ozero(X3615))
        | c_Orderings_Oord__class_Oless__eq(X3615,X3614,c_Groups_Ozero__class_Ozero(X3615))
        | ~ class_Groups_Olinordered__ab__group__add(X3615) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3615,X3614,c_Groups_Ozero__class_Ozero(X3615))
        | c_Orderings_Oord__class_Oless__eq(X3615,c_Groups_Oplus__class_Oplus(X3615,X3614,X3614),c_Groups_Ozero__class_Ozero(X3615))
        | ~ class_Groups_Olinordered__ab__group__add(X3615) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).

fof(i_0_1888,plain,
    ! [X3624,X3625] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3625,c_Groups_Oplus__class_Oplus(X3625,X3624,X3624),c_Groups_Ozero__class_Ozero(X3625))
        | c_Orderings_Oord__class_Oless(X3625,X3624,c_Groups_Ozero__class_Ozero(X3625))
        | ~ class_Groups_Olinordered__ab__group__add(X3625) )
      & ( ~ c_Orderings_Oord__class_Oless(X3625,X3624,c_Groups_Ozero__class_Ozero(X3625))
        | c_Orderings_Oord__class_Oless(X3625,c_Groups_Oplus__class_Oplus(X3625,X3624,X3624),c_Groups_Ozero__class_Ozero(X3625))
        | ~ class_Groups_Olinordered__ab__group__add(X3625) ) ),
    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_1889,plain,
    ! [X3767,X3768] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3768,c_Groups_Oplus__class_Oplus(X3768,X3767,X3767),c_Groups_Ozero__class_Ozero(X3768))
        | c_Orderings_Oord__class_Oless(X3768,X3767,c_Groups_Ozero__class_Ozero(X3768))
        | ~ class_Rings_Olinordered__idom(X3768) )
      & ( ~ c_Orderings_Oord__class_Oless(X3768,X3767,c_Groups_Ozero__class_Ozero(X3768))
        | c_Orderings_Oord__class_Oless(X3768,c_Groups_Oplus__class_Oplus(X3768,X3767,X3767),c_Groups_Ozero__class_Ozero(X3768))
        | ~ class_Rings_Olinordered__idom(X3768) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

cnf(i_0_1890,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_1382]) ).

cnf(i_0_1891,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_1383]) ).

fof(i_0_1892,plain,
    ! [X3343,X3344,X3345,X3346] :
      ( ~ class_Rings_Ocomm__semiring__1(X3346)
      | c_Groups_Oplus__class_Oplus(X3346,c_Groups_Oplus__class_Oplus(X3346,X3345,X3344),X3343) = c_Groups_Oplus__class_Oplus(X3346,c_Groups_Oplus__class_Oplus(X3346,X3345,X3343),X3344) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_1893,plain,
    ! [X3352,X3353,X3354,X3355] :
      ( ~ class_Groups_Oab__semigroup__add(X3355)
      | c_Groups_Oplus__class_Oplus(X3355,c_Groups_Oplus__class_Oplus(X3355,X3354,X3353),X3352) = c_Groups_Oplus__class_Oplus(X3355,X3354,c_Groups_Oplus__class_Oplus(X3355,X3353,X3352)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_1894,plain,
    ! [X3339,X3340,X3341,X3342] :
      ( ~ class_Rings_Ocomm__semiring__1(X3342)
      | c_Groups_Oplus__class_Oplus(X3342,c_Groups_Oplus__class_Oplus(X3342,X3341,X3340),X3339) = c_Groups_Oplus__class_Oplus(X3342,X3341,c_Groups_Oplus__class_Oplus(X3342,X3340,X3339)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_1895,plain,
    ! [X3335,X3336,X3337,X3338] :
      ( ~ class_Rings_Ocomm__semiring__1(X3338)
      | c_Groups_Oplus__class_Oplus(X3338,X3337,c_Groups_Oplus__class_Oplus(X3338,X3336,X3335)) = c_Groups_Oplus__class_Oplus(X3338,c_Groups_Oplus__class_Oplus(X3338,X3337,X3336),X3335) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_1896,plain,
    ! [X3331,X3332,X3333,X3334] :
      ( ~ class_Rings_Ocomm__semiring__1(X3334)
      | c_Groups_Oplus__class_Oplus(X3334,X3333,c_Groups_Oplus__class_Oplus(X3334,X3332,X3331)) = c_Groups_Oplus__class_Oplus(X3334,X3332,c_Groups_Oplus__class_Oplus(X3334,X3333,X3331)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_1897,plain,
    ! [X4170,X4171] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4171,X4170))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4171),X4170) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4171),X4170)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4171,X4170)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).

fof(i_0_1898,plain,
    ! [X4174,X4175] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4175,X4174))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4175),X4174) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4175),X4174)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4175,X4174)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).

fof(i_0_1899,plain,
    ! [X4168,X4169] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4169,X4168),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4168,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4169)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4168,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4169))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4169,X4168),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff])]) ).

fof(i_0_1900,plain,
    ! [X4172,X4173] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4173,X4172),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4172,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4173)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4172,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4173))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4173,X4172),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff])]) ).

fof(i_0_1901,plain,
    ! [X3671,X3672,X3673] :
      ( ~ class_Fields_Olinordered__field(X3673)
      | ~ c_Orderings_Oord__class_Oless__eq(X3673,c_Rings_Oinverse__class_Oinverse(X3673,X3672),c_Rings_Oinverse__class_Oinverse(X3673,X3671))
      | ~ c_Orderings_Oord__class_Oless(X3673,c_Groups_Ozero__class_Ozero(X3673),X3672)
      | c_Orderings_Oord__class_Oless__eq(X3673,X3671,X3672) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le])]) ).

fof(i_0_1902,plain,
    ! [X3560,X3561,X3562] :
      ( ~ class_Fields_Olinordered__field(X3562)
      | ~ c_Orderings_Oord__class_Oless(X3562,c_Rings_Oinverse__class_Oinverse(X3562,X3561),c_Rings_Oinverse__class_Oinverse(X3562,X3560))
      | ~ c_Orderings_Oord__class_Oless(X3562,c_Groups_Ozero__class_Ozero(X3562),X3561)
      | c_Orderings_Oord__class_Oless(X3562,X3560,X3561) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).

fof(i_0_1903,plain,
    ! [X3668,X3669,X3670] :
      ( ~ class_Fields_Olinordered__field(X3670)
      | ~ c_Orderings_Oord__class_Oless__eq(X3670,c_Rings_Oinverse__class_Oinverse(X3670,X3669),c_Rings_Oinverse__class_Oinverse(X3670,X3668))
      | ~ c_Orderings_Oord__class_Oless(X3670,X3668,c_Groups_Ozero__class_Ozero(X3670))
      | c_Orderings_Oord__class_Oless__eq(X3670,X3668,X3669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le__neg])]) ).

fof(i_0_1904,plain,
    ! [X3557,X3558,X3559] :
      ( ~ class_Fields_Olinordered__field(X3559)
      | ~ c_Orderings_Oord__class_Oless(X3559,c_Rings_Oinverse__class_Oinverse(X3559,X3558),c_Rings_Oinverse__class_Oinverse(X3559,X3557))
      | ~ c_Orderings_Oord__class_Oless(X3559,X3557,c_Groups_Ozero__class_Ozero(X3559))
      | c_Orderings_Oord__class_Oless(X3559,X3557,X3558) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).

cnf(i_0_1905,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1375]) ).

cnf(i_0_1906,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_1384]) ).

fof(i_0_1907,plain,
    ! [X3044,X3045,X3046,X3047] :
      ( ~ class_Groups_Oab__semigroup__mult(X3047)
      | hAPP(c_Groups_Otimes__class_Otimes(X3047,hAPP(c_Groups_Otimes__class_Otimes(X3047,X3046),X3045)),X3044) = hAPP(c_Groups_Otimes__class_Otimes(X3047,X3046),hAPP(c_Groups_Otimes__class_Otimes(X3047,X3045),X3044)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).

fof(i_0_1908,plain,
    ! [X2624,X2625,X2626,X2627] :
      ( ~ class_Rings_Ocomm__semiring__1(X2627)
      | hAPP(c_Groups_Otimes__class_Otimes(X2627,hAPP(c_Groups_Otimes__class_Otimes(X2627,X2626),X2625)),X2624) = hAPP(c_Groups_Otimes__class_Otimes(X2627,X2626),hAPP(c_Groups_Otimes__class_Otimes(X2627,X2625),X2624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).

fof(i_0_1909,plain,
    ! [X2628,X2629,X2630,X2631] :
      ( ~ class_Rings_Ocomm__semiring__1(X2631)
      | hAPP(c_Groups_Otimes__class_Otimes(X2631,X2630),hAPP(c_Groups_Otimes__class_Otimes(X2631,X2629),X2628)) = hAPP(c_Groups_Otimes__class_Otimes(X2631,hAPP(c_Groups_Otimes__class_Otimes(X2631,X2630),X2629)),X2628) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).

cnf(i_0_1910,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_1911,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_one__code__numeral__code]) ).

cnf(i_0_1912,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]) ).

cnf(i_0_1913,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]) ).

fof(i_0_1914,plain,
    ! [X4292,X4293] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4293,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4293),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4292)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4292) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4292,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4293),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4292)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4293)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4293,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4292,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4293),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4292)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4293,X4292))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4293,c_Int_OPls) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1385])])]) ).

fof(i_0_1915,plain,
    ! [X3662,X3663] :
      ( ( X3663 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3663),X3663),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3662),X3662)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X3662 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3663),X3663),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3662),X3662)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X3663 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X3662 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3663),X3663),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3662),X3662)) = 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_1916,plain,
    ! [X4388,X4389,X4390] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4390,X4389),X4388) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4390,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4389,X4388)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_1917,plain,
    ! [X4072,X4073,X4074] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4074,X4073),X4072) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4074,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4073,X4072)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_1918,plain,
    ! [X4385,X4386,X4387] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4387,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4386,X4385)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4386,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4387,X4385)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_1919,plain,
    ! [X4069,X4070,X4071] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4071,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4070,X4069)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4070,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4071,X4069)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_1920,plain,
    ! [X4061,X4062] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4062,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4061,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4062,X4061)
        | X4062 = X4061 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4062,X4061)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4062,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4061,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( X4062 != X4061
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4062,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4061,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])])]) ).

fof(i_0_1921,plain,
    ! [X4867,X4868] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4868,X4867))
        | X4867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4868) )
      & ( X4867 != 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,X4868,X4867)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4868)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4868,X4867)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).

fof(i_0_1922,plain,
    ! [X4857,X4858] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4858,X4857))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4858)
        | X4857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4858)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X4858,X4857)) )
      & ( X4857 != 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,X4858,X4857)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).

fof(i_0_1923,plain,
    ! [X4084,X4085] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4085,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4084)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4085,X4084) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4085,X4084)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4085,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4084) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

fof(i_0_1924,plain,
    ! [X4082,X4083] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4083,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4082,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4083,X4082) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4083,X4082)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4083,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4082,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_1925,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_1386]) ).

fof(i_0_1926,plain,
    ! [X4105,X4106] :
      ( ~ class_RealVector_Oreal__normed__field(X4106)
      | ~ class_SEQ_Obanach(X4106)
      | c_Deriv_Oderiv(X4106,c_Transcendental_Oexp(X4106),X4105,hAPP(c_Transcendental_Oexp(X4106),X4105)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__exp])]) ).

fof(i_0_1927,plain,
    ! [X4248,X4249] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4249)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4248)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4249),X4248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_1928,plain,
    ! [X4534,X4535] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4535)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4535),X4534)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4534)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4535),X4534)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4535)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4534)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4535),X4534)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).

fof(i_0_1929,plain,
    ! [X2600,X2601] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2601)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2600)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2601),X2600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).

fof(i_0_1930,plain,
    ! [X5028,X5029,X5030] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X5030)
      | ~ c_Orderings_Oord__class_Oless(X5030,c_Groups_Ozero__class_Ozero(X5030),X5029)
      | c_Rings_Oinverse__class_Odivide(X5030,c_Groups_Oabs__class_Oabs(X5030,X5028),X5029) = c_Groups_Oabs__class_Oabs(X5030,c_Rings_Oinverse__class_Odivide(X5030,X5028,X5029)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

fof(i_0_1931,plain,
    ! [X4439,X4440,X4441,X4442] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4442,X4441)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4440,X4441) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4442,X4439)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4440,X4439) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_1932,plain,
    ! [X5008,X5009,X5010] :
      ( ~ class_Rings_Olinordered__idom(X5010)
      | c_Groups_Oabs__class_Oabs(X5010,c_Power_Opower__class_Opower(X5010,c_Groups_Ouminus__class_Ouminus(X5010,X5009),X5008)) = c_Groups_Oabs__class_Oabs(X5010,c_Power_Opower__class_Opower(X5010,X5009,X5008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).

fof(i_0_1933,plain,
    ! [X4505,X4506,X4507] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4507,X4505)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4507,X4506),X4505) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4506,X4505)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4507,X4506),X4505) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1387])])]) ).

fof(i_0_1934,plain,
    ! [X4502,X4503,X4504] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4504,X4503),X4502)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4504,X4502) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_1935,plain,
    ! [X4499,X4500,X4501] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4501,X4500),X4499)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4500,X4499) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_1936,plain,
    ! [X4436,X4437,X4438] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4438,X4437),X4436)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4438,X4436) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_1937,plain,
    ! [X3608,X3609,X3610] :
      ( ( X3609 = c_Groups_Ozero__class_Ozero(X3610)
        | c_Groups_Oplus__class_Oplus(X3610,X3609,X3608) != c_Groups_Ozero__class_Ozero(X3610)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3608)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3609)
        | ~ class_Groups_Oordered__comm__monoid__add(X3610) )
      & ( X3608 = c_Groups_Ozero__class_Ozero(X3610)
        | c_Groups_Oplus__class_Oplus(X3610,X3609,X3608) != c_Groups_Ozero__class_Ozero(X3610)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3608)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3609)
        | ~ class_Groups_Oordered__comm__monoid__add(X3610) )
      & ( X3609 != c_Groups_Ozero__class_Ozero(X3610)
        | X3608 != c_Groups_Ozero__class_Ozero(X3610)
        | c_Groups_Oplus__class_Oplus(X3610,X3609,X3608) = c_Groups_Ozero__class_Ozero(X3610)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3608)
        | ~ c_Orderings_Oord__class_Oless__eq(X3610,c_Groups_Ozero__class_Ozero(X3610),X3609)
        | ~ class_Groups_Oordered__comm__monoid__add(X3610) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_1938,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_1388]) ).

cnf(i_0_1939,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_1389]) ).

cnf(i_0_1940,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_1390]) ).

cnf(i_0_1941,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_1391]) ).

fof(i_0_1942,plain,
    ! [X3677,X3678,X3679] :
      ( ~ class_Fields_Olinordered__field(X3679)
      | ~ c_Orderings_Oord__class_Oless__eq(X3679,X3678,X3677)
      | ~ c_Orderings_Oord__class_Oless(X3679,c_Groups_Ozero__class_Ozero(X3679),X3678)
      | c_Orderings_Oord__class_Oless__eq(X3679,c_Rings_Oinverse__class_Oinverse(X3679,X3677),c_Rings_Oinverse__class_Oinverse(X3679,X3678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le])]) ).

fof(i_0_1943,plain,
    ! [X3568,X3569,X3570] :
      ( ~ class_Fields_Olinordered__field(X3570)
      | ~ c_Orderings_Oord__class_Oless(X3570,X3569,X3568)
      | ~ c_Orderings_Oord__class_Oless(X3570,c_Groups_Ozero__class_Ozero(X3570),X3569)
      | c_Orderings_Oord__class_Oless(X3570,c_Rings_Oinverse__class_Oinverse(X3570,X3568),c_Rings_Oinverse__class_Oinverse(X3570,X3569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).

fof(i_0_1944,plain,
    ! [X3674,X3675,X3676] :
      ( ~ class_Fields_Olinordered__field(X3676)
      | ~ c_Orderings_Oord__class_Oless__eq(X3676,X3675,X3674)
      | ~ c_Orderings_Oord__class_Oless(X3676,X3674,c_Groups_Ozero__class_Ozero(X3676))
      | c_Orderings_Oord__class_Oless__eq(X3676,c_Rings_Oinverse__class_Oinverse(X3676,X3674),c_Rings_Oinverse__class_Oinverse(X3676,X3675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le__neg])]) ).

fof(i_0_1945,plain,
    ! [X3565,X3566,X3567] :
      ( ~ class_Fields_Olinordered__field(X3567)
      | ~ c_Orderings_Oord__class_Oless(X3567,X3566,X3565)
      | ~ c_Orderings_Oord__class_Oless(X3567,X3565,c_Groups_Ozero__class_Ozero(X3567))
      | c_Orderings_Oord__class_Oless(X3567,c_Rings_Oinverse__class_Oinverse(X3567,X3565),c_Rings_Oinverse__class_Oinverse(X3567,X3566)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).

fof(i_0_1946,plain,
    ! [X3314,X3315,X3316,X3317] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3316,X3317),X3315,X3314)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3316,X3317),X3315,X3314)
        | ~ class_Orderings_Oord(X3317) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3316,X3317),X3314,X3315)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3316,X3317),X3315,X3314)
        | ~ class_Orderings_Oord(X3317) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3316,X3317),X3315,X3314)
        | c_Orderings_Oord__class_Oless__eq(tc_fun(X3316,X3317),X3314,X3315)
        | c_Orderings_Oord__class_Oless(tc_fun(X3316,X3317),X3315,X3314)
        | ~ class_Orderings_Oord(X3317) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1392])])]) ).

fof(i_0_1947,plain,
    ! [X4165,X4166,X4167] :
      ( ~ class_RealVector_Oreal__normed__field(X4167)
      | ~ class_SEQ_Obanach(X4167)
      | hAPP(c_Groups_Otimes__class_Otimes(X4167,hAPP(c_Transcendental_Oexp(X4167),X4166)),hAPP(c_Transcendental_Oexp(X4167),X4165)) = hAPP(c_Transcendental_Oexp(X4167),c_Groups_Oplus__class_Oplus(X4167,X4166,X4165)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__exp__exp])]) ).

fof(i_0_1948,plain,
    ! [X4162,X4163,X4164] :
      ( ~ class_RealVector_Oreal__normed__field(X4164)
      | ~ class_SEQ_Obanach(X4164)
      | hAPP(c_Transcendental_Oexp(X4164),c_Groups_Oplus__class_Oplus(X4164,X4163,X4162)) = hAPP(c_Groups_Otimes__class_Otimes(X4164,hAPP(c_Transcendental_Oexp(X4164),X4163)),hAPP(c_Transcendental_Oexp(X4164),X4162)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__add])]) ).

fof(i_0_1949,plain,
    ! [X4887,X4888,X4889,X4890] :
      ( ~ class_Groups_Omonoid__mult(X4890)
      | c_Power_Opower__class_Opower(X4890,X4889,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4888),X4887)) = c_Power_Opower__class_Opower(X4890,c_Power_Opower__class_Opower(X4890,X4889,X4888),X4887) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).

fof(i_0_1950,plain,
    ! [X4737,X4738,X4739,X4740] :
      ( ~ class_Rings_Ocomm__semiring__1(X4740)
      | c_Power_Opower__class_Opower(X4740,c_Power_Opower__class_Opower(X4740,X4739,X4738),X4737) = c_Power_Opower__class_Opower(X4740,X4739,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4738),X4737)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).

cnf(i_0_1951,plain,
    c_Int_Opred(c_Int_OBit0(X1)) = c_Int_OBit1(c_Int_Opred(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

fof(i_0_1952,plain,
    ! [X4275,X4276] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4276,X4275)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4275)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4276),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4275)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4276,X4275)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4276),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4275)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4276,X4275)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4276,X4275)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4276),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4275)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4275)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4276,X4275)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4276),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4275)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_1953,plain,
    ! [X4150,X4151] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4151),X4151)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4150),X4150)),
    inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).

fof(i_0_1954,plain,
    ! [X4407,X4408,X4409] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4409),X4408)),X4407) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4409),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4408),X4407)),
    inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).

fof(i_0_1955,plain,
    ! [X4045,X4046,X4047] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4047),X4046)),X4045) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4047),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4046),X4045)),
    inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).

fof(i_0_1956,plain,
    ! [X2565,X2566,X2567] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2567),X2566)),X2565) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2567),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2566),X2565)),
    inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).

fof(i_0_1957,plain,
    ! [X5014,X5015,X5016] :
      ( ~ class_Rings_Olinordered__idom(X5016)
      | ~ c_Orderings_Oord__class_Oless__eq(X5016,c_Groups_Ozero__class_Ozero(X5016),X5015)
      | hAPP(c_Groups_Otimes__class_Otimes(X5016,c_Groups_Oabs__class_Oabs(X5016,X5014)),X5015) = c_Groups_Oabs__class_Oabs(X5016,hAPP(c_Groups_Otimes__class_Otimes(X5016,X5014),X5015)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).

fof(i_0_1958,plain,
    ! [X2777,X2778,X2779,X2780] :
      ( ~ class_Rings_Odivision__ring(X2780)
      | hAPP(c_Groups_Otimes__class_Otimes(X2780,X2779),c_Rings_Oinverse__class_Odivide(X2780,X2778,X2777)) = c_Rings_Oinverse__class_Odivide(X2780,hAPP(c_Groups_Otimes__class_Otimes(X2780,X2779),X2778),X2777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).

fof(i_0_1959,plain,
    ! [X3304,X3305] :
      ( ( c_Orderings_Oord__class_Oless(X3305,c_Groups_Ozero__class_Ozero(X3305),X3304)
        | ~ c_Orderings_Oord__class_Oless__eq(X3305,c_Groups_Oone__class_Oone(X3305),c_Rings_Oinverse__class_Oinverse(X3305,X3304))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3305) )
      & ( c_Orderings_Oord__class_Oless__eq(X3305,X3304,c_Groups_Oone__class_Oone(X3305))
        | ~ c_Orderings_Oord__class_Oless__eq(X3305,c_Groups_Oone__class_Oone(X3305),c_Rings_Oinverse__class_Oinverse(X3305,X3304))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3305) )
      & ( ~ c_Orderings_Oord__class_Oless(X3305,c_Groups_Ozero__class_Ozero(X3305),X3304)
        | ~ c_Orderings_Oord__class_Oless__eq(X3305,X3304,c_Groups_Oone__class_Oone(X3305))
        | c_Orderings_Oord__class_Oless__eq(X3305,c_Groups_Oone__class_Oone(X3305),c_Rings_Oinverse__class_Oinverse(X3305,X3304))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3305) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse__iff])])]) ).

fof(i_0_1960,plain,
    ! [X3308,X3309] :
      ( ~ class_Fields_Olinordered__field(X3309)
      | ~ c_Orderings_Oord__class_Oless(X3309,c_Groups_Ozero__class_Ozero(X3309),X3308)
      | ~ c_Orderings_Oord__class_Oless__eq(X3309,X3308,c_Groups_Oone__class_Oone(X3309))
      | c_Orderings_Oord__class_Oless__eq(X3309,c_Groups_Oone__class_Oone(X3309),c_Rings_Oinverse__class_Oinverse(X3309,X3308)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse])]) ).

fof(i_0_1961,plain,
    ! [X3684,X3685] :
      ( ( c_Orderings_Oord__class_Oless(X3685,c_Groups_Ozero__class_Ozero(X3685),X3684)
        | ~ c_Orderings_Oord__class_Oless(X3685,c_Groups_Oone__class_Oone(X3685),c_Rings_Oinverse__class_Oinverse(X3685,X3684))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3685) )
      & ( c_Orderings_Oord__class_Oless(X3685,X3684,c_Groups_Oone__class_Oone(X3685))
        | ~ c_Orderings_Oord__class_Oless(X3685,c_Groups_Oone__class_Oone(X3685),c_Rings_Oinverse__class_Oinverse(X3685,X3684))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3685) )
      & ( ~ c_Orderings_Oord__class_Oless(X3685,c_Groups_Ozero__class_Ozero(X3685),X3684)
        | ~ c_Orderings_Oord__class_Oless(X3685,X3684,c_Groups_Oone__class_Oone(X3685))
        | c_Orderings_Oord__class_Oless(X3685,c_Groups_Oone__class_Oone(X3685),c_Rings_Oinverse__class_Oinverse(X3685,X3684))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3685) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff])])]) ).

fof(i_0_1962,plain,
    ! [X3682,X3683] :
      ( ~ class_Fields_Olinordered__field(X3683)
      | ~ c_Orderings_Oord__class_Oless(X3683,c_Groups_Ozero__class_Ozero(X3683),X3682)
      | ~ c_Orderings_Oord__class_Oless(X3683,X3682,c_Groups_Oone__class_Oone(X3683))
      | c_Orderings_Oord__class_Oless(X3683,c_Groups_Oone__class_Oone(X3683),c_Rings_Oinverse__class_Oinverse(X3683,X3682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse])]) ).

fof(i_0_1963,plain,
    ! [X3896] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3896)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3896),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__ge__add__one__self__aux])]) ).

fof(i_0_1964,plain,
    ! [X4864,X4865,X4866] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4866,X4865),X4864) = c_Power_Opower__class_Opower(tc_Int_Oint,X4866,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4865),X4864)),
    inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).

fof(i_0_1965,plain,
    ! [X3889,X3890,X3891] :
      ( ~ class_RealVector_Oreal__normed__field(X3891)
      | c_Deriv_Oderiv(X3891,c_Groups_Otimes__class_Otimes(X3891,X3890),X3889,X3890) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__cmult__Id])]) ).

fof(i_0_1966,plain,
    ! [X4516,X4517,X4518] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4518,X4517)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4518),X4516),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4517),X4516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).

fof(i_0_1967,plain,
    ! [X4519,X4520,X4521] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4521,X4520)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4519),X4521),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4519),X4520)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).

fof(i_0_1968,plain,
    ! [X2710,X2711,X2712,X2713] :
      ( ~ class_Fields_Ofield__inverse__zero(X2713)
      | X2712 = c_Groups_Ozero__class_Ozero(X2713)
      | c_Rings_Oinverse__class_Odivide(X2713,hAPP(c_Groups_Otimes__class_Otimes(X2713,X2712),X2711),hAPP(c_Groups_Otimes__class_Otimes(X2713,X2712),X2710)) = c_Rings_Oinverse__class_Odivide(X2713,X2711,X2710) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_1969,plain,
    ! [X2714,X2715,X2716,X2717] :
      ( ~ class_Fields_Ofield__inverse__zero(X2717)
      | X2716 = c_Groups_Ozero__class_Ozero(X2717)
      | c_Rings_Oinverse__class_Odivide(X2717,hAPP(c_Groups_Otimes__class_Otimes(X2717,X2715),X2716),hAPP(c_Groups_Otimes__class_Otimes(X2717,X2714),X2716)) = c_Rings_Oinverse__class_Odivide(X2717,X2715,X2714) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_1970,plain,
    ! [X4912,X4913,X4914,X4915] :
      ( ( c_Power_Opower__class_Opower(X4915,X4914,X4913) != c_Power_Opower__class_Opower(X4915,X4914,X4912)
        | X4913 = X4912
        | ~ c_Orderings_Oord__class_Oless(X4915,c_Groups_Oone__class_Oone(X4915),X4914)
        | ~ class_Rings_Olinordered__semidom(X4915) )
      & ( X4913 != X4912
        | c_Power_Opower__class_Opower(X4915,X4914,X4913) = c_Power_Opower__class_Opower(X4915,X4914,X4912)
        | ~ c_Orderings_Oord__class_Oless(X4915,c_Groups_Oone__class_Oone(X4915),X4914)
        | ~ class_Rings_Olinordered__semidom(X4915) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).

fof(i_0_1971,plain,
    ! [X4906,X4907,X4908] :
      ( ~ class_Rings_Olinordered__semidom(X4908)
      | ~ c_Orderings_Oord__class_Oless__eq(X4908,c_Groups_Oone__class_Oone(X4908),X4907)
      | c_Orderings_Oord__class_Oless__eq(X4908,c_Groups_Oone__class_Oone(X4908),c_Power_Opower__class_Opower(X4908,X4907,X4906)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).

fof(i_0_1972,plain,
    ! [X4896,X4897,X4898] :
      ( ~ class_Rings_Olinordered__semidom(X4898)
      | ~ c_Orderings_Oord__class_Oless__eq(X4898,c_Groups_Ozero__class_Ozero(X4898),X4897)
      | c_Orderings_Oord__class_Oless__eq(X4898,c_Groups_Ozero__class_Ozero(X4898),c_Power_Opower__class_Opower(X4898,X4897,X4896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).

fof(i_0_1973,plain,
    ! [X4903,X4904,X4905] :
      ( ~ class_Rings_Olinordered__semidom(X4905)
      | ~ c_Orderings_Oord__class_Oless(X4905,c_Groups_Ozero__class_Ozero(X4905),X4904)
      | c_Orderings_Oord__class_Oless(X4905,c_Groups_Ozero__class_Ozero(X4905),c_Power_Opower__class_Opower(X4905,X4904,X4903)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(i_0_1974,plain,
    ! [X3793] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3793))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3793)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3793) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3793)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3793))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3793) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__iff])])]) ).

fof(i_0_1975,plain,
    ! [X3792] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3792))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3792)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__imp__ge__one])]) ).

fof(i_0_1976,plain,
    ! [X3790] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3790))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3790)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3790) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3790)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3790))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3790) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__iff])])]) ).

fof(i_0_1977,plain,
    ! [X3786] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3786))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3786)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3786) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__imp__gt__one])]) ).

fof(i_0_1978,plain,
    ! [X3788] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3788),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3788,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3788) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3788,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3788),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3788) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__zero__iff])])]) ).

fof(i_0_1979,plain,
    ! [X2705,X2706,X2707,X2708,X2709] :
      ( ( c_Rings_Oinverse__class_Odivide(X2709,X2706,X2708) != c_Rings_Oinverse__class_Odivide(X2709,X2705,X2707)
        | hAPP(c_Groups_Otimes__class_Otimes(X2709,X2706),X2707) = hAPP(c_Groups_Otimes__class_Otimes(X2709,X2705),X2708)
        | X2707 = c_Groups_Ozero__class_Ozero(X2709)
        | X2708 = c_Groups_Ozero__class_Ozero(X2709)
        | ~ class_Fields_Ofield(X2709) )
      & ( hAPP(c_Groups_Otimes__class_Otimes(X2709,X2706),X2707) != hAPP(c_Groups_Otimes__class_Otimes(X2709,X2705),X2708)
        | c_Rings_Oinverse__class_Odivide(X2709,X2706,X2708) = c_Rings_Oinverse__class_Odivide(X2709,X2705,X2707)
        | X2707 = c_Groups_Ozero__class_Ozero(X2709)
        | X2708 = c_Groups_Ozero__class_Ozero(X2709)
        | ~ class_Fields_Ofield(X2709) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

fof(i_0_1980,plain,
    ! [X4515] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4515,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4515),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4515),X4515))),
    inference(variable_rename,[status(thm)],[fact_le__cube]) ).

fof(i_0_1981,plain,
    ! [X3680,X3681] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3681,c_Rings_Oinverse__class_Oinverse(X3681,X3680),c_Groups_Oone__class_Oone(X3681))
        | c_Orderings_Oord__class_Oless__eq(X3681,X3680,c_Groups_Ozero__class_Ozero(X3681))
        | c_Orderings_Oord__class_Oless__eq(X3681,c_Groups_Oone__class_Oone(X3681),X3680)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3681) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3681,X3680,c_Groups_Ozero__class_Ozero(X3681))
        | c_Orderings_Oord__class_Oless__eq(X3681,c_Rings_Oinverse__class_Oinverse(X3681,X3680),c_Groups_Oone__class_Oone(X3681))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3681) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3681,c_Groups_Oone__class_Oone(X3681),X3680)
        | c_Orderings_Oord__class_Oless__eq(X3681,c_Rings_Oinverse__class_Oinverse(X3681,X3680),c_Groups_Oone__class_Oone(X3681))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__1__iff])])]) ).

fof(i_0_1982,plain,
    ! [X3306,X3307] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3307,c_Rings_Oinverse__class_Oinverse(X3307,X3306),c_Groups_Oone__class_Oone(X3307))
        | c_Orderings_Oord__class_Oless__eq(X3307,X3306,c_Groups_Ozero__class_Ozero(X3307))
        | c_Orderings_Oord__class_Oless(X3307,c_Groups_Oone__class_Oone(X3307),X3306)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3307) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3307,X3306,c_Groups_Ozero__class_Ozero(X3307))
        | c_Orderings_Oord__class_Oless(X3307,c_Rings_Oinverse__class_Oinverse(X3307,X3306),c_Groups_Oone__class_Oone(X3307))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3307) )
      & ( ~ c_Orderings_Oord__class_Oless(X3307,c_Groups_Oone__class_Oone(X3307),X3306)
        | c_Orderings_Oord__class_Oless(X3307,c_Rings_Oinverse__class_Oinverse(X3307,X3306),c_Groups_Oone__class_Oone(X3307))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3307) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__1__iff])])]) ).

fof(i_0_1983,plain,
    ! [X4280,X4281] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4281),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4280))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4281,X4280)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4281,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4281,X4280)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4281),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4280)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4281,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4281),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4280)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1394])])]) ).

fof(i_0_1984,plain,
    ! [X4057] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4057),X4057) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

fof(i_0_1985,plain,
    ! [X3862,X3863,X3864,X3865] :
      ( ( X3863 = c_Groups_Ozero__class_Ozero(X3865)
        | X3864 = hAPP(c_Groups_Otimes__class_Otimes(X3865,c_Int_Onumber__class_Onumber__of(X3865,X3862)),X3863)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) != c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) )
      & ( X3863 != c_Groups_Ozero__class_Ozero(X3865)
        | c_Int_Onumber__class_Onumber__of(X3865,X3862) = c_Groups_Ozero__class_Ozero(X3865)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) != c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) )
      & ( X3863 = c_Groups_Ozero__class_Ozero(X3865)
        | X3863 != c_Groups_Ozero__class_Ozero(X3865)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) = c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) )
      & ( c_Int_Onumber__class_Onumber__of(X3865,X3862) != c_Groups_Ozero__class_Ozero(X3865)
        | X3863 != c_Groups_Ozero__class_Ozero(X3865)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) = c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) )
      & ( X3863 = c_Groups_Ozero__class_Ozero(X3865)
        | X3864 != hAPP(c_Groups_Otimes__class_Otimes(X3865,c_Int_Onumber__class_Onumber__of(X3865,X3862)),X3863)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) = c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) )
      & ( c_Int_Onumber__class_Onumber__of(X3865,X3862) != c_Groups_Ozero__class_Ozero(X3865)
        | X3864 != hAPP(c_Groups_Otimes__class_Otimes(X3865,c_Int_Onumber__class_Onumber__of(X3865,X3862)),X3863)
        | c_Rings_Oinverse__class_Odivide(X3865,X3864,X3863) = c_Int_Onumber__class_Onumber__of(X3865,X3862)
        | ~ class_Fields_Ofield__inverse__zero(X3865)
        | ~ class_Int_Onumber(X3865) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).

fof(i_0_1986,plain,
    ! [X3858,X3859,X3860,X3861] :
      ( ( X3858 = c_Groups_Ozero__class_Ozero(X3861)
        | hAPP(c_Groups_Otimes__class_Otimes(X3861,c_Int_Onumber__class_Onumber__of(X3861,X3860)),X3858) = X3859
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) != c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) )
      & ( X3858 != c_Groups_Ozero__class_Ozero(X3861)
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) = c_Groups_Ozero__class_Ozero(X3861)
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) != c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) )
      & ( X3858 = c_Groups_Ozero__class_Ozero(X3861)
        | X3858 != c_Groups_Ozero__class_Ozero(X3861)
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) = c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) )
      & ( c_Int_Onumber__class_Onumber__of(X3861,X3860) != c_Groups_Ozero__class_Ozero(X3861)
        | X3858 != c_Groups_Ozero__class_Ozero(X3861)
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) = c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) )
      & ( X3858 = c_Groups_Ozero__class_Ozero(X3861)
        | hAPP(c_Groups_Otimes__class_Otimes(X3861,c_Int_Onumber__class_Onumber__of(X3861,X3860)),X3858) != X3859
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) = c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) )
      & ( c_Int_Onumber__class_Onumber__of(X3861,X3860) != c_Groups_Ozero__class_Ozero(X3861)
        | hAPP(c_Groups_Otimes__class_Otimes(X3861,c_Int_Onumber__class_Onumber__of(X3861,X3860)),X3858) != X3859
        | c_Int_Onumber__class_Onumber__of(X3861,X3860) = c_Rings_Oinverse__class_Odivide(X3861,X3859,X3858)
        | ~ class_Fields_Ofield__inverse__zero(X3861)
        | ~ class_Int_Onumber(X3861) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).

fof(i_0_1987,plain,
    ! [X3787] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3787)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3787,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3787),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__zero])]) ).

fof(i_0_1988,plain,
    ! [X4086] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4086)
      | 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),X4086)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

cnf(i_0_1989,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,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1395]) ).

cnf(i_0_1990,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1396]) ).

cnf(i_0_1991,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_1397]) ).

cnf(i_0_1992,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_1398]) ).

fof(i_0_1993,plain,
    ! [X2783,X2784] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2784),X2783),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2784),X2784)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2783,X2784),
    inference(variable_rename,[status(thm)],[fact_real__divide__square__eq]) ).

cnf(i_0_1994,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_1386]) ).

fof(i_0_1995,plain,
    ! [X4859,X4860] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4860)
      | 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,X4860,X4859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).

fof(i_0_1996,plain,
    ! [X4087,X4088] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4088,X4087)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4088,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4087) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

fof(i_0_1997,plain,
    ! [X4461,X4462] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4462,X4461),X4462),
    inference(variable_rename,[status(thm)],[i_0_1399]) ).

fof(i_0_1998,plain,
    ! [X4459,X4460] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4460,X4459),X4459),
    inference(variable_rename,[status(thm)],[i_0_1400]) ).

fof(i_0_1999,plain,
    ! [X2578,X2579,X2580,X2581] :
      ( ~ class_Rings_Ocomm__semiring__1(X2581)
      | hAPP(c_Groups_Otimes__class_Otimes(X2581,X2580),hAPP(c_Groups_Otimes__class_Otimes(X2581,X2579),X2578)) = hAPP(c_Groups_Otimes__class_Otimes(X2581,X2579),hAPP(c_Groups_Otimes__class_Otimes(X2581,X2580),X2578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).

fof(i_0_2000,plain,
    ! [X4297,X4298] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4298,c_Int_OPls)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4298)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4297)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4298,c_Int_OPls)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4298)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4297)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4298),X4297)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1401])]) ).

fof(i_0_2001,plain,
    ! [X3169,X3170,X3171,X3172,X3173] :
      ( ~ class_Orderings_Oord(X3173)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3172,X3173),X3171,X3170)
      | c_Orderings_Oord__class_Oless__eq(X3173,hAPP(X3171,X3169),hAPP(X3170,X3169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_2002,plain,
    ! [X3131,X3132,X3133,X3134,X3135] :
      ( ~ class_Orderings_Oord(X3135)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3134,X3135),X3133,X3132)
      | c_Orderings_Oord__class_Oless__eq(X3135,hAPP(X3133,X3131),hAPP(X3132,X3131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_2003,plain,
    ! [X4572,X4573,X4574] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4574,X4573)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4574,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4573,X4572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_2004,plain,
    ! [X4486,X4487,X4488] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4488,X4487)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4488,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4487,X4486)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_2005,plain,
    ! [X4569,X4570,X4571] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4571,X4570)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4571,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4569,X4570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_2006,plain,
    ! [X4489,X4490,X4491] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4491,X4490)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4491,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4489,X4490)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_2007,plain,
    ! [X4578,X4579,X4580] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4580,X4579)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4580,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4579,X4578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_2008,plain,
    ! [X4453,X4454,X4455] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4455,X4454)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4455,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4454,X4453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_2009,plain,
    ! [X4575,X4576,X4577] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4577,X4576)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4577,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4575,X4576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_2010,plain,
    ! [X4450,X4451,X4452] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4452,X4451)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4452,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4450,X4451)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_2011,plain,
    ! [X3916,X3917] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3917),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3916))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3917,X3916) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3917,X3916)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3917),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3916)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__le__cancel__iff])]) ).

fof(i_0_2012,plain,
    ! [X4033,X4034] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4034),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4033))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4034,X4033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__less__cancel])]) ).

fof(i_0_2013,plain,
    ! [X4031,X4032] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4032),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4031))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4032,X4031) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4032,X4031)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4032),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4031)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__less__cancel__iff])]) ).

cnf(i_0_2014,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_1390]) ).

cnf(i_0_2015,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_1391]) ).

cnf(i_0_2016,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_1388]) ).

cnf(i_0_2017,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_1389]) ).

fof(i_0_2018,plain,
    ! [X3840,X3841,X3842] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3842,c_Int_Onumber__class_Onumber__of(X3842,X3841),c_Int_Onumber__class_Onumber__of(X3842,X3840))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3841,X3840)
        | ~ class_Int_Onumber__ring(X3842)
        | ~ class_Rings_Olinordered__idom(X3842) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3841,X3840)
        | c_Orderings_Oord__class_Oless__eq(X3842,c_Int_Onumber__class_Onumber__of(X3842,X3841),c_Int_Onumber__class_Onumber__of(X3842,X3840))
        | ~ class_Int_Onumber__ring(X3842)
        | ~ class_Rings_Olinordered__idom(X3842) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_2019,plain,
    ! [X3821,X3822,X3823] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3823,c_Int_Onumber__class_Onumber__of(X3823,X3822),c_Int_Onumber__class_Onumber__of(X3823,X3821))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3822,X3821)
        | ~ class_Int_Onumber__ring(X3823)
        | ~ class_Rings_Olinordered__idom(X3823) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3822,X3821)
        | c_Orderings_Oord__class_Oless(X3823,c_Int_Onumber__class_Onumber__of(X3823,X3822),c_Int_Onumber__class_Onumber__of(X3823,X3821))
        | ~ class_Int_Onumber__ring(X3823)
        | ~ class_Rings_Olinordered__idom(X3823) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_2020,plain,
    ! [X3158,X3159,X3160,X3161] :
      ( ~ class_Orderings_Opreorder(X3161)
      | ~ c_Orderings_Oord__class_Oless__eq(X3161,X3160,X3159)
      | ~ c_Orderings_Oord__class_Oless__eq(X3161,X3159,X3158)
      | c_Orderings_Oord__class_Oless__eq(X3161,X3160,X3158) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_2021,plain,
    ! [X3165,X3166,X3167,X3168] :
      ( ~ class_Orderings_Oorder(X3168)
      | ~ c_Orderings_Oord__class_Oless__eq(X3168,X3167,X3166)
      | ~ c_Orderings_Oord__class_Oless__eq(X3168,X3165,X3167)
      | c_Orderings_Oord__class_Oless__eq(X3168,X3165,X3166) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_2022,plain,
    ! [X3257,X3258,X3259,X3260] :
      ( ~ class_Orderings_Opreorder(X3260)
      | ~ c_Orderings_Oord__class_Oless(X3260,X3259,X3258)
      | ~ c_Orderings_Oord__class_Oless__eq(X3260,X3258,X3257)
      | c_Orderings_Oord__class_Oless(X3260,X3259,X3257) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_2023,plain,
    ! [X3249,X3250,X3251,X3252] :
      ( ~ class_Orderings_Opreorder(X3252)
      | ~ c_Orderings_Oord__class_Oless__eq(X3252,X3251,X3250)
      | ~ c_Orderings_Oord__class_Oless(X3252,X3250,X3249)
      | c_Orderings_Oord__class_Oless(X3252,X3251,X3249) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_2024,plain,
    ! [X3187,X3188,X3189,X3190] :
      ( ~ class_Orderings_Opreorder(X3190)
      | ~ c_Orderings_Oord__class_Oless(X3190,X3189,X3188)
      | ~ c_Orderings_Oord__class_Oless(X3190,X3188,X3187)
      | c_Orderings_Oord__class_Oless(X3190,X3189,X3187) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_2025,plain,
    ! [X3253,X3254,X3255,X3256] :
      ( ~ class_Orderings_Oorder(X3256)
      | ~ c_Orderings_Oord__class_Oless(X3256,X3255,X3254)
      | ~ c_Orderings_Oord__class_Oless__eq(X3256,X3253,X3255)
      | c_Orderings_Oord__class_Oless(X3256,X3253,X3254) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_2026,plain,
    ! [X3245,X3246,X3247,X3248] :
      ( ~ class_Orderings_Oorder(X3248)
      | ~ c_Orderings_Oord__class_Oless__eq(X3248,X3247,X3246)
      | ~ c_Orderings_Oord__class_Oless(X3248,X3245,X3247)
      | c_Orderings_Oord__class_Oless(X3248,X3245,X3246) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_2027,plain,
    ! [X3183,X3184,X3185,X3186] :
      ( ~ class_Orderings_Oorder(X3186)
      | ~ c_Orderings_Oord__class_Oless(X3186,X3185,X3184)
      | ~ c_Orderings_Oord__class_Oless(X3186,X3183,X3185)
      | c_Orderings_Oord__class_Oless(X3186,X3183,X3184) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_2028,plain,
    ! [X3994,X3995,X3996] :
      ( ~ class_Groups_Oab__group__add(X3996)
      | c_Groups_Ouminus__class_Ouminus(X3996,c_Groups_Oplus__class_Oplus(X3996,X3995,X3994)) = c_Groups_Oplus__class_Oplus(X3996,c_Groups_Ouminus__class_Ouminus(X3996,X3995),c_Groups_Ouminus__class_Ouminus(X3996,X3994)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_2029,plain,
    ! [X3991,X3992,X3993] :
      ( ~ class_Groups_Ogroup__add(X3993)
      | c_Groups_Ouminus__class_Ouminus(X3993,c_Groups_Oplus__class_Oplus(X3993,X3992,X3991)) = c_Groups_Oplus__class_Oplus(X3993,c_Groups_Ouminus__class_Ouminus(X3993,X3991),c_Groups_Ouminus__class_Ouminus(X3993,X3992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

fof(i_0_2030,plain,
    ! [X3815,X3816,X3817] :
      ( ~ class_Int_Onumber__ring(X3817)
      | c_Groups_Oplus__class_Oplus(X3817,c_Int_Onumber__class_Onumber__of(X3817,X3816),c_Int_Onumber__class_Onumber__of(X3817,X3815)) = c_Int_Onumber__class_Onumber__of(X3817,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3816,X3815)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_2031,plain,
    ! [X3818,X3819,X3820] :
      ( ~ class_Int_Onumber__ring(X3820)
      | c_Int_Onumber__class_Onumber__of(X3820,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3819,X3818)) = c_Groups_Oplus__class_Oplus(X3820,c_Int_Onumber__class_Onumber__of(X3820,X3819),c_Int_Onumber__class_Onumber__of(X3820,X3818)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_2032,plain,
    ! [X3946,X3947,X3948] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3948,c_Groups_Ouminus__class_Ouminus(X3948,X3947),c_Groups_Ouminus__class_Ouminus(X3948,X3946))
        | c_Orderings_Oord__class_Oless__eq(X3948,X3946,X3947)
        | ~ class_Lattices_Oboolean__algebra(X3948) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3948,X3946,X3947)
        | c_Orderings_Oord__class_Oless__eq(X3948,c_Groups_Ouminus__class_Ouminus(X3948,X3947),c_Groups_Ouminus__class_Ouminus(X3948,X3946))
        | ~ class_Lattices_Oboolean__algebra(X3948) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_2033,plain,
    ! [X3937,X3938,X3939] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3939,c_Groups_Ouminus__class_Ouminus(X3939,X3938),c_Groups_Ouminus__class_Ouminus(X3939,X3937))
        | c_Orderings_Oord__class_Oless__eq(X3939,X3937,X3938)
        | ~ class_Groups_Oordered__ab__group__add(X3939) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3939,X3937,X3938)
        | c_Orderings_Oord__class_Oless__eq(X3939,c_Groups_Ouminus__class_Ouminus(X3939,X3938),c_Groups_Ouminus__class_Ouminus(X3939,X3937))
        | ~ class_Groups_Oordered__ab__group__add(X3939) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_2034,plain,
    ! [X3949,X3950,X3951] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3951,c_Groups_Ouminus__class_Ouminus(X3951,X3950),c_Groups_Ouminus__class_Ouminus(X3951,X3949))
        | c_Orderings_Oord__class_Oless(X3951,X3949,X3950)
        | ~ class_Groups_Oordered__ab__group__add(X3951) )
      & ( ~ c_Orderings_Oord__class_Oless(X3951,X3949,X3950)
        | c_Orderings_Oord__class_Oless(X3951,c_Groups_Ouminus__class_Ouminus(X3951,X3950),c_Groups_Ouminus__class_Ouminus(X3951,X3949))
        | ~ class_Groups_Oordered__ab__group__add(X3951) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_2035,plain,
    ! [X3854,X3855,X3856,X3857] :
      ( ( c_Int_Onumber__class_Onumber__of(X3857,X3854) = c_Groups_Ozero__class_Ozero(X3857)
        | hAPP(c_Groups_Otimes__class_Otimes(X3857,X3856),c_Int_Onumber__class_Onumber__of(X3857,X3854)) = X3855
        | X3856 != c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) )
      & ( c_Int_Onumber__class_Onumber__of(X3857,X3854) != c_Groups_Ozero__class_Ozero(X3857)
        | X3856 = c_Groups_Ozero__class_Ozero(X3857)
        | X3856 != c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) )
      & ( c_Int_Onumber__class_Onumber__of(X3857,X3854) = c_Groups_Ozero__class_Ozero(X3857)
        | c_Int_Onumber__class_Onumber__of(X3857,X3854) != c_Groups_Ozero__class_Ozero(X3857)
        | X3856 = c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) )
      & ( X3856 != c_Groups_Ozero__class_Ozero(X3857)
        | c_Int_Onumber__class_Onumber__of(X3857,X3854) != c_Groups_Ozero__class_Ozero(X3857)
        | X3856 = c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) )
      & ( c_Int_Onumber__class_Onumber__of(X3857,X3854) = c_Groups_Ozero__class_Ozero(X3857)
        | hAPP(c_Groups_Otimes__class_Otimes(X3857,X3856),c_Int_Onumber__class_Onumber__of(X3857,X3854)) != X3855
        | X3856 = c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) )
      & ( X3856 != c_Groups_Ozero__class_Ozero(X3857)
        | hAPP(c_Groups_Otimes__class_Otimes(X3857,X3856),c_Int_Onumber__class_Onumber__of(X3857,X3854)) != X3855
        | X3856 = c_Rings_Oinverse__class_Odivide(X3857,X3855,c_Int_Onumber__class_Onumber__of(X3857,X3854))
        | ~ class_Fields_Ofield__inverse__zero(X3857)
        | ~ class_Int_Onumber(X3857) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).

fof(i_0_2036,plain,
    ! [X3866,X3867,X3868,X3869] :
      ( ( c_Int_Onumber__class_Onumber__of(X3869,X3867) = c_Groups_Ozero__class_Ozero(X3869)
        | X3868 = hAPP(c_Groups_Otimes__class_Otimes(X3869,X3866),c_Int_Onumber__class_Onumber__of(X3869,X3867))
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) != X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) )
      & ( c_Int_Onumber__class_Onumber__of(X3869,X3867) != c_Groups_Ozero__class_Ozero(X3869)
        | X3866 = c_Groups_Ozero__class_Ozero(X3869)
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) != X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) )
      & ( c_Int_Onumber__class_Onumber__of(X3869,X3867) = c_Groups_Ozero__class_Ozero(X3869)
        | c_Int_Onumber__class_Onumber__of(X3869,X3867) != c_Groups_Ozero__class_Ozero(X3869)
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) = X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) )
      & ( X3866 != c_Groups_Ozero__class_Ozero(X3869)
        | c_Int_Onumber__class_Onumber__of(X3869,X3867) != c_Groups_Ozero__class_Ozero(X3869)
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) = X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) )
      & ( c_Int_Onumber__class_Onumber__of(X3869,X3867) = c_Groups_Ozero__class_Ozero(X3869)
        | X3868 != hAPP(c_Groups_Otimes__class_Otimes(X3869,X3866),c_Int_Onumber__class_Onumber__of(X3869,X3867))
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) = X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) )
      & ( X3866 != c_Groups_Ozero__class_Ozero(X3869)
        | X3868 != hAPP(c_Groups_Otimes__class_Otimes(X3869,X3866),c_Int_Onumber__class_Onumber__of(X3869,X3867))
        | c_Rings_Oinverse__class_Odivide(X3869,X3868,c_Int_Onumber__class_Onumber__of(X3869,X3867)) = X3866
        | ~ class_Fields_Ofield__inverse__zero(X3869)
        | ~ class_Int_Onumber(X3869) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).

fof(i_0_2037,plain,
    ! [X3581,X3582,X3583] :
      ( ~ class_Rings_Odivision__ring(X3583)
      | X3582 = c_Groups_Ozero__class_Ozero(X3583)
      | X3581 = c_Groups_Ozero__class_Ozero(X3583)
      | c_Rings_Oinverse__class_Oinverse(X3583,hAPP(c_Groups_Otimes__class_Otimes(X3583,X3582),X3581)) = hAPP(c_Groups_Otimes__class_Otimes(X3583,c_Rings_Oinverse__class_Oinverse(X3583,X3581)),c_Rings_Oinverse__class_Oinverse(X3583,X3582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).

fof(i_0_2038,plain,
    ! [X5002,X5003,X5004] :
      ( ~ class_Rings_Olinordered__idom(X5004)
      | c_Orderings_Oord__class_Oless__eq(X5004,c_Groups_Ozero__class_Ozero(X5004),c_Power_Opower__class_Opower(X5004,c_Groups_Oabs__class_Oabs(X5004,X5003),X5002)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).

fof(i_0_2039,plain,
    ! [X2842,X2843] :
      ( ~ class_Rings_Olinordered__ring(X2843)
      | ~ c_Orderings_Oord__class_Oless(X2843,hAPP(c_Groups_Otimes__class_Otimes(X2843,X2842),X2842),c_Groups_Ozero__class_Ozero(X2843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1402])]) ).

fof(i_0_2040,plain,
    ! [X3988,X3989,X3990] :
      ( ~ class_Groups_Ogroup__add(X3990)
      | c_Groups_Oplus__class_Oplus(X3990,X3989,c_Groups_Oplus__class_Oplus(X3990,c_Groups_Ouminus__class_Ouminus(X3990,X3989),X3988)) = X3988 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_2041,plain,
    ! [X4399,X4400,X4401] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4401,X4400)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4400,X4399)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4401,X4399) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_2042,plain,
    ! [X4037,X4038,X4039] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4039,X4038)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4038,X4037)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4039,X4037) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_2043,plain,
    ! [X2865,X2866,X2867] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2867,X2866)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2866,X2865)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2867,X2865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).

fof(i_0_2044,plain,
    ! [X3780,X3781] :
      ( ( hAPP(c_Transcendental_Oln,X3781) != hAPP(c_Transcendental_Oln,X3780)
        | X3781 = X3780
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3780)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3781) )
      & ( X3781 != X3780
        | hAPP(c_Transcendental_Oln,X3781) = hAPP(c_Transcendental_Oln,X3780)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3780)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3781) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__inj__iff])])]) ).

cnf(i_0_2045,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1403]) ).

fof(i_0_2046,plain,
    ! [X3546,X3547,X3548] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(X3548)
      | c_Groups_Osgn__class_Osgn(X3548,hAPP(c_Groups_Otimes__class_Otimes(X3548,X3547),X3546)) = hAPP(c_Groups_Otimes__class_Otimes(X3548,c_Groups_Osgn__class_Osgn(X3548,X3547)),c_Groups_Osgn__class_Osgn(X3548,X3546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__mult])]) ).

fof(i_0_2047,plain,
    ! [X3549,X3550,X3551] :
      ( ~ class_Rings_Olinordered__idom(X3551)
      | c_Groups_Osgn__class_Osgn(X3551,hAPP(c_Groups_Otimes__class_Otimes(X3551,X3550),X3549)) = hAPP(c_Groups_Otimes__class_Otimes(X3551,c_Groups_Osgn__class_Osgn(X3551,X3550)),c_Groups_Osgn__class_Osgn(X3551,X3549)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_2048,plain,
    ! [X3395,X3396,X3397] :
      ( ~ class_Fields_Ofield__inverse__zero(X3397)
      | c_Rings_Oinverse__class_Oinverse(X3397,hAPP(c_Groups_Otimes__class_Otimes(X3397,X3396),X3395)) = hAPP(c_Groups_Otimes__class_Otimes(X3397,c_Rings_Oinverse__class_Oinverse(X3397,X3396)),c_Rings_Oinverse__class_Oinverse(X3397,X3395)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib])]) ).

fof(i_0_2049,plain,
    ! [X3934,X3935,X3936] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3936,c_Groups_Ouminus__class_Ouminus(X3936,X3935),X3934)
        | c_Orderings_Oord__class_Oless__eq(X3936,c_Groups_Ouminus__class_Ouminus(X3936,X3934),X3935)
        | ~ class_Groups_Oordered__ab__group__add(X3936) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3936,c_Groups_Ouminus__class_Ouminus(X3936,X3934),X3935)
        | c_Orderings_Oord__class_Oless__eq(X3936,c_Groups_Ouminus__class_Ouminus(X3936,X3935),X3934)
        | ~ class_Groups_Oordered__ab__group__add(X3936) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_2050,plain,
    ! [X3952,X3953,X3954] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3954,c_Groups_Ouminus__class_Ouminus(X3954,X3953),X3952)
        | c_Orderings_Oord__class_Oless(X3954,c_Groups_Ouminus__class_Ouminus(X3954,X3952),X3953)
        | ~ class_Groups_Oordered__ab__group__add(X3954) )
      & ( ~ c_Orderings_Oord__class_Oless(X3954,c_Groups_Ouminus__class_Ouminus(X3954,X3952),X3953)
        | c_Orderings_Oord__class_Oless(X3954,c_Groups_Ouminus__class_Ouminus(X3954,X3953),X3952)
        | ~ class_Groups_Oordered__ab__group__add(X3954) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_2051,plain,
    ! [X3931,X3932,X3933] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3933,X3932,c_Groups_Ouminus__class_Ouminus(X3933,X3931))
        | c_Orderings_Oord__class_Oless__eq(X3933,X3931,c_Groups_Ouminus__class_Ouminus(X3933,X3932))
        | ~ class_Groups_Oordered__ab__group__add(X3933) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3933,X3931,c_Groups_Ouminus__class_Ouminus(X3933,X3932))
        | c_Orderings_Oord__class_Oless__eq(X3933,X3932,c_Groups_Ouminus__class_Ouminus(X3933,X3931))
        | ~ class_Groups_Oordered__ab__group__add(X3933) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_2052,plain,
    ! [X3955,X3956,X3957] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3957,X3956,c_Groups_Ouminus__class_Ouminus(X3957,X3955))
        | c_Orderings_Oord__class_Oless(X3957,X3955,c_Groups_Ouminus__class_Ouminus(X3957,X3956))
        | ~ class_Groups_Oordered__ab__group__add(X3957) )
      & ( ~ c_Orderings_Oord__class_Oless(X3957,X3955,c_Groups_Ouminus__class_Ouminus(X3957,X3956))
        | c_Orderings_Oord__class_Oless(X3957,X3956,c_Groups_Ouminus__class_Ouminus(X3957,X3955))
        | ~ class_Groups_Oordered__ab__group__add(X3957) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_2053,plain,
    ! [X3899,X3900] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3900),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3899)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3900,X3899)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

cnf(i_0_2054,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X1)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
    inference(split_conjunct,[status(thm)],[i_0_1404]) ).

fof(i_0_2055,plain,
    ! [X4233,X4234] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4234,X4233)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4234),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4233)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_2056,plain,
    ! [X4702,X4703] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4703,X4702)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4703),hAPP(c_NthRoot_Osqrt,X4702)),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__divide]) ).

fof(i_0_2057,plain,
    ! [X4929,X4930,X4931] :
      ( ~ class_Rings_Odivision__ring(X4931)
      | X4930 = c_Groups_Ozero__class_Ozero(X4931)
      | c_Rings_Oinverse__class_Oinverse(X4931,c_Power_Opower__class_Opower(X4931,X4930,X4929)) = c_Power_Opower__class_Opower(X4931,c_Rings_Oinverse__class_Oinverse(X4931,X4930),X4929) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse])]) ).

fof(i_0_2058,plain,
    ! [X4145,X4146,X4147] :
      ( ~ class_Rings_Odivision__ring(X4147)
      | X4146 = c_Groups_Ozero__class_Ozero(X4147)
      | c_Groups_Ouminus__class_Ouminus(X4147,c_Rings_Oinverse__class_Odivide(X4147,X4145,X4146)) = c_Rings_Oinverse__class_Odivide(X4147,X4145,c_Groups_Ouminus__class_Ouminus(X4147,X4146)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

fof(i_0_2059,plain,
    ! [X3834,X3835,X3836] :
      ( ~ class_Int_Onumber__ring(X3836)
      | hAPP(c_Groups_Otimes__class_Otimes(X3836,c_Int_Onumber__class_Onumber__of(X3836,X3835)),c_Int_Onumber__class_Onumber__of(X3836,X3834)) = c_Int_Onumber__class_Onumber__of(X3836,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3835),X3834)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_2060,plain,
    ! [X3837,X3838,X3839] :
      ( ~ class_Int_Onumber__ring(X3839)
      | c_Int_Onumber__class_Onumber__of(X3839,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3838),X3837)) = hAPP(c_Groups_Otimes__class_Otimes(X3839,c_Int_Onumber__class_Onumber__of(X3839,X3838)),c_Int_Onumber__class_Onumber__of(X3839,X3837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_2061,plain,
    ! [X3573,X3574] :
      ( ~ class_Fields_Olinordered__field(X3574)
      | ~ c_Orderings_Oord__class_Oless(X3574,c_Groups_Ozero__class_Ozero(X3574),c_Rings_Oinverse__class_Oinverse(X3574,X3573))
      | X3573 = c_Groups_Ozero__class_Ozero(X3574)
      | c_Orderings_Oord__class_Oless(X3574,c_Groups_Ozero__class_Ozero(X3574),X3573) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).

fof(i_0_2062,plain,
    ! [X3563,X3564] :
      ( ~ class_Fields_Olinordered__field(X3564)
      | ~ c_Orderings_Oord__class_Oless(X3564,c_Rings_Oinverse__class_Oinverse(X3564,X3563),c_Groups_Ozero__class_Ozero(X3564))
      | X3563 = c_Groups_Ozero__class_Ozero(X3564)
      | c_Orderings_Oord__class_Oless(X3564,X3563,c_Groups_Ozero__class_Ozero(X3564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).

fof(i_0_2063,plain,
    ! [X3912,X3913] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3913),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3912))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3913,X3912) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3913,X3912)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3913),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3912)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_2064,plain,
    ! [X4692,X4693] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4693),hAPP(c_NthRoot_Osqrt,X4692))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4693,X4692) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4693,X4692)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4693),hAPP(c_NthRoot_Osqrt,X4692)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__iff])]) ).

fof(i_0_2065,plain,
    ! [X3901,X3902] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3902),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3901))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3902,X3901) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3902,X3901)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3902),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3901)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_2066,plain,
    ! [X4696,X4697] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4697),hAPP(c_NthRoot_Osqrt,X4696))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4697,X4696) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4697,X4696)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4697),hAPP(c_NthRoot_Osqrt,X4696)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__iff])]) ).

fof(i_0_2067,plain,
    ! [X4006,X4007,X4008] :
      ( ~ class_RealVector_Oreal__normed__field(X4008)
      | c_Rings_Oinverse__class_Odivide(X4008,c_Groups_Ouminus__class_Ouminus(X4008,X4007),X4006) = c_Groups_Ouminus__class_Ouminus(X4008,c_Rings_Oinverse__class_Odivide(X4008,X4007,X4006)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ominus])]) ).

fof(i_0_2068,plain,
    ! [X5005,X5006,X5007] :
      ( ~ class_Rings_Olinordered__idom(X5007)
      | c_Groups_Oabs__class_Oabs(X5007,c_Power_Opower__class_Opower(X5007,X5006,X5005)) = c_Power_Opower__class_Opower(X5007,c_Groups_Oabs__class_Oabs(X5007,X5006),X5005) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).

fof(i_0_2069,plain,
    ! [X3997,X3998,X3999] :
      ( ~ class_Rings_Odivision__ring(X3999)
      | c_Groups_Ouminus__class_Ouminus(X3999,c_Rings_Oinverse__class_Odivide(X3999,X3998,X3997)) = c_Rings_Oinverse__class_Odivide(X3999,c_Groups_Ouminus__class_Ouminus(X3999,X3998),X3997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_2070,plain,
    ! [X4891,X4892,X4893] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X4893)
      | c_Rings_Oinverse__class_Oinverse(X4893,c_Power_Opower__class_Opower(X4893,X4892,X4891)) = c_Power_Opower__class_Opower(X4893,c_Rings_Oinverse__class_Oinverse(X4893,X4892),X4891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inverse])]) ).

fof(i_0_2071,plain,
    ! [X4000,X4001,X4002] :
      ( ~ class_Fields_Ofield__inverse__zero(X4002)
      | c_Groups_Ouminus__class_Ouminus(X4002,c_Rings_Oinverse__class_Odivide(X4002,X4001,X4000)) = c_Rings_Oinverse__class_Odivide(X4002,X4001,c_Groups_Ouminus__class_Ouminus(X4002,X4000)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

cnf(i_0_2072,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).

fof(i_0_2073,plain,
    ! [X2726] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2726),X2726))
        | X2726 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X2726 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2726),X2726)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1405])]) ).

fof(i_0_2074,plain,
    ! [X4556,X4557,X4558] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4558),X4557) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4558),X4556)
        | X4557 = X4556
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4558) )
      & ( X4557 != X4556
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4558),X4557) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4558),X4556)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4558) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).

fof(i_0_2075,plain,
    ! [X4109,X4110] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ouminus__class_Ouminus(X4110,X4109),c_Groups_Ozero__class_Ozero(X4110))
        | c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ozero__class_Ozero(X4110),X4109)
        | ~ class_Groups_Oordered__ab__group__add(X4110) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ozero__class_Ozero(X4110),X4109)
        | c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ouminus__class_Ouminus(X4110,X4109),c_Groups_Ozero__class_Ozero(X4110))
        | ~ class_Groups_Oordered__ab__group__add(X4110) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_2076,plain,
    ! [X4117,X4118] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4118,c_Groups_Ouminus__class_Ouminus(X4118,X4117),c_Groups_Ozero__class_Ozero(X4118))
        | c_Orderings_Oord__class_Oless(X4118,c_Groups_Ozero__class_Ozero(X4118),X4117)
        | ~ class_Groups_Oordered__ab__group__add(X4118) )
      & ( ~ c_Orderings_Oord__class_Oless(X4118,c_Groups_Ozero__class_Ozero(X4118),X4117)
        | c_Orderings_Oord__class_Oless(X4118,c_Groups_Ouminus__class_Ouminus(X4118,X4117),c_Groups_Ozero__class_Ozero(X4118))
        | ~ class_Groups_Oordered__ab__group__add(X4118) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_2077,plain,
    ! [X3555,X3556] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Ozero__class_Ozero(X3556),c_Rings_Oinverse__class_Oinverse(X3556,X3555))
        | c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Ozero__class_Ozero(X3556),X3555)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3556) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Ozero__class_Ozero(X3556),X3555)
        | c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Ozero__class_Ozero(X3556),c_Rings_Oinverse__class_Oinverse(X3556,X3555))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3556) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative])])]) ).

fof(i_0_2078,plain,
    ! [X3666,X3667] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),c_Groups_Osgn__class_Osgn(X3667,X3666))
        | c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),X3666)
        | ~ class_Rings_Olinordered__idom(X3667) )
      & ( ~ c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),X3666)
        | c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),c_Groups_Osgn__class_Osgn(X3667,X3666))
        | ~ class_Rings_Olinordered__idom(X3667) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

fof(i_0_2079,plain,
    ! [X3579,X3580] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3580,c_Groups_Ozero__class_Ozero(X3580),c_Rings_Oinverse__class_Oinverse(X3580,X3579))
        | c_Orderings_Oord__class_Oless(X3580,c_Groups_Ozero__class_Ozero(X3580),X3579)
        | ~ class_Fields_Olinordered__field__inverse__zero(X3580) )
      & ( ~ c_Orderings_Oord__class_Oless(X3580,c_Groups_Ozero__class_Ozero(X3580),X3579)
        | c_Orderings_Oord__class_Oless(X3580,c_Groups_Ozero__class_Ozero(X3580),c_Rings_Oinverse__class_Oinverse(X3580,X3579))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3580) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).

fof(i_0_2080,plain,
    ! [X3553,X3554] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3554,c_Rings_Oinverse__class_Oinverse(X3554,X3553),c_Groups_Ozero__class_Ozero(X3554))
        | c_Orderings_Oord__class_Oless__eq(X3554,X3553,c_Groups_Ozero__class_Ozero(X3554))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3554) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3554,X3553,c_Groups_Ozero__class_Ozero(X3554))
        | c_Orderings_Oord__class_Oless__eq(X3554,c_Rings_Oinverse__class_Oinverse(X3554,X3553),c_Groups_Ozero__class_Ozero(X3554))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3554) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive])])]) ).

fof(i_0_2081,plain,
    ! [X3664,X3665] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3665,c_Groups_Osgn__class_Osgn(X3665,X3664),c_Groups_Ozero__class_Ozero(X3665))
        | c_Orderings_Oord__class_Oless(X3665,X3664,c_Groups_Ozero__class_Ozero(X3665))
        | ~ class_Rings_Olinordered__idom(X3665) )
      & ( ~ c_Orderings_Oord__class_Oless(X3665,X3664,c_Groups_Ozero__class_Ozero(X3665))
        | c_Orderings_Oord__class_Oless(X3665,c_Groups_Osgn__class_Osgn(X3665,X3664),c_Groups_Ozero__class_Ozero(X3665))
        | ~ class_Rings_Olinordered__idom(X3665) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_2082,plain,
    ! [X3577,X3578] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3578,c_Rings_Oinverse__class_Oinverse(X3578,X3577),c_Groups_Ozero__class_Ozero(X3578))
        | c_Orderings_Oord__class_Oless(X3578,X3577,c_Groups_Ozero__class_Ozero(X3578))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3578) )
      & ( ~ c_Orderings_Oord__class_Oless(X3578,X3577,c_Groups_Ozero__class_Ozero(X3578))
        | c_Orderings_Oord__class_Oless(X3578,c_Rings_Oinverse__class_Oinverse(X3578,X3577),c_Groups_Ozero__class_Ozero(X3578))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3578) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).

fof(i_0_2083,plain,
    ! [X4113,X4114] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4114,c_Groups_Ozero__class_Ozero(X4114),c_Groups_Ouminus__class_Ouminus(X4114,X4113))
        | c_Orderings_Oord__class_Oless__eq(X4114,X4113,c_Groups_Ozero__class_Ozero(X4114))
        | ~ class_Groups_Oordered__ab__group__add(X4114) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4114,X4113,c_Groups_Ozero__class_Ozero(X4114))
        | c_Orderings_Oord__class_Oless__eq(X4114,c_Groups_Ozero__class_Ozero(X4114),c_Groups_Ouminus__class_Ouminus(X4114,X4113))
        | ~ class_Groups_Oordered__ab__group__add(X4114) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_2084,plain,
    ! [X4119,X4120] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4120,c_Groups_Ozero__class_Ozero(X4120),c_Groups_Ouminus__class_Ouminus(X4120,X4119))
        | c_Orderings_Oord__class_Oless(X4120,X4119,c_Groups_Ozero__class_Ozero(X4120))
        | ~ class_Groups_Oordered__ab__group__add(X4120) )
      & ( ~ c_Orderings_Oord__class_Oless(X4120,X4119,c_Groups_Ozero__class_Ozero(X4120))
        | c_Orderings_Oord__class_Oless(X4120,c_Groups_Ozero__class_Ozero(X4120),c_Groups_Ouminus__class_Ouminus(X4120,X4119))
        | ~ class_Groups_Oordered__ab__group__add(X4120) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_2085,plain,
    ! [X3104,X3105,X3106] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3106,X3105,X3104)
        | ~ c_Orderings_Oord__class_Oless(X3106,X3105,X3104)
        | ~ class_Orderings_Opreorder(X3106) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3106,X3104,X3105)
        | ~ c_Orderings_Oord__class_Oless(X3106,X3105,X3104)
        | ~ class_Orderings_Opreorder(X3106) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3106,X3105,X3104)
        | c_Orderings_Oord__class_Oless__eq(X3106,X3104,X3105)
        | c_Orderings_Oord__class_Oless(X3106,X3105,X3104)
        | ~ class_Orderings_Opreorder(X3106) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])])]) ).

fof(i_0_2086,plain,
    ! [X4306,X4307] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4307,c_Groups_Ozero__class_Ozero(X4307),c_Int_Onumber__class_Onumber__of(X4307,X4306))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4306)
        | ~ class_Int_Onumber__ring(X4307)
        | ~ class_Rings_Olinordered__idom(X4307) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4306)
        | c_Orderings_Oord__class_Oless__eq(X4307,c_Groups_Ozero__class_Ozero(X4307),c_Int_Onumber__class_Onumber__of(X4307,X4306))
        | ~ class_Int_Onumber__ring(X4307)
        | ~ class_Rings_Olinordered__idom(X4307) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_2087,plain,
    ! [X4310,X4311] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4311,c_Groups_Ozero__class_Ozero(X4311),c_Int_Onumber__class_Onumber__of(X4311,X4310))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4310)
        | ~ class_Int_Onumber__ring(X4311)
        | ~ class_Rings_Olinordered__idom(X4311) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4310)
        | c_Orderings_Oord__class_Oless(X4311,c_Groups_Ozero__class_Ozero(X4311),c_Int_Onumber__class_Onumber__of(X4311,X4310))
        | ~ class_Int_Onumber__ring(X4311)
        | ~ class_Rings_Olinordered__idom(X4311) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_2088,plain,
    ! [X4308,X4309] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4309,c_Int_Onumber__class_Onumber__of(X4309,X4308),c_Groups_Ozero__class_Ozero(X4309))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4308,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X4309)
        | ~ class_Rings_Olinordered__idom(X4309) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4308,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(X4309,c_Int_Onumber__class_Onumber__of(X4309,X4308),c_Groups_Ozero__class_Ozero(X4309))
        | ~ class_Int_Onumber__ring(X4309)
        | ~ class_Rings_Olinordered__idom(X4309) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

fof(i_0_2089,plain,
    ! [X4312,X4313] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4313,c_Int_Onumber__class_Onumber__of(X4313,X4312),c_Groups_Ozero__class_Ozero(X4313))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4312,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X4313)
        | ~ class_Rings_Olinordered__idom(X4313) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4312,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(X4313,c_Int_Onumber__class_Onumber__of(X4313,X4312),c_Groups_Ozero__class_Ozero(X4313))
        | ~ class_Int_Onumber__ring(X4313)
        | ~ class_Rings_Olinordered__idom(X4313) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_2090,plain,
    ! [X3897,X3898] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3898,X3897)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3898),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__less__mono])]) ).

fof(i_0_2091,plain,
    ! [X3943,X3944,X3945] :
      ( ~ class_Lattices_Oboolean__algebra(X3945)
      | ~ c_Orderings_Oord__class_Oless__eq(X3945,X3944,X3943)
      | c_Orderings_Oord__class_Oless__eq(X3945,c_Groups_Ouminus__class_Ouminus(X3945,X3943),c_Groups_Ouminus__class_Ouminus(X3945,X3944)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_2092,plain,
    ! [X3940,X3941,X3942] :
      ( ~ class_Groups_Oordered__ab__group__add(X3942)
      | ~ c_Orderings_Oord__class_Oless__eq(X3942,X3941,X3940)
      | c_Orderings_Oord__class_Oless__eq(X3942,c_Groups_Ouminus__class_Ouminus(X3942,X3940),c_Groups_Ouminus__class_Ouminus(X3942,X3941)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

fof(i_0_2093,plain,
    ! [X4719] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4719)
      | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4719),X4719) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4719)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sqrt__divide__self__eq])]) ).

fof(i_0_2094,plain,
    ! [X3714] :
      ( ~ class_Rings_Olinordered__semidom(X3714)
      | c_Orderings_Oord__class_Oless(X3714,c_Groups_Ozero__class_Ozero(X3714),c_Groups_Oplus__class_Oplus(X3714,c_Groups_Oone__class_Oone(X3714),c_Groups_Oone__class_Oone(X3714))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_2095,plain,
    ! [X3985,X3986,X3987] :
      ( ~ class_Groups_Ogroup__add(X3987)
      | c_Groups_Oplus__class_Oplus(X3987,c_Groups_Ouminus__class_Ouminus(X3987,X3986),c_Groups_Oplus__class_Oplus(X3987,X3986,X3985)) = X3985 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_2096,plain,
    ! [X4177] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4177))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4177) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4177)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4177)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__exp__iff])]) ).

fof(i_0_2097,plain,
    ! [X4180] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4180))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4180) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4180)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4180)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__exp__iff])]) ).

fof(i_0_2098,plain,
    ! [X4176] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4176),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4176,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4176,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4176),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__le__one__iff])]) ).

fof(i_0_2099,plain,
    ! [X4179] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4179),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4179,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4179,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4179),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__less__one__iff])]) ).

fof(i_0_2100,plain,
    ! [X4107,X4108] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4108,c_Groups_Ouminus__class_Ouminus(X4108,X4107),X4107)
        | c_Orderings_Oord__class_Oless__eq(X4108,c_Groups_Ozero__class_Ozero(X4108),X4107)
        | ~ class_Groups_Olinordered__ab__group__add(X4108) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4108,c_Groups_Ozero__class_Ozero(X4108),X4107)
        | c_Orderings_Oord__class_Oless__eq(X4108,c_Groups_Ouminus__class_Ouminus(X4108,X4107),X4107)
        | ~ class_Groups_Olinordered__ab__group__add(X4108) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_2101,plain,
    ! [X4115,X4116] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4116,c_Groups_Ouminus__class_Ouminus(X4116,X4115),X4115)
        | c_Orderings_Oord__class_Oless(X4116,c_Groups_Ozero__class_Ozero(X4116),X4115)
        | ~ class_Groups_Olinordered__ab__group__add(X4116) )
      & ( ~ c_Orderings_Oord__class_Oless(X4116,c_Groups_Ozero__class_Ozero(X4116),X4115)
        | c_Orderings_Oord__class_Oless(X4116,c_Groups_Ouminus__class_Ouminus(X4116,X4115),X4115)
        | ~ class_Groups_Olinordered__ab__group__add(X4116) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).

fof(i_0_2102,plain,
    ! [X4111,X4112] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4112,X4111,c_Groups_Ouminus__class_Ouminus(X4112,X4111))
        | c_Orderings_Oord__class_Oless__eq(X4112,X4111,c_Groups_Ozero__class_Ozero(X4112))
        | ~ class_Groups_Olinordered__ab__group__add(X4112) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4112,X4111,c_Groups_Ozero__class_Ozero(X4112))
        | c_Orderings_Oord__class_Oless__eq(X4112,X4111,c_Groups_Ouminus__class_Ouminus(X4112,X4111))
        | ~ class_Groups_Olinordered__ab__group__add(X4112) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_2103,plain,
    ! [X4121,X4122] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4122,X4121,c_Groups_Ouminus__class_Ouminus(X4122,X4121))
        | c_Orderings_Oord__class_Oless(X4122,X4121,c_Groups_Ozero__class_Ozero(X4122))
        | ~ class_Rings_Olinordered__idom(X4122) )
      & ( ~ c_Orderings_Oord__class_Oless(X4122,X4121,c_Groups_Ozero__class_Ozero(X4122))
        | c_Orderings_Oord__class_Oless(X4122,X4121,c_Groups_Ouminus__class_Ouminus(X4122,X4121))
        | ~ class_Rings_Olinordered__idom(X4122) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_2104,plain,
    ! [X4729,X4730] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4730,X4729)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4730),X4729),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).

fof(i_0_2105,plain,
    ! [X4380,X4381,X4382] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,X4382)
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | X4382 = X4381
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4382,X4381) )
      & ( ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | X4382 = X4381
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4382,X4381) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,X4382)
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4382,X4381) )
      & ( ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4382,X4381) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,X4382)
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | X4382 = X4381
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382)) )
      & ( ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | X4382 = X4381
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,X4382)
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382)) )
      & ( ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382))
        | ~ hBOOL(hAPP(hAPP(X4380,X4381),X4382)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_2106,plain,
    ! [X3976,X3977,X3978] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3978)
      | hAPP(c_Groups_Otimes__class_Otimes(X3978,c_Groups_Ouminus__class_Ouminus(X3978,X3977)),X3976) = c_Groups_Ouminus__class_Ouminus(X3978,hAPP(c_Groups_Otimes__class_Otimes(X3978,X3977),X3976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).

fof(i_0_2107,plain,
    ! [X3973,X3974,X3975] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3975)
      | hAPP(c_Groups_Otimes__class_Otimes(X3975,c_Groups_Ouminus__class_Ouminus(X3975,X3974)),X3973) = c_Groups_Ouminus__class_Ouminus(X3975,hAPP(c_Groups_Otimes__class_Otimes(X3975,X3974),X3973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).

fof(i_0_2108,plain,
    ! [X3967,X3968,X3969] :
      ( ~ class_Rings_Oring(X3969)
      | c_Groups_Ouminus__class_Ouminus(X3969,hAPP(c_Groups_Otimes__class_Otimes(X3969,X3968),X3967)) = hAPP(c_Groups_Otimes__class_Otimes(X3969,c_Groups_Ouminus__class_Ouminus(X3969,X3968)),X3967) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_2109,plain,
    ! [X3571,X3572] :
      ( ~ class_Fields_Olinordered__field(X3572)
      | ~ c_Orderings_Oord__class_Oless(X3572,X3571,c_Groups_Ozero__class_Ozero(X3572))
      | c_Orderings_Oord__class_Oless(X3572,c_Rings_Oinverse__class_Oinverse(X3572,X3571),c_Groups_Ozero__class_Ozero(X3572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).

fof(i_0_2110,plain,
    ! [X3575,X3576] :
      ( ~ class_Fields_Olinordered__field(X3576)
      | ~ c_Orderings_Oord__class_Oless(X3576,c_Groups_Ozero__class_Ozero(X3576),X3575)
      | c_Orderings_Oord__class_Oless(X3576,c_Groups_Ozero__class_Ozero(X3576),c_Rings_Oinverse__class_Oinverse(X3576,X3575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).

fof(i_0_2111,plain,
    ! [X3903,X3904] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3904)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3903)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3904),X3903)),
    inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(i_0_2112,plain,
    ! [X4698,X4699] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4699),X4698)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4699)),hAPP(c_NthRoot_Osqrt,X4698)),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__mult]) ).

fof(i_0_2113,plain,
    ! [X3270,X3271,X3272] :
      ( ( c_Orderings_Oord__class_Oless(X3272,X3271,X3270)
        | X3271 = X3270
        | ~ c_Orderings_Oord__class_Oless__eq(X3272,X3271,X3270)
        | ~ class_Orderings_Olinorder(X3272) )
      & ( X3271 != X3270
        | ~ c_Orderings_Oord__class_Oless(X3272,X3271,X3270)
        | ~ c_Orderings_Oord__class_Oless__eq(X3272,X3271,X3270)
        | ~ class_Orderings_Olinorder(X3272) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1407])])]) ).

fof(i_0_2114,plain,
    ! [X4992,X4993] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4993,X4992)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X4993),hAPP(c_Transcendental_Oarctan,X4992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arctan__monotone_H])]) ).

fof(i_0_2115,plain,
    ! [X4690,X4691] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4691,X4690)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4691),hAPP(c_NthRoot_Osqrt,X4690)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__mono])]) ).

fof(i_0_2116,plain,
    ! [X4994,X4995] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4995,X4994)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X4995),hAPP(c_Transcendental_Oarctan,X4994)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arctan__monotone])]) ).

fof(i_0_2117,plain,
    ! [X4694,X4695] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4695,X4694)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4695),hAPP(c_NthRoot_Osqrt,X4694)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__mono])]) ).

fof(i_0_2118,plain,
    ! [X3401,X3402,X3403] :
      ( ~ class_Fields_Ofield__inverse__zero(X3403)
      | c_Rings_Oinverse__class_Oinverse(X3403,c_Rings_Oinverse__class_Odivide(X3403,X3402,X3401)) = c_Rings_Oinverse__class_Odivide(X3403,X3401,X3402) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__divide])]) ).

fof(i_0_2119,plain,
    ! [X3162,X3163,X3164] :
      ( ~ class_Orderings_Oorder(X3164)
      | ~ c_Orderings_Oord__class_Oless__eq(X3164,X3163,X3162)
      | ~ c_Orderings_Oord__class_Oless__eq(X3164,X3162,X3163)
      | X3162 = X3163 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_2120,plain,
    ! [X3155,X3156,X3157] :
      ( ~ class_Orderings_Oorder(X3157)
      | ~ c_Orderings_Oord__class_Oless__eq(X3157,X3156,X3155)
      | ~ c_Orderings_Oord__class_Oless__eq(X3157,X3155,X3156)
      | X3156 = X3155 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_2121,plain,
    ! [X3136,X3137,X3138] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3138,X3136,X3137)
        | X3136 = X3137
        | ~ c_Orderings_Oord__class_Oless__eq(X3138,X3137,X3136)
        | ~ class_Orderings_Oorder(X3138) )
      & ( X3136 != X3137
        | c_Orderings_Oord__class_Oless__eq(X3138,X3136,X3137)
        | ~ c_Orderings_Oord__class_Oless__eq(X3138,X3137,X3136)
        | ~ class_Orderings_Oorder(X3138) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_2122,plain,
    ! [X3125,X3126,X3127] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3127,X3126,X3125)
        | X3126 != X3125
        | ~ class_Orderings_Oorder(X3127) )
      & ( c_Orderings_Oord__class_Oless__eq(X3127,X3125,X3126)
        | X3126 != X3125
        | ~ class_Orderings_Oorder(X3127) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3127,X3126,X3125)
        | ~ c_Orderings_Oord__class_Oless__eq(X3127,X3125,X3126)
        | X3126 = X3125
        | ~ class_Orderings_Oorder(X3127) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_2123,plain,
    ! [X4686] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4686))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4686) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4686)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4686)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__1__iff])]) ).

fof(i_0_2124,plain,
    ! [X4710] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4710))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4710) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4710)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4710)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff])]) ).

fof(i_0_2125,plain,
    ! [X4685] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4685))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4685) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4685)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4685)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__1__iff])]) ).

fof(i_0_2126,plain,
    ! [X4709] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4709))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4709) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4709)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4709)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__0__iff])]) ).

fof(i_0_2127,plain,
    ! [X4687] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4687),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4687,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4687,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4687),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_2128,plain,
    ! [X4711] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4711),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4711),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_2129,plain,
    ! [X4684] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4684),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4684,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4684,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4684),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_2130,plain,
    ! [X4708] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4708),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4708,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4708,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4708),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_2131,plain,
    ! [X3648,X3649] :
      ( ~ class_Rings_Olinordered__semidom(X3649)
      | c_Orderings_Oord__class_Oless(X3649,X3648,c_Groups_Oplus__class_Oplus(X3649,X3648,c_Groups_Oone__class_Oone(X3649))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_2132,plain,
    ! [X4747,X4748,X4749] :
      ( ( X4748 = c_Groups_Ozero__class_Ozero(X4749)
        | c_Power_Opower__class_Opower(X4749,X4748,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4747)) != c_Groups_Ozero__class_Ozero(X4749)
        | ~ class_Power_Opower(X4749)
        | ~ class_Rings_Omult__zero(X4749)
        | ~ class_Rings_Ono__zero__divisors(X4749)
        | ~ class_Rings_Ozero__neq__one(X4749) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4747) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4749,X4748,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4747)) != c_Groups_Ozero__class_Ozero(X4749)
        | ~ class_Power_Opower(X4749)
        | ~ class_Rings_Omult__zero(X4749)
        | ~ class_Rings_Ono__zero__divisors(X4749)
        | ~ class_Rings_Ozero__neq__one(X4749) )
      & ( X4748 != c_Groups_Ozero__class_Ozero(X4749)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4747) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4749,X4748,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4747)) = c_Groups_Ozero__class_Ozero(X4749)
        | ~ class_Power_Opower(X4749)
        | ~ class_Rings_Omult__zero(X4749)
        | ~ class_Rings_Ono__zero__divisors(X4749)
        | ~ class_Rings_Ozero__neq__one(X4749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of])])]) ).

fof(i_0_2133,plain,
    ! [X3372,X3373,X3374,X3375] :
      ( ~ class_Groups_Ocancel__semigroup__add(X3375)
      | c_Groups_Oplus__class_Oplus(X3375,X3374,X3373) != c_Groups_Oplus__class_Oplus(X3375,X3372,X3373)
      | X3374 = X3372 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_2134,plain,
    ! [X3360,X3361,X3362,X3363] :
      ( ( c_Groups_Oplus__class_Oplus(X3363,X3362,X3361) != c_Groups_Oplus__class_Oplus(X3363,X3360,X3361)
        | X3362 = X3360
        | ~ class_Groups_Ocancel__semigroup__add(X3363) )
      & ( X3362 != X3360
        | c_Groups_Oplus__class_Oplus(X3363,X3362,X3361) = c_Groups_Oplus__class_Oplus(X3363,X3360,X3361)
        | ~ class_Groups_Ocancel__semigroup__add(X3363) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_2135,plain,
    ! [X3368,X3369,X3370,X3371] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X3371)
      | c_Groups_Oplus__class_Oplus(X3371,X3370,X3369) != c_Groups_Oplus__class_Oplus(X3371,X3370,X3368)
      | X3369 = X3368 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_2136,plain,
    ! [X3364,X3365,X3366,X3367] :
      ( ~ class_Groups_Ocancel__semigroup__add(X3367)
      | c_Groups_Oplus__class_Oplus(X3367,X3366,X3365) != c_Groups_Oplus__class_Oplus(X3367,X3366,X3364)
      | X3365 = X3364 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_2137,plain,
    ! [X3356,X3357,X3358,X3359] :
      ( ( c_Groups_Oplus__class_Oplus(X3359,X3358,X3357) != c_Groups_Oplus__class_Oplus(X3359,X3358,X3356)
        | X3357 = X3356
        | ~ class_Groups_Ocancel__semigroup__add(X3359) )
      & ( X3357 != X3356
        | c_Groups_Oplus__class_Oplus(X3359,X3358,X3357) = c_Groups_Oplus__class_Oplus(X3359,X3358,X3356)
        | ~ class_Groups_Ocancel__semigroup__add(X3359) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_2138,plain,
    ! [X3207,X3208,X3209] :
      ( ~ class_Orderings_Oorder(X3209)
      | ~ c_Orderings_Oord__class_Oless(X3209,X3208,X3207)
      | ~ c_Orderings_Oord__class_Oless(X3209,X3207,X3208) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1408])]) ).

fof(i_0_2139,plain,
    ! [X3095,X3096,X3097] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3097,X3096,X3095)
        | c_Orderings_Oord__class_Oless(X3097,X3095,X3096)
        | ~ class_Orderings_Olinorder(X3097) )
      & ( ~ c_Orderings_Oord__class_Oless(X3097,X3095,X3096)
        | ~ c_Orderings_Oord__class_Oless__eq(X3097,X3096,X3095)
        | ~ class_Orderings_Olinorder(X3097) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1409])])]) ).

fof(i_0_2140,plain,
    ! [X3276,X3277,X3278] :
      ( ~ class_Orderings_Olinorder(X3278)
      | ~ c_Orderings_Oord__class_Oless__eq(X3278,X3277,X3276)
      | ~ c_Orderings_Oord__class_Oless(X3278,X3276,X3277) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])]) ).

fof(i_0_2141,plain,
    ! [X3092,X3093,X3094] :
      ( ( c_Orderings_Oord__class_Oless(X3094,X3093,X3092)
        | c_Orderings_Oord__class_Oless__eq(X3094,X3092,X3093)
        | ~ class_Orderings_Olinorder(X3094) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3094,X3092,X3093)
        | ~ c_Orderings_Oord__class_Oless(X3094,X3093,X3092)
        | ~ class_Orderings_Olinorder(X3094) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1411])])]) ).

fof(i_0_2142,plain,
    ! [X3237,X3238,X3239] :
      ( ( c_Orderings_Oord__class_Oless(X3239,X3238,X3237)
        | c_Orderings_Oord__class_Oless(X3239,X3237,X3238)
        | X3238 = X3237
        | ~ class_Orderings_Olinorder(X3239) )
      & ( ~ c_Orderings_Oord__class_Oless(X3239,X3237,X3238)
        | ~ c_Orderings_Oord__class_Oless(X3239,X3238,X3237)
        | ~ class_Orderings_Olinorder(X3239) )
      & ( X3238 != X3237
        | ~ c_Orderings_Oord__class_Oless(X3239,X3238,X3237)
        | ~ class_Orderings_Olinorder(X3239) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1412])])]) ).

fof(i_0_2143,plain,
    ! [X3222,X3223,X3224] :
      ( ~ class_Orderings_Opreorder(X3224)
      | ~ c_Orderings_Oord__class_Oless(X3224,X3223,X3222)
      | ~ c_Orderings_Oord__class_Oless(X3224,X3222,X3223) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1413])]) ).

fof(i_0_2144,plain,
    ! [X3219,X3220,X3221] :
      ( ~ class_Orderings_Opreorder(X3221)
      | ~ c_Orderings_Oord__class_Oless(X3221,X3220,X3219)
      | ~ c_Orderings_Oord__class_Oless(X3221,X3219,X3220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])]) ).

fof(i_0_2145,plain,
    ! [X3210,X3211,X3212] :
      ( ~ class_Orderings_Opreorder(X3212)
      | ~ c_Orderings_Oord__class_Oless(X3212,X3211,X3210)
      | ~ c_Orderings_Oord__class_Oless(X3212,X3210,X3211) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1415])]) ).

fof(i_0_2146,plain,
    ! [X3180,X3181,X3182] :
      ( ~ class_Orderings_Opreorder(X3182)
      | ~ c_Orderings_Oord__class_Oless(X3182,X3181,X3180)
      | ~ c_Orderings_Oord__class_Oless(X3182,X3180,X3181) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1416])]) ).

fof(i_0_2147,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(i_0_2148,plain,
    ! [X4178] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4178)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__gt__one])]) ).

fof(i_0_2149,plain,
    ! [X4277] :
      ( ( ~ 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,X4277))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4277) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4277)
        | 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,X4277)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

fof(i_0_2150,plain,
    ! [X4142,X4143,X4144] :
      ( ~ class_Rings_Odivision__ring(X4144)
      | X4143 = c_Groups_Ozero__class_Ozero(X4144)
      | c_Rings_Oinverse__class_Odivide(X4144,c_Groups_Ouminus__class_Ouminus(X4144,X4142),c_Groups_Ouminus__class_Ouminus(X4144,X4143)) = c_Rings_Oinverse__class_Odivide(X4144,X4142,X4143) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_2151,plain,
    ! [X4397,X4398] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4398,X4397)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4397,X4398)
      | X4398 = X4397 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

fof(i_0_2152,plain,
    ! [X4035,X4036] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4036,X4035)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4035,X4036)
      | X4036 = X4035 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_2153,plain,
    ! [X2868,X2869] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2869,X2868)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2868,X2869)
      | X2869 = X2868 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).

cnf(i_0_2154,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1417]) ).

fof(i_0_2155,plain,
    ! [X4394,X4395,X4396] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4396,X4395) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4394,X4395)
        | X4396 = X4394 )
      & ( X4396 != X4394
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4396,X4395) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4394,X4395) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_2156,plain,
    ! [X4391,X4392,X4393] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4393,X4392) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4393,X4391)
        | X4392 = X4391 )
      & ( X4392 != X4391
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4393,X4392) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4393,X4391) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_2157,plain,
    ! [X4003,X4004,X4005] :
      ( ~ class_Fields_Ofield__inverse__zero(X4005)
      | c_Rings_Oinverse__class_Odivide(X4005,c_Groups_Ouminus__class_Ouminus(X4005,X4004),c_Groups_Ouminus__class_Ouminus(X4005,X4003)) = c_Rings_Oinverse__class_Odivide(X4005,X4004,X4003) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_2158,plain,
    ! [X4688] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4688)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4688)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__one])]) ).

fof(i_0_2159,plain,
    ! [X4712] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4712)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__zero])]) ).

fof(i_0_2160,plain,
    ! [X3785] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3785)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3785)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__ge__zero])]) ).

fof(i_0_2161,plain,
    ! [X4706] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4706)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,X4706)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__zero])]) ).

fof(i_0_2162,plain,
    ! [X3791] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3791)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X3791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__gt__zero])]) ).

fof(i_0_2163,plain,
    ! [X4229,X4230] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4230)),X4229) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4230),X4229)),
    inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).

fof(i_0_2164,plain,
    ! [X3961,X3962,X3963] :
      ( ~ class_Rings_Oring(X3963)
      | hAPP(c_Groups_Otimes__class_Otimes(X3963,c_Groups_Ouminus__class_Ouminus(X3963,X3962)),c_Groups_Ouminus__class_Ouminus(X3963,X3961)) = hAPP(c_Groups_Otimes__class_Otimes(X3963,X3962),X3961) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_2165,plain,
    ! [X2575,X2576,X2577] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X2577)
      | hAPP(c_Groups_Otimes__class_Otimes(X2577,X2576),hAPP(c_Groups_Otimes__class_Otimes(X2577,X2576),X2575)) = hAPP(c_Groups_Otimes__class_Otimes(X2577,X2576),X2575) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).

fof(i_0_2166,plain,
    ! [X3964,X3965,X3966] :
      ( ~ class_Rings_Oring(X3966)
      | hAPP(c_Groups_Otimes__class_Otimes(X3966,c_Groups_Ouminus__class_Ouminus(X3966,X3965)),X3964) = hAPP(c_Groups_Otimes__class_Otimes(X3966,X3965),c_Groups_Ouminus__class_Ouminus(X3966,X3964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

fof(i_0_2167,plain,
    ! [X3982,X3983,X3984] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3984)
      | hAPP(c_Groups_Otimes__class_Otimes(X3984,X3983),c_Groups_Ouminus__class_Ouminus(X3984,X3982)) = c_Groups_Ouminus__class_Ouminus(X3984,hAPP(c_Groups_Otimes__class_Otimes(X3984,X3983),X3982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).

fof(i_0_2168,plain,
    ! [X3979,X3980,X3981] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3981)
      | hAPP(c_Groups_Otimes__class_Otimes(X3981,X3980),c_Groups_Ouminus__class_Ouminus(X3981,X3979)) = c_Groups_Ouminus__class_Ouminus(X3981,hAPP(c_Groups_Otimes__class_Otimes(X3981,X3980),X3979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).

fof(i_0_2169,plain,
    ! [X3970,X3971,X3972] :
      ( ~ class_Rings_Oring(X3972)
      | c_Groups_Ouminus__class_Ouminus(X3972,hAPP(c_Groups_Otimes__class_Otimes(X3972,X3971),X3970)) = hAPP(c_Groups_Otimes__class_Otimes(X3972,X3971),c_Groups_Ouminus__class_Ouminus(X3972,X3970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_2170,plain,
    ! [X3782] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3782)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X3782),X3782) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__less__self])]) ).

fof(i_0_2171,plain,
    ! [X4583,X4584,X4586,X4587,X4588] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4584,X4583)
        | X4583 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4584,esk10_2(X4583,X4584)) )
      & ( X4586 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4587,X4588)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4587,X4586) ) ),
    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_2172,plain,
    ! [X4477,X4478,X4480,X4481,X4482] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4478,X4477)
        | X4477 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4478,esk9_2(X4477,X4478)) )
      & ( X4480 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4481,X4482)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4481,X4480) ) ),
    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])])])])]) ).

fof(i_0_2173,plain,
    ! [X4204] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4204)
      | hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4204)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X4204)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__inverse])]) ).

fof(i_0_2174,plain,
    ! [X4475,X4476] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4476,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4476,X4475)),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_2175,plain,
    ! [X4473,X4474] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4474,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4473,X4474)),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_2176,plain,
    ! [X4055,X4056] :
      ( ( X4056 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4056),X4055) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4056) )
      & ( X4055 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4056),X4055) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4056) )
      & ( X4056 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X4055 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4056),X4055) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4056) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).

fof(i_0_2177,plain,
    ! [X3282,X3283,X3284] :
      ( ~ class_Orderings_Oorder(X3284)
      | X3283 = X3282
      | ~ c_Orderings_Oord__class_Oless__eq(X3284,X3283,X3282)
      | c_Orderings_Oord__class_Oless(X3284,X3283,X3282) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_2178,plain,
    ! [X3267,X3268,X3269] :
      ( ~ class_Orderings_Oorder(X3269)
      | ~ c_Orderings_Oord__class_Oless__eq(X3269,X3268,X3267)
      | c_Orderings_Oord__class_Oless(X3269,X3268,X3267)
      | X3268 = X3267 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_2179,plain,
    ! [X3264,X3265,X3266] :
      ( ~ class_Orderings_Oorder(X3266)
      | ~ c_Orderings_Oord__class_Oless__eq(X3266,X3265,X3264)
      | X3265 = X3264
      | c_Orderings_Oord__class_Oless(X3266,X3265,X3264) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_2180,plain,
    ! [X3261,X3262,X3263] :
      ( ~ class_Orderings_Oorder(X3263)
      | ~ c_Orderings_Oord__class_Oless__eq(X3263,X3262,X3261)
      | X3261 = X3262
      | c_Orderings_Oord__class_Oless(X3263,X3262,X3261) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_2181,plain,
    ! [X3107,X3108,X3109] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3109,X3108,X3107)
        | c_Orderings_Oord__class_Oless(X3109,X3108,X3107)
        | X3108 = X3107
        | ~ class_Orderings_Oorder(X3109) )
      & ( ~ c_Orderings_Oord__class_Oless(X3109,X3108,X3107)
        | c_Orderings_Oord__class_Oless__eq(X3109,X3108,X3107)
        | ~ class_Orderings_Oorder(X3109) )
      & ( X3108 != X3107
        | c_Orderings_Oord__class_Oless__eq(X3109,X3108,X3107)
        | ~ class_Orderings_Oorder(X3109) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_2182,plain,
    ! [X3101,X3102,X3103] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3103,X3102,X3101)
        | ~ c_Orderings_Oord__class_Oless(X3103,X3102,X3101)
        | ~ class_Orderings_Oorder(X3103) )
      & ( X3102 != X3101
        | ~ c_Orderings_Oord__class_Oless(X3103,X3102,X3101)
        | ~ class_Orderings_Oorder(X3103) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3103,X3102,X3101)
        | X3102 = X3101
        | c_Orderings_Oord__class_Oless(X3103,X3102,X3101)
        | ~ class_Orderings_Oorder(X3103) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_2183,plain,
    ! [X3285,X3286,X3287] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3287,X3286,X3285)
        | X3286 = X3285
        | c_Orderings_Oord__class_Oless(X3287,X3286,X3285)
        | ~ class_Orderings_Olinorder(X3287) )
      & ( X3286 != X3285
        | c_Orderings_Oord__class_Oless__eq(X3287,X3286,X3285)
        | c_Orderings_Oord__class_Oless(X3287,X3286,X3285)
        | ~ class_Orderings_Olinorder(X3287) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1418])])]) ).

fof(i_0_2184,plain,
    ! [X3279,X3280,X3281] :
      ( ~ class_Orderings_Oorder(X3281)
      | X3280 = X3279
      | ~ c_Orderings_Oord__class_Oless__eq(X3281,X3279,X3280)
      | c_Orderings_Oord__class_Oless(X3281,X3279,X3280) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_2185,plain,
    ! [X3958,X3959,X3960] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(X3960,X3959),X3959) != hAPP(c_Groups_Otimes__class_Otimes(X3960,X3958),X3958)
        | X3959 = X3958
        | X3959 = c_Groups_Ouminus__class_Ouminus(X3960,X3958)
        | ~ class_Rings_Oidom(X3960) )
      & ( X3959 != X3958
        | hAPP(c_Groups_Otimes__class_Otimes(X3960,X3959),X3959) = hAPP(c_Groups_Otimes__class_Otimes(X3960,X3958),X3958)
        | ~ class_Rings_Oidom(X3960) )
      & ( X3959 != c_Groups_Ouminus__class_Ouminus(X3960,X3958)
        | hAPP(c_Groups_Otimes__class_Otimes(X3960,X3959),X3959) = hAPP(c_Groups_Otimes__class_Otimes(X3960,X3958),X3958)
        | ~ class_Rings_Oidom(X3960) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_2186,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_0)
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096])]) ).

fof(i_0_2187,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0)
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1419])])]) ).

fof(i_0_2188,plain,
    ! [X3273,X3274,X3275] :
      ( ~ class_Orderings_Opreorder(X3275)
      | ~ c_Orderings_Oord__class_Oless(X3275,X3274,X3273)
      | c_Orderings_Oord__class_Oless__eq(X3275,X3274,X3273) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_2189,plain,
    ! [X4302,X4303] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4303,X4302)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X4303),X4302) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X4303),X4302)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4303,X4302) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).

fof(i_0_2190,plain,
    ! [X4273,X4274] :
      ( ~ class_Int_Onumber__ring(X4274)
      | c_Int_Onumber__class_Onumber__of(X4274,c_Int_Opred(X4273)) = c_Groups_Oplus__class_Oplus(X4274,c_Groups_Ouminus__class_Ouminus(X4274,c_Groups_Oone__class_Oone(X4274)),c_Int_Onumber__class_Onumber__of(X4274,X4273)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).

fof(i_0_2191,plain,
    ! [X5022,X5023] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X5023)
      | c_Orderings_Oord__class_Oless__eq(X5023,c_Groups_Ouminus__class_Ouminus(X5023,c_Groups_Oabs__class_Oabs(X5023,X5022)),c_Groups_Ozero__class_Ozero(X5023)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_2192,plain,
    ! [X2931,X2932] :
      ( ~ class_Rings_Olinordered__ring(X2932)
      | c_Orderings_Oord__class_Oless__eq(X2932,c_Groups_Ozero__class_Ozero(X2932),hAPP(c_Groups_Otimes__class_Otimes(X2932,X2931),X2931)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_2193,plain,
    ! [X4081] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4081)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4081) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4081)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4081) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_2194,plain,
    ! [X2722,X2723,X2724,X2725] :
      ( ( X2722 = c_Groups_Ozero__class_Ozero(X2725)
        | hAPP(c_Groups_Otimes__class_Otimes(X2725,X2724),X2722) = X2723
        | X2724 != c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) )
      & ( X2722 != c_Groups_Ozero__class_Ozero(X2725)
        | X2724 = c_Groups_Ozero__class_Ozero(X2725)
        | X2724 != c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) )
      & ( X2722 = c_Groups_Ozero__class_Ozero(X2725)
        | X2722 != c_Groups_Ozero__class_Ozero(X2725)
        | X2724 = c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) )
      & ( X2724 != c_Groups_Ozero__class_Ozero(X2725)
        | X2722 != c_Groups_Ozero__class_Ozero(X2725)
        | X2724 = c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) )
      & ( X2722 = c_Groups_Ozero__class_Ozero(X2725)
        | hAPP(c_Groups_Otimes__class_Otimes(X2725,X2724),X2722) != X2723
        | X2724 = c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) )
      & ( X2724 != c_Groups_Ozero__class_Ozero(X2725)
        | hAPP(c_Groups_Otimes__class_Otimes(X2725,X2724),X2722) != X2723
        | X2724 = c_Rings_Oinverse__class_Odivide(X2725,X2723,X2722)
        | ~ class_Fields_Ofield__inverse__zero(X2725) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_2195,plain,
    ! [X2746,X2747,X2748,X2749] :
      ( ( X2747 != c_Rings_Oinverse__class_Odivide(X2749,X2746,X2748)
        | hAPP(c_Groups_Otimes__class_Otimes(X2749,X2747),X2748) = X2746
        | X2748 = c_Groups_Ozero__class_Ozero(X2749)
        | ~ class_Rings_Odivision__ring(X2749) )
      & ( hAPP(c_Groups_Otimes__class_Otimes(X2749,X2747),X2748) != X2746
        | X2747 = c_Rings_Oinverse__class_Odivide(X2749,X2746,X2748)
        | X2748 = c_Groups_Ozero__class_Ozero(X2749)
        | ~ class_Rings_Odivision__ring(X2749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).

fof(i_0_2196,plain,
    ! [X2718,X2719,X2720,X2721] :
      ( ( X2719 = c_Groups_Ozero__class_Ozero(X2721)
        | X2720 = hAPP(c_Groups_Otimes__class_Otimes(X2721,X2718),X2719)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) != X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) )
      & ( X2719 != c_Groups_Ozero__class_Ozero(X2721)
        | X2718 = c_Groups_Ozero__class_Ozero(X2721)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) != X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) )
      & ( X2719 = c_Groups_Ozero__class_Ozero(X2721)
        | X2719 != c_Groups_Ozero__class_Ozero(X2721)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) = X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) )
      & ( X2718 != c_Groups_Ozero__class_Ozero(X2721)
        | X2719 != c_Groups_Ozero__class_Ozero(X2721)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) = X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) )
      & ( X2719 = c_Groups_Ozero__class_Ozero(X2721)
        | X2720 != hAPP(c_Groups_Otimes__class_Otimes(X2721,X2718),X2719)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) = X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) )
      & ( X2718 != c_Groups_Ozero__class_Ozero(X2721)
        | X2720 != hAPP(c_Groups_Otimes__class_Otimes(X2721,X2718),X2719)
        | c_Rings_Oinverse__class_Odivide(X2721,X2720,X2719) = X2718
        | ~ class_Fields_Ofield__inverse__zero(X2721) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_2197,plain,
    ! [X2742,X2743,X2744,X2745] :
      ( ( c_Rings_Oinverse__class_Odivide(X2745,X2743,X2744) != X2742
        | X2743 = hAPP(c_Groups_Otimes__class_Otimes(X2745,X2742),X2744)
        | X2744 = c_Groups_Ozero__class_Ozero(X2745)
        | ~ class_Rings_Odivision__ring(X2745) )
      & ( X2743 != hAPP(c_Groups_Otimes__class_Otimes(X2745,X2742),X2744)
        | c_Rings_Oinverse__class_Odivide(X2745,X2743,X2744) = X2742
        | X2744 = c_Groups_Ozero__class_Ozero(X2745)
        | ~ class_Rings_Odivision__ring(X2745) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_2198,plain,
    ! [X3870,X3871] :
      ( ~ class_Int_Onumber(X3871)
      | ~ class_Rings_Odivision__ring(X3871)
      | c_Rings_Oinverse__class_Oinverse(X3871,c_Int_Onumber__class_Onumber__of(X3871,X3870)) = c_Rings_Oinverse__class_Odivide(X3871,c_Groups_Oone__class_Oone(X3871),c_Int_Onumber__class_Onumber__of(X3871,X3870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide__number__of])]) ).

fof(i_0_2199,plain,
    ! [X4471,X4472] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4472,X4471)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4472,X4471) )
      & ( X4472 != X4471
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4472,X4471) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4472,X4471)
        | X4472 = X4471
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4472,X4471) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

fof(i_0_2200,plain,
    ! [X4469,X4470] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4470,X4469)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4470,X4469)
        | X4470 = X4469 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4470,X4469)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4470,X4469) )
      & ( X4470 != X4469
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4470,X4469) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_2201,plain,
    ! [X4465,X4466] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4466,X4465)
      | X4466 = X4465
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4466,X4465) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_2202,plain,
    ! [X4093,X4094] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4094,X4093)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4094,X4093) )
      & ( X4094 != X4093
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4094,X4093) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4094,X4093)
        | X4094 = X4093
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4094,X4093) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_2203,plain,
    ! [X2872,X2873] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2873,X2872)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2873,X2872)
        | X2873 = X2872 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2873,X2872)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2873,X2872) )
      & ( X2873 != X2872
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2873,X2872) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).

fof(i_0_2204,plain,
    ! [X2870,X2871] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2871,X2870)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2871,X2870) )
      & ( X2871 != X2870
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2871,X2870) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2871,X2870)
        | X2871 = X2870
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2871,X2870) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).

fof(i_0_2205,plain,
    ! [X4013,X4014,X4015,X4016] :
      ( ~ class_Groups_Ouminus(X4016)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4015,X4016),X4014),X4013) = c_Groups_Ouminus__class_Ouminus(X4016,hAPP(X4014,X4013)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_2206,plain,
    ! [X4157] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4157),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[i_0_1420]) ).

fof(i_0_2207,plain,
    ! [X4159] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4159),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[i_0_1421]) ).

fof(i_0_2208,plain,
    ! [X4138,X4139] :
      ( ~ class_Rings_Ocomm__ring__1(X4139)
      | c_Groups_Ouminus__class_Ouminus(X4139,X4138) = hAPP(c_Groups_Otimes__class_Otimes(X4139,c_Groups_Ouminus__class_Ouminus(X4139,c_Groups_Oone__class_Oone(X4139))),X4138) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).

fof(i_0_2209,plain,
    ! [X4202,X4203] :
      ( ( c_Groups_Osgn__class_Osgn(X4203,X4202) != c_Groups_Ouminus__class_Ouminus(X4203,c_Groups_Oone__class_Oone(X4203))
        | c_Orderings_Oord__class_Oless(X4203,X4202,c_Groups_Ozero__class_Ozero(X4203))
        | ~ class_Rings_Olinordered__idom(X4203) )
      & ( ~ c_Orderings_Oord__class_Oless(X4203,X4202,c_Groups_Ozero__class_Ozero(X4203))
        | c_Groups_Osgn__class_Osgn(X4203,X4202) = c_Groups_Ouminus__class_Ouminus(X4203,c_Groups_Oone__class_Oone(X4203))
        | ~ class_Rings_Olinordered__idom(X4203) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_2210,plain,
    ! [X4200,X4201] :
      ( ~ class_Rings_Olinordered__idom(X4201)
      | ~ c_Orderings_Oord__class_Oless(X4201,X4200,c_Groups_Ozero__class_Ozero(X4201))
      | c_Groups_Osgn__class_Osgn(X4201,X4200) = c_Groups_Ouminus__class_Ouminus(X4201,c_Groups_Oone__class_Oone(X4201)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_2211,plain,
    ! [X4581,X4582] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4582,X4581)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4582,X4581) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_2212,plain,
    ! [X4467,X4468] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4468,X4467)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4468,X4467) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_2213,plain,
    ! [X4463,X4464] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4464,X4463)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4464,X4463) )
      & ( X4464 != X4463
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4464,X4463) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_2214,plain,
    ! [X2738,X2739,X2740,X2741] :
      ( ~ class_Rings_Odivision__ring(X2741)
      | X2740 = c_Groups_Ozero__class_Ozero(X2741)
      | X2739 != hAPP(c_Groups_Otimes__class_Otimes(X2741,X2738),X2740)
      | c_Rings_Oinverse__class_Odivide(X2741,X2739,X2740) = X2738 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_2215,plain,
    ! [X2734,X2735,X2736,X2737] :
      ( ~ class_Rings_Odivision__ring(X2737)
      | X2736 = c_Groups_Ozero__class_Ozero(X2737)
      | hAPP(c_Groups_Otimes__class_Otimes(X2737,X2735),X2736) != X2734
      | X2735 = c_Rings_Oinverse__class_Odivide(X2737,X2734,X2736) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_2216,plain,
    ! [X5026,X5027] :
      ( ( ~ c_Orderings_Oord__class_Oless(X5027,X5026,c_Groups_Ozero__class_Ozero(X5027))
        | c_Groups_Oabs__class_Oabs(X5027,X5026) = c_Groups_Ouminus__class_Ouminus(X5027,X5026)
        | ~ class_Groups_Oabs__if(X5027) )
      & ( c_Orderings_Oord__class_Oless(X5027,X5026,c_Groups_Ozero__class_Ozero(X5027))
        | c_Groups_Oabs__class_Oabs(X5027,X5026) = X5026
        | ~ class_Groups_Oabs__if(X5027) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1422])])]) ).

fof(i_0_2217,plain,
    ! [X5020,X5021] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X5021)
      | ~ c_Orderings_Oord__class_Oless__eq(X5021,X5020,c_Groups_Ozero__class_Ozero(X5021))
      | c_Groups_Oabs__class_Oabs(X5021,X5020) = c_Groups_Ouminus__class_Ouminus(X5021,X5020) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

fof(i_0_2218,plain,
    ! [X5024,X5025] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X5025)
      | ~ c_Orderings_Oord__class_Oless(X5025,X5024,c_Groups_Ozero__class_Ozero(X5025))
      | c_Groups_Oabs__class_Oabs(X5025,X5024) = c_Groups_Ouminus__class_Ouminus(X5025,X5024) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_2219,plain,
    ! [X4182] :
      ( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X4182)) != X4182
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4182) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4182)
        | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X4182)) = X4182 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__ln__iff])]) ).

fof(i_0_2220,plain,
    ! [X4181] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4181)
      | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X4181)) = X4181 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__ln])]) ).

fof(i_0_2221,plain,
    ! [X2560,X2561] :
      ( hAPP(X2561,esk1_2(X2560,X2561)) != hAPP(X2560,esk1_2(X2560,X2561))
      | X2561 = X2560 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_2222,plain,
    ! [X3590,X3591,X3592] :
      ( ~ class_Rings_Odivision__ring(X3592)
      | c_Rings_Oinverse__class_Odivide(X3592,X3591,X3590) = hAPP(c_Groups_Otimes__class_Otimes(X3592,X3591),c_Rings_Oinverse__class_Oinverse(X3592,X3590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__inverse])]) ).

fof(i_0_2223,plain,
    ! [X3587,X3588,X3589] :
      ( ~ class_Fields_Ofield(X3589)
      | c_Rings_Oinverse__class_Odivide(X3589,X3588,X3587) = hAPP(c_Groups_Otimes__class_Otimes(X3589,X3588),c_Rings_Oinverse__class_Oinverse(X3589,X3587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__divide__inverse])]) ).

fof(i_0_2224,plain,
    ! [X4909,X4910,X4911] :
      ( ( X4910 = c_Groups_Ozero__class_Ozero(X4911)
        | c_Power_Opower__class_Opower(X4911,X4910,X4909) != c_Groups_Ozero__class_Ozero(X4911)
        | ~ class_Power_Opower(X4911)
        | ~ class_Rings_Omult__zero(X4911)
        | ~ class_Rings_Ono__zero__divisors(X4911)
        | ~ class_Rings_Ozero__neq__one(X4911) )
      & ( X4909 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4911,X4910,X4909) != c_Groups_Ozero__class_Ozero(X4911)
        | ~ class_Power_Opower(X4911)
        | ~ class_Rings_Omult__zero(X4911)
        | ~ class_Rings_Ono__zero__divisors(X4911)
        | ~ class_Rings_Ozero__neq__one(X4911) )
      & ( X4910 != c_Groups_Ozero__class_Ozero(X4911)
        | X4909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4911,X4910,X4909) = c_Groups_Ozero__class_Ozero(X4911)
        | ~ class_Power_Opower(X4911)
        | ~ class_Rings_Omult__zero(X4911)
        | ~ class_Rings_Ono__zero__divisors(X4911)
        | ~ class_Rings_Ozero__neq__one(X4911) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).

fof(i_0_2225,plain,
    ! [X4198,X4199] :
      ( ( X4198 != c_Groups_Ozero__class_Ozero(X4199)
        | c_Groups_Osgn__class_Osgn(X4199,X4198) = c_Groups_Ozero__class_Ozero(X4199)
        | ~ class_Groups_Osgn__if(X4199) )
      & ( ~ c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),X4198)
        | c_Groups_Osgn__class_Osgn(X4199,X4198) = c_Groups_Oone__class_Oone(X4199)
        | X4198 = c_Groups_Ozero__class_Ozero(X4199)
        | ~ class_Groups_Osgn__if(X4199) )
      & ( c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),X4198)
        | c_Groups_Osgn__class_Osgn(X4199,X4198) = c_Groups_Ouminus__class_Ouminus(X4199,c_Groups_Oone__class_Oone(X4199))
        | X4198 = c_Groups_Ozero__class_Ozero(X4199)
        | ~ class_Groups_Osgn__if(X4199) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1423])])]) ).

fof(i_0_2226,plain,
    ! [X4750,X4751] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4750) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4751,c_Groups_Ozero__class_Ozero(X4751),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4750)) = c_Groups_Oone__class_Oone(X4751)
        | ~ class_Power_Opower(X4751)
        | ~ class_Rings_Osemiring__0(X4751) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4751,c_Groups_Ozero__class_Ozero(X4751),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4750)) = c_Groups_Ozero__class_Ozero(X4751)
        | ~ class_Power_Opower(X4751)
        | ~ class_Rings_Osemiring__0(X4751) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of])])]) ).

fof(i_0_2227,plain,
    ! [X4154,X4155] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4155,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4154)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X4155 = X4154 )
      & ( X4155 != X4154
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4155,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4154)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])]) ).

fof(i_0_2228,plain,
    ! [X4514] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4514,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4514),X4514)),
    inference(variable_rename,[status(thm)],[fact_le__square]) ).

fof(i_0_2229,plain,
    ! [X4426,X4427,X4428] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4428),X4427) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4426),X4427)
        | X4428 = X4426
        | X4427 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4428 != X4426
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4428),X4427) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4426),X4427) )
      & ( X4427 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4428),X4427) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4426),X4427) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).

fof(i_0_2230,plain,
    ! [X2594,X2595,X2596] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2595),X2596) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2594),X2596)
        | X2595 = X2594
        | X2596 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X2595 != X2594
        | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2595),X2596) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2594),X2596)
        | X2596 = 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_2231,plain,
    ! [X4562,X4563,X4564] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4563) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4562)
        | X4564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X4563 = X4562 )
      & ( X4564 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4563) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4562) )
      & ( X4563 != X4562
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4563) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4564),X4562) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_2232,plain,
    ! [X4429,X4430,X4431] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4430) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4429)
        | X4430 = X4429
        | X4431 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4430 != X4429
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4430) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4429) )
      & ( X4431 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4430) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4431),X4429) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).

fof(i_0_2233,plain,
    ! [X2591,X2592,X2593] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2593),X2592) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2593),X2591)
        | X2592 = X2591
        | X2593 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X2592 != X2591
        | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2593),X2592) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2593),X2591)
        | X2593 = 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_2234,plain,
    ! [X3312,X3313] :
      ( ~ class_Rings_Olinordered__idom(X3313)
      | ~ c_Orderings_Oord__class_Oless(X3313,c_Groups_Ozero__class_Ozero(X3313),X3312)
      | c_Groups_Osgn__class_Osgn(X3313,X3312) = c_Groups_Oone__class_Oone(X3313) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_2235,plain,
    ! [X3310,X3311] :
      ( ( c_Groups_Osgn__class_Osgn(X3311,X3310) != c_Groups_Oone__class_Oone(X3311)
        | c_Orderings_Oord__class_Oless(X3311,c_Groups_Ozero__class_Ozero(X3311),X3310)
        | ~ class_Rings_Olinordered__idom(X3311) )
      & ( ~ c_Orderings_Oord__class_Oless(X3311,c_Groups_Ozero__class_Ozero(X3311),X3310)
        | c_Groups_Osgn__class_Osgn(X3311,X3310) = c_Groups_Oone__class_Oone(X3311)
        | ~ class_Rings_Olinordered__idom(X3311) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).

fof(i_0_2236,plain,
    ! [X3240,X3241,X3242] :
      ( ( X3241 = X3240
        | c_Orderings_Oord__class_Oless(X3242,X3241,X3240)
        | c_Orderings_Oord__class_Oless(X3242,X3240,X3241)
        | ~ class_Orderings_Olinorder(X3242) )
      & ( ~ c_Orderings_Oord__class_Oless(X3242,X3241,X3240)
        | X3241 != X3240
        | ~ class_Orderings_Olinorder(X3242) )
      & ( ~ c_Orderings_Oord__class_Oless(X3242,X3240,X3241)
        | X3241 != X3240
        | ~ class_Orderings_Olinorder(X3242) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_2237,plain,
    ! [X3234,X3235,X3236] :
      ( ~ class_Orderings_Olinorder(X3236)
      | c_Orderings_Oord__class_Oless(X3236,X3235,X3234)
      | X3235 = X3234
      | c_Orderings_Oord__class_Oless(X3236,X3234,X3235) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_2238,plain,
    ! [X3231,X3232,X3233] :
      ( ( c_Orderings_Oord__class_Oless(X3233,X3231,X3232)
        | X3231 = X3232
        | c_Orderings_Oord__class_Oless(X3233,X3232,X3231)
        | ~ class_Orderings_Olinorder(X3233) )
      & ( X3231 != X3232
        | ~ c_Orderings_Oord__class_Oless(X3233,X3231,X3232)
        | c_Orderings_Oord__class_Oless(X3233,X3232,X3231)
        | ~ class_Orderings_Olinorder(X3233) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1424])])]) ).

fof(i_0_2239,plain,
    ! [X3228,X3229,X3230] :
      ( ~ class_Orderings_Olinorder(X3230)
      | X3229 = X3228
      | c_Orderings_Oord__class_Oless(X3230,X3229,X3228)
      | c_Orderings_Oord__class_Oless(X3230,X3228,X3229) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1425])]) ).

fof(i_0_2240,plain,
    ! [X3177,X3178,X3179] :
      ( ~ class_Orderings_Olinorder(X3179)
      | c_Orderings_Oord__class_Oless(X3179,X3178,X3177)
      | X3178 = X3177
      | c_Orderings_Oord__class_Oless(X3179,X3177,X3178) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1426])]) ).

fof(i_0_2241,plain,
    ! [X2755,X2756,X2757] :
      ( ~ class_Rings_Olinordered__idom(X2757)
      | X2756 = X2755
      | c_Orderings_Oord__class_Oless(X2757,X2756,X2755)
      | c_Orderings_Oord__class_Oless(X2757,X2755,X2756) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1427])]) ).

fof(i_0_2242,plain,
    ! [X3174,X3175,X3176] :
      ( ~ class_Orderings_Olinorder(X3176)
      | c_Orderings_Oord__class_Oless__eq(X3176,X3175,X3174)
      | c_Orderings_Oord__class_Oless__eq(X3176,X3174,X3175) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1428])]) ).

fof(i_0_2243,plain,
    ! [X3122,X3123,X3124] :
      ( ~ class_Orderings_Olinorder(X3124)
      | c_Orderings_Oord__class_Oless__eq(X3124,X3123,X3122)
      | c_Orderings_Oord__class_Oless__eq(X3124,X3122,X3123) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_2244,plain,
    ! [X3110,X3111,X3112] :
      ( ~ class_Orderings_Olinorder(X3112)
      | c_Orderings_Oord__class_Oless(X3112,X3111,X3110)
      | c_Orderings_Oord__class_Oless__eq(X3112,X3110,X3111) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1429])]) ).

fof(i_0_2245,plain,
    ! [X3113,X3114,X3115] :
      ( ~ class_Orderings_Olinorder(X3115)
      | c_Orderings_Oord__class_Oless__eq(X3115,X3114,X3113)
      | c_Orderings_Oord__class_Oless(X3115,X3113,X3114) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1430])]) ).

fof(i_0_2246,plain,
    ! [X3098,X3099,X3100] :
      ( ~ class_Orderings_Olinorder(X3100)
      | c_Orderings_Oord__class_Oless__eq(X3100,X3099,X3098)
      | c_Orderings_Oord__class_Oless(X3100,X3098,X3099) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_2247,plain,
    ! [X3789] :
      ( ( hAPP(c_Transcendental_Oln,X3789) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X3789 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3789) )
      & ( X3789 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | hAPP(c_Transcendental_Oln,X3789) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3789) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__eq__zero__iff])])]) ).

fof(i_0_2248,plain,
    ! [X4713] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4713)
      | hAPP(c_NthRoot_Osqrt,X4713) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | X4713 = 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_2249,plain,
    ! [X3328,X3329,X3330] :
      ( ~ class_Rings_Ocomm__semiring__1(X3330)
      | c_Groups_Oplus__class_Oplus(X3330,X3329,X3328) = c_Groups_Oplus__class_Oplus(X3330,X3328,X3329) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_2250,plain,
    ! [X4135,X4136,X4137] :
      ( ~ class_Groups_Ogroup__add(X4137)
      | c_Groups_Oplus__class_Oplus(X4137,X4136,X4135) != c_Groups_Ozero__class_Ozero(X4137)
      | c_Groups_Ouminus__class_Ouminus(X4137,X4136) = X4135 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_2251,plain,
    ! [X4128,X4129,X4130] :
      ( ( X4129 != c_Groups_Ouminus__class_Ouminus(X4130,X4128)
        | c_Groups_Oplus__class_Oplus(X4130,X4129,X4128) = c_Groups_Ozero__class_Ozero(X4130)
        | ~ class_Groups_Ogroup__add(X4130) )
      & ( c_Groups_Oplus__class_Oplus(X4130,X4129,X4128) != c_Groups_Ozero__class_Ozero(X4130)
        | X4129 = c_Groups_Ouminus__class_Ouminus(X4130,X4128)
        | ~ class_Groups_Ogroup__add(X4130) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_2252,plain,
    ! [X4123,X4124,X4125] :
      ( ( c_Groups_Oplus__class_Oplus(X4125,X4124,X4123) != c_Groups_Ozero__class_Ozero(X4125)
        | X4123 = c_Groups_Ouminus__class_Ouminus(X4125,X4124)
        | ~ class_Groups_Ogroup__add(X4125) )
      & ( X4123 != c_Groups_Ouminus__class_Ouminus(X4125,X4124)
        | c_Groups_Oplus__class_Oplus(X4125,X4124,X4123) = c_Groups_Ozero__class_Ozero(X4125)
        | ~ class_Groups_Ogroup__add(X4125) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).

fof(i_0_2253,plain,
    ! [X3660,X3661] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3661,X3660) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3661),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3660)),
    inference(variable_rename,[status(thm)],[fact_real__divide__def]) ).

fof(i_0_2254,plain,
    ! [X3658,X3659] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3659,X3658) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3659),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3658)),
    inference(variable_rename,[status(thm)],[fact_divide__real__def]) ).

fof(i_0_2255,plain,
    ! [X3918,X3919] :
      ( ~ class_RealVector_Oreal__normed__field(X3919)
      | ~ class_SEQ_Obanach(X3919)
      | hAPP(c_Transcendental_Oexp(X3919),c_Groups_Ouminus__class_Ouminus(X3919,X3918)) = c_Rings_Oinverse__class_Oinverse(X3919,hAPP(c_Transcendental_Oexp(X3919),X3918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__minus])]) ).

fof(i_0_2256,plain,
    ! [X4707] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4707)
      | hAPP(c_NthRoot_Osqrt,X4707) != 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_2257,plain,
    ! [X2934] :
      ( ~ class_Rings_Olinordered__semidom(X2934)
      | ~ c_Orderings_Oord__class_Oless__eq(X2934,c_Groups_Oone__class_Oone(X2934),c_Groups_Ozero__class_Ozero(X2934)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1431])]) ).

fof(i_0_2258,plain,
    ! [X2754] :
      ( ~ class_Rings_Olinordered__semidom(X2754)
      | ~ c_Orderings_Oord__class_Oless(X2754,c_Groups_Oone__class_Oone(X2754),c_Groups_Ozero__class_Ozero(X2754)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1432])]) ).

fof(i_0_2259,plain,
    ! [X4373,X4374] :
      ( X4374 = X4373
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4374,X4373)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4373,X4374) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1433])]) ).

fof(i_0_2260,plain,
    ! [X4371,X4372] :
      ( ( X4372 = X4371
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4372,X4371)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4371,X4372) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4372,X4371)
        | X4372 != X4371 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4371,X4372)
        | X4372 != X4371 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_2261,plain,
    ! [X4050,X4051] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4051,X4050)
      | X4051 = X4050
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4050,X4051) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_2262,plain,
    ! [X3688,X3689] :
      ( ~ class_Rings_Odivision__ring(X3689)
      | X3688 = c_Groups_Ozero__class_Ozero(X3689)
      | hAPP(c_Groups_Otimes__class_Otimes(X3689,c_Rings_Oinverse__class_Oinverse(X3689,X3688)),X3688) = c_Groups_Oone__class_Oone(X3689) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).

fof(i_0_2263,plain,
    ! [X3686,X3687] :
      ( ~ class_Fields_Ofield(X3687)
      | X3686 = c_Groups_Ozero__class_Ozero(X3687)
      | hAPP(c_Groups_Otimes__class_Otimes(X3687,c_Rings_Oinverse__class_Oinverse(X3687,X3686)),X3686) = c_Groups_Oone__class_Oone(X3687) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).

fof(i_0_2264,plain,
    ! [X4231] :
      ( ( X4231 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4231) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4231)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4231) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X4231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4231)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4231) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X4231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1434])])]) ).

fof(i_0_2265,plain,
    ! [X3895] :
      ( ( X3895 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3895) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3895)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3895) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X3895 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3895)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3895) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | X3895 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1435])])]) ).

fof(i_0_2266,plain,
    ! [X3894] :
      ( ( X3894 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3894) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3894)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3894) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X3894 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3894)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3894) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | X3894 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])])]) ).

fof(i_0_2267,plain,
    ! [X2727,X2728,X2729] :
      ( ( c_Rings_Oinverse__class_Odivide(X2729,X2727,X2728) != c_Groups_Oone__class_Oone(X2729)
        | X2727 = X2728
        | X2728 = c_Groups_Ozero__class_Ozero(X2729)
        | ~ class_Rings_Odivision__ring(X2729) )
      & ( X2727 != X2728
        | c_Rings_Oinverse__class_Odivide(X2729,X2727,X2728) = c_Groups_Oone__class_Oone(X2729)
        | X2728 = c_Groups_Ozero__class_Ozero(X2729)
        | ~ class_Rings_Odivision__ring(X2729) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_2268,plain,
    ! [X4404,X4405] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4405,X4404)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4404,X4405) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_2269,plain,
    ! [X4040,X4041] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4041,X4040)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4040,X4041) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_2270,plain,
    ! [X2863,X2864] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2864,X2863)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2863,X2864) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(i_0_2271,plain,
    ! [X4383,X4384] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4384,X4383) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4383,X4384),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_2272,plain,
    ! [X4067,X4068] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4068,X4067) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4067,X4068),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_2273,plain,
    ! [X4871,X4872,X4873] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X4873)
      | X4872 = c_Groups_Ozero__class_Ozero(X4873)
      | c_Power_Opower__class_Opower(X4873,X4872,X4871) != c_Groups_Ozero__class_Ozero(X4873) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).

fof(i_0_2274,plain,
    ! [X3769,X3770] :
      ( ( c_Groups_Oplus__class_Oplus(X3770,X3769,X3769) != c_Groups_Ozero__class_Ozero(X3770)
        | X3769 = c_Groups_Ozero__class_Ozero(X3770)
        | ~ class_Groups_Olinordered__ab__group__add(X3770) )
      & ( X3769 != c_Groups_Ozero__class_Ozero(X3770)
        | c_Groups_Oplus__class_Oplus(X3770,X3769,X3769) = c_Groups_Ozero__class_Ozero(X3770)
        | ~ class_Groups_Olinordered__ab__group__add(X3770) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_2275,plain,
    ! [X3408,X3409] :
      ( ( c_Groups_Ozero__class_Ozero(X3409) != c_Groups_Oplus__class_Oplus(X3409,X3408,X3408)
        | X3408 = c_Groups_Ozero__class_Ozero(X3409)
        | ~ class_Groups_Olinordered__ab__group__add(X3409) )
      & ( X3408 != c_Groups_Ozero__class_Ozero(X3409)
        | c_Groups_Ozero__class_Ozero(X3409) = c_Groups_Oplus__class_Oplus(X3409,X3408,X3408)
        | ~ class_Groups_Olinordered__ab__group__add(X3409) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_2276,plain,
    ! [X3743] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3743)
      | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X3743) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sgn__pos])]) ).

fof(i_0_2277,plain,
    ! [X4140,X4141] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(X4141,X4140),X4140) != c_Groups_Oone__class_Oone(X4141)
        | X4140 = c_Groups_Oone__class_Oone(X4141)
        | X4140 = c_Groups_Ouminus__class_Ouminus(X4141,c_Groups_Oone__class_Oone(X4141))
        | ~ class_Rings_Oring__1__no__zero__divisors(X4141) )
      & ( X4140 != c_Groups_Oone__class_Oone(X4141)
        | hAPP(c_Groups_Otimes__class_Otimes(X4141,X4140),X4140) = c_Groups_Oone__class_Oone(X4141)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4141) )
      & ( X4140 != c_Groups_Ouminus__class_Ouminus(X4141,c_Groups_Oone__class_Oone(X4141))
        | hAPP(c_Groups_Otimes__class_Otimes(X4141,X4140),X4140) = c_Groups_Oone__class_Oone(X4141)
        | ~ class_Rings_Oring__1__no__zero__divisors(X4141) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).

fof(i_0_2278,plain,
    ! [X4152,X4153] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4153,X4152) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X4152 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4153) )
      & ( X4152 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4153)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4153,X4152) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff])]) ).

fof(i_0_2279,plain,
    ! [X3414,X3415,X3416] :
      ( ( X3415 != c_Groups_Oplus__class_Oplus(X3416,X3415,X3414)
        | X3414 = c_Groups_Ozero__class_Ozero(X3416)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3416) )
      & ( X3414 != c_Groups_Ozero__class_Ozero(X3416)
        | X3415 = c_Groups_Oplus__class_Oplus(X3416,X3415,X3414)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3416) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_2280,plain,
    ! [X3225,X3226,X3227] :
      ( ~ class_Orderings_Oorder(X3227)
      | ~ c_Orderings_Oord__class_Oless(X3227,X3226,X3225)
      | X3226 != X3225 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_2281,plain,
    ! [X3216,X3217,X3218] :
      ( ~ class_Orderings_Oorder(X3218)
      | ~ c_Orderings_Oord__class_Oless(X3218,X3217,X3216)
      | X3217 != X3216 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_2282,plain,
    ! [X3213,X3214,X3215] :
      ( ~ class_Orderings_Oorder(X3215)
      | ~ c_Orderings_Oord__class_Oless(X3215,X3214,X3213)
      | X3213 != X3214 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_2283,plain,
    ! [X4279] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4279) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4279,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4279,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4279) = 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_2284,plain,
    ! [X4278] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4278)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4278,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4278,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4278) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

fof(i_0_2285,plain,
    ! [X4304,X4305] :
      ( ~ class_Fields_Ofield__inverse__zero(X4305)
      | ~ class_Int_Onumber__ring(X4305)
      | c_Rings_Oinverse__class_Odivide(X4305,X4304,c_Int_Onumber__class_Onumber__of(X4305,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X4305) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_2286,plain,
    ! [X4413] :
      ( ( X4413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4413) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4413)
        | X4413 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_2287,plain,
    ! [X3243,X3244] :
      ( ~ class_Orderings_Opreorder(X3244)
      | ~ c_Orderings_Oord__class_Oless(X3244,X3243,X3243) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1437])]) ).

fof(i_0_2288,plain,
    ! [X4148,X4149] :
      ( ~ class_Rings_Odivision__ring(X4149)
      | X4148 = c_Groups_Ozero__class_Ozero(X4149)
      | c_Rings_Oinverse__class_Oinverse(X4149,c_Groups_Ouminus__class_Ouminus(X4149,X4148)) = c_Groups_Ouminus__class_Ouminus(X4149,c_Rings_Oinverse__class_Oinverse(X4149,X4148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).

fof(i_0_2289,plain,
    ! [X4425] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4425,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X4425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4425 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4425,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).

fof(i_0_2290,plain,
    ! [X3584,X3585,X3586] :
      ( ~ class_Rings_Odivision__ring(X3586)
      | hAPP(c_Groups_Otimes__class_Otimes(X3586,X3585),X3584) != c_Groups_Oone__class_Oone(X3586)
      | c_Rings_Oinverse__class_Oinverse(X3586,X3585) = X3584 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).

fof(i_0_2291,plain,
    ! [X4133,X4134] :
      ( ~ class_Groups_Oab__group__add(X4134)
      | c_Groups_Oplus__class_Oplus(X4134,c_Groups_Ouminus__class_Ouminus(X4134,X4133),X4133) = c_Groups_Ozero__class_Ozero(X4134) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_2292,plain,
    ! [X4131,X4132] :
      ( ~ class_Groups_Ogroup__add(X4132)
      | c_Groups_Oplus__class_Oplus(X4132,c_Groups_Ouminus__class_Ouminus(X4132,X4131),X4131) = c_Groups_Ozero__class_Ozero(X4132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_2293,plain,
    ! [X4126,X4127] :
      ( ~ class_Groups_Ogroup__add(X4127)
      | c_Groups_Oplus__class_Oplus(X4127,X4126,c_Groups_Ouminus__class_Ouminus(X4127,X4126)) = c_Groups_Ozero__class_Ozero(X4127) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_2294,plain,
    ! [X4420,X4421] :
      ( ( X4421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4421,X4420) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4420 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4421,X4420) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4421 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X4420 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4421,X4420) = 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_2295,plain,
    ! [X4415,X4416] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4416,X4415)
      | X4415 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).

fof(i_0_2296,plain,
    ! [X3736] :
      ( X3736 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3736)),X3736) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__left])]) ).

fof(i_0_2297,plain,
    ! [X4418,X4419] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4419,X4418) != X4419
      | X4418 = 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_2298,plain,
    ! [X4414] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4414,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1438]) ).

fof(i_0_2299,plain,
    ! [X4412] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4412,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1439]) ).

fof(i_0_2300,plain,
    ! [X4366] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1440]) ).

fof(i_0_2301,plain,
    ! [X4156] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4156)),
    inference(variable_rename,[status(thm)],[fact_exp__ge__zero]) ).

fof(i_0_2302,plain,
    ! [X4158] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4158)),
    inference(variable_rename,[status(thm)],[fact_exp__gt__zero]) ).

fof(i_0_2303,plain,
    ! [X5032] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X5032) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X5032,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5032)),
    inference(variable_rename,[status(thm)],[fact_real__sgn__eq]) ).

fof(i_0_2304,plain,
    ! [X4378,X4379] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4379,X4378)
      | X4379 != X4378 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_2305,plain,
    ! [X4376,X4377] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4377,X4376)
      | X4376 != X4377 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

fof(i_0_2306,plain,
    ! [X2764,X2765,X2766] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(X2766,X2765),X2764) != c_Groups_Ozero__class_Ozero(X2766)
        | X2765 = c_Groups_Ozero__class_Ozero(X2766)
        | X2764 = c_Groups_Ozero__class_Ozero(X2766)
        | ~ class_Rings_Oring__no__zero__divisors(X2766) )
      & ( X2765 != c_Groups_Ozero__class_Ozero(X2766)
        | hAPP(c_Groups_Otimes__class_Otimes(X2766,X2765),X2764) = c_Groups_Ozero__class_Ozero(X2766)
        | ~ class_Rings_Oring__no__zero__divisors(X2766) )
      & ( X2764 != c_Groups_Ozero__class_Ozero(X2766)
        | hAPP(c_Groups_Otimes__class_Otimes(X2766,X2765),X2764) = c_Groups_Ozero__class_Ozero(X2766)
        | ~ class_Rings_Oring__no__zero__divisors(X2766) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_2307,plain,
    ! [X2761,X2762,X2763] :
      ( ~ class_Rings_Ono__zero__divisors(X2763)
      | X2762 = c_Groups_Ozero__class_Ozero(X2763)
      | X2761 = c_Groups_Ozero__class_Ozero(X2763)
      | hAPP(c_Groups_Otimes__class_Otimes(X2763,X2762),X2761) != c_Groups_Ozero__class_Ozero(X2763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_2308,plain,
    ! [X2758,X2759,X2760] :
      ( ~ class_Rings_Ono__zero__divisors(X2760)
      | hAPP(c_Groups_Otimes__class_Otimes(X2760,X2759),X2758) != c_Groups_Ozero__class_Ozero(X2760)
      | X2759 = c_Groups_Ozero__class_Ozero(X2760)
      | X2758 = c_Groups_Ozero__class_Ozero(X2760) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_2309,plain,
    ! [X3692,X3693] :
      ( ~ class_Rings_Odivision__ring(X3693)
      | X3692 = c_Groups_Ozero__class_Ozero(X3693)
      | c_Rings_Oinverse__class_Oinverse(X3693,X3692) = c_Rings_Oinverse__class_Odivide(X3693,c_Groups_Oone__class_Oone(X3693),X3692) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__divide])]) ).

fof(i_0_2310,plain,
    ! [X2572,X2573,X2574] :
      ( ~ class_Rings_Ocomm__semiring__1(X2574)
      | hAPP(c_Groups_Otimes__class_Otimes(X2574,X2573),X2572) = hAPP(c_Groups_Otimes__class_Otimes(X2574,X2572),X2573) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(i_0_2311,plain,
    ! [X3914,X3915] :
      ( ~ class_RealVector_Oreal__normed__vector(X3915)
      | c_Groups_Osgn__class_Osgn(X3915,c_Groups_Ouminus__class_Ouminus(X3915,X3914)) = c_Groups_Ouminus__class_Ouminus(X3915,c_Groups_Osgn__class_Osgn(X3915,X3914)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__minus])]) ).

fof(i_0_2312,plain,
    ! [X4009,X4010] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X4010)
      | c_Rings_Oinverse__class_Oinverse(X4010,c_Groups_Ouminus__class_Ouminus(X4010,X4009)) = c_Groups_Ouminus__class_Ouminus(X4010,c_Rings_Oinverse__class_Oinverse(X4010,X4009)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).

fof(i_0_2313,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_2314,plain,
    ! [X4290,X4291] :
      ( ~ class_Int_Onumber__ring(X4291)
      | c_Groups_Oplus__class_Oplus(X4291,c_Int_Onumber__class_Onumber__of(X4291,c_Int_OPls),X4290) = X4290 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_2315,plain,
    ! [X4288,X4289] :
      ( ~ class_Int_Onumber__ring(X4289)
      | c_Groups_Oplus__class_Oplus(X4289,X4288,c_Int_Onumber__class_Onumber__of(X4289,c_Int_OPls)) = X4288 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

cnf(i_0_2316,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1441]) ).

cnf(i_0_2317,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_1442]) ).

fof(i_0_2318,plain,
    ! [X4942,X4943] :
      ( ( X4942 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4943,c_Groups_Ozero__class_Ozero(X4943),X4942) = c_Groups_Oone__class_Oone(X4943)
        | ~ class_Power_Opower(X4943)
        | ~ class_Rings_Osemiring__0(X4943) )
      & ( X4942 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X4943,c_Groups_Ozero__class_Ozero(X4943),X4942) = c_Groups_Ozero__class_Ozero(X4943)
        | ~ class_Power_Opower(X4943)
        | ~ class_Rings_Osemiring__0(X4943) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).

fof(i_0_2319,plain,
    ! [X3908,X3909] :
      ( ~ class_Int_Onumber__ring(X3909)
      | c_Int_Onumber__class_Onumber__of(X3909,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3908)) = c_Groups_Ouminus__class_Ouminus(X3909,c_Int_Onumber__class_Onumber__of(X3909,X3908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_2320,plain,
    ! [X3910,X3911] :
      ( ~ class_Int_Onumber__ring(X3911)
      | c_Groups_Ouminus__class_Ouminus(X3911,c_Int_Onumber__class_Onumber__of(X3911,X3910)) = c_Int_Onumber__class_Onumber__of(X3911,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3910)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_2321,plain,
    ! [X4375] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4375,X4375),
    inference(variable_rename,[status(thm)],[i_0_1443]) ).

fof(i_0_2322,plain,
    ! [X4370] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4370,X4370),
    inference(variable_rename,[status(thm)],[i_0_1444]) ).

fof(i_0_2323,plain,
    ! [X3690,X3691] :
      ( ~ class_Rings_Odivision__ring(X3691)
      | X3690 = c_Groups_Ozero__class_Ozero(X3691)
      | hAPP(c_Groups_Otimes__class_Otimes(X3691,X3690),c_Rings_Oinverse__class_Oinverse(X3691,X3690)) = c_Groups_Oone__class_Oone(X3691) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).

fof(i_0_2324,plain,
    ! [X3595,X3596] :
      ( ~ class_Rings_Odivision__ring(X3596)
      | c_Rings_Oinverse__class_Oinverse(X3596,X3595) = c_Rings_Oinverse__class_Odivide(X3596,c_Groups_Oone__class_Oone(X3596),X3595) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide])]) ).

fof(i_0_2325,plain,
    ! [X3593,X3594] :
      ( ~ class_Fields_Ofield(X3594)
      | c_Rings_Oinverse__class_Oinverse(X3594,X3593) = c_Rings_Oinverse__class_Odivide(X3594,c_Groups_Oone__class_Oone(X3594),X3593) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__class_Onormalizing__field__rules_I2_J])]) ).

fof(i_0_2326,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_2327,plain,
    ! [X4232] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4232),X4232) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_2328,plain,
    ! [X2732,X2733] :
      ( ( X2732 != c_Groups_Ozero__class_Ozero(X2733)
        | c_Rings_Oinverse__class_Odivide(X2733,X2732,X2732) = c_Groups_Ozero__class_Ozero(X2733)
        | ~ class_Rings_Odivision__ring__inverse__zero(X2733) )
      & ( X2732 = c_Groups_Ozero__class_Ozero(X2733)
        | c_Rings_Oinverse__class_Odivide(X2733,X2732,X2732) = c_Groups_Oone__class_Oone(X2733)
        | ~ class_Rings_Odivision__ring__inverse__zero(X2733) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_2329,plain,
    ! [X2933] :
      ( ~ class_Rings_Olinordered__semidom(X2933)
      | c_Orderings_Oord__class_Oless__eq(X2933,c_Groups_Ozero__class_Ozero(X2933),c_Groups_Oone__class_Oone(X2933)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_2330,plain,
    ! [X2753] :
      ( ~ class_Rings_Olinordered__semidom(X2753)
      | c_Orderings_Oord__class_Oless(X2753,c_Groups_Ozero__class_Ozero(X2753),c_Groups_Oone__class_Oone(X2753)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_2331,plain,
    ! [X4410,X4411] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4411),X4410) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4410),X4411),
    inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).

fof(i_0_2332,plain,
    ! [X4048,X4049] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4049),X4048) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4048),X4049),
    inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).

fof(i_0_2333,plain,
    ! [X2563,X2564] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2564),X2563) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2563),X2564),
    inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).

fof(i_0_2334,plain,
    ! [X4881,X4882] :
      ( ~ class_Groups_Omonoid__mult(X4882)
      | c_Power_Opower__class_Opower(X4882,c_Groups_Oone__class_Oone(X4882),X4881) = c_Groups_Oone__class_Oone(X4882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).

fof(i_0_2335,plain,
    ! [X2844,X2845] :
      ( ~ class_RealVector_Oreal__normed__field(X2845)
      | c_Rings_Oinverse__class_Odivide(X2845,c_Groups_Ozero__class_Ozero(X2845),X2844) = c_Groups_Ozero__class_Ozero(X2845) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ozero])]) ).

fof(i_0_2336,plain,
    ! [X2773,X2774] :
      ( ~ class_Rings_Odivision__ring(X2774)
      | c_Rings_Oinverse__class_Odivide(X2774,c_Groups_Ozero__class_Ozero(X2774),X2773) = c_Groups_Ozero__class_Ozero(X2774) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_2337,plain,
    ! [X2775,X2776] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X2776)
      | c_Rings_Oinverse__class_Odivide(X2776,X2775,c_Groups_Ozero__class_Ozero(X2776)) = c_Groups_Ozero__class_Ozero(X2776) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_2338,plain,
    ! [X2730,X2731] :
      ( ~ class_Rings_Odivision__ring(X2731)
      | X2730 = c_Groups_Ozero__class_Ozero(X2731)
      | c_Rings_Oinverse__class_Odivide(X2731,X2730,X2730) = c_Groups_Oone__class_Oone(X2731) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_2339,plain,
    ! [X4227] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4227)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4227)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_2340,plain,
    ! [X4991] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4991)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X4991)),
    inference(variable_rename,[status(thm)],[fact_arctan__minus]) ).

fof(i_0_2341,plain,
    ! [X4700] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4700)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4700)),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__minus]) ).

fof(i_0_2342,plain,
    ! [X4701] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4701)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X4701)),
    inference(variable_rename,[status(thm)],[fact_real__sqrt__inverse]) ).

fof(i_0_2343,plain,
    ! [X4432,X4433] :
      ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4433),X4432) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X4433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X4432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4433 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4433),X4432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X4432 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4433),X4432) = 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_2344,plain,
    ! [X4920,X4921] :
      ( ~ class_Power_Opower(X4921)
      | c_Power_Opower__class_Opower(X4921,X4920,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4921) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).

fof(i_0_2345,plain,
    ! [X4731,X4732] :
      ( ~ class_Rings_Ocomm__semiring__1(X4732)
      | c_Power_Opower__class_Opower(X4732,X4731,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4732) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).

fof(i_0_2346,plain,
    ! [X3412,X3413] :
      ( ~ class_Groups_Omonoid__add(X3413)
      | c_Groups_Oplus__class_Oplus(X3413,c_Groups_Ozero__class_Ozero(X3413),X3412) = X3412 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_2347,plain,
    ! [X3410,X3411] :
      ( ~ class_Groups_Ocomm__monoid__add(X3411)
      | c_Groups_Oplus__class_Oplus(X3411,c_Groups_Ozero__class_Ozero(X3411),X3410) = X3410 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_2348,plain,
    ! [X3419,X3420] :
      ( ~ class_Rings_Ocomm__semiring__1(X3420)
      | c_Groups_Oplus__class_Oplus(X3420,c_Groups_Ozero__class_Ozero(X3420),X3419) = X3419 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_2349,plain,
    ! [X3406,X3407] :
      ( ~ class_Groups_Omonoid__add(X3407)
      | c_Groups_Oplus__class_Oplus(X3407,X3406,c_Groups_Ozero__class_Ozero(X3407)) = X3406 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_2350,plain,
    ! [X3404,X3405] :
      ( ~ class_Groups_Ocomm__monoid__add(X3405)
      | c_Groups_Oplus__class_Oplus(X3405,X3404,c_Groups_Ozero__class_Ozero(X3405)) = X3404 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_2351,plain,
    ! [X3417,X3418] :
      ( ~ class_Rings_Ocomm__semiring__1(X3418)
      | c_Groups_Oplus__class_Oplus(X3418,X3417,c_Groups_Ozero__class_Ozero(X3418)) = X3417 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_2352,plain,
    ! [X2781,X2782] :
      ( ~ class_Rings_Odivision__ring(X2782)
      | c_Rings_Oinverse__class_Odivide(X2782,X2781,c_Groups_Oone__class_Oone(X2782)) = X2781 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_2353,plain,
    ! [X4548,X4549] :
      ( X4549 != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4549),X4548)
      | X4548 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X4549 = 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_2354,plain,
    ! [X4526,X4527] :
      ( ( X4527 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4527),X4526) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X4526 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4527),X4526) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X4527 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X4526 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4527),X4526) = 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_2355,plain,
    ! [X4529,X4530] :
      ( ( X4530 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4530),X4529) )
      & ( X4529 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4530),X4529) )
      & ( X4530 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X4529 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4530),X4529) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).

fof(i_0_2356,plain,
    ! [X4894,X4895] :
      ( ~ class_Groups_Omonoid__mult(X4895)
      | c_Power_Opower__class_Opower(X4895,X4894,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4894 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).

fof(i_0_2357,plain,
    ! [X4745,X4746] :
      ( ~ class_Rings_Ocomm__semiring__1(X4746)
      | c_Power_Opower__class_Opower(X4746,X4745,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4745 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).

fof(i_0_2358,plain,
    ! [X3128,X3129,X3130] :
      ( ~ class_Orderings_Opreorder(X3130)
      | X3129 != X3128
      | c_Orderings_Oord__class_Oless__eq(X3130,X3129,X3128) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_2359,plain,
    ! [X3383,X3384,X3385] :
      ( ~ class_Rings_Odivision__ring(X3385)
      | c_Rings_Oinverse__class_Oinverse(X3385,X3384) != c_Rings_Oinverse__class_Oinverse(X3385,X3383)
      | X3384 = c_Groups_Ozero__class_Ozero(X3385)
      | X3383 = c_Groups_Ozero__class_Ozero(X3385)
      | X3384 = X3383 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).

fof(i_0_2360,plain,
    ! [X2860,X2861] :
      ( ~ class_RealVector_Oreal__normed__algebra(X2861)
      | hAPP(c_Groups_Otimes__class_Otimes(X2861,c_Groups_Ozero__class_Ozero(X2861)),X2860) = c_Groups_Ozero__class_Ozero(X2861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).

fof(i_0_2361,plain,
    ! [X2858,X2859] :
      ( ~ class_RealVector_Oreal__normed__algebra(X2859)
      | hAPP(c_Groups_Otimes__class_Otimes(X2859,c_Groups_Ozero__class_Ozero(X2859)),X2858) = c_Groups_Ozero__class_Ozero(X2859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).

fof(i_0_2362,plain,
    ! [X2769,X2770] :
      ( ~ class_Rings_Omult__zero(X2770)
      | hAPP(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_mult__zero__left])]) ).

fof(i_0_2363,plain,
    ! [X2588,X2589] :
      ( ~ class_Rings_Ocomm__semiring__1(X2589)
      | hAPP(c_Groups_Otimes__class_Otimes(X2589,c_Groups_Ozero__class_Ozero(X2589)),X2588) = c_Groups_Ozero__class_Ozero(X2589) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

cnf(i_0_2364,plain,
    c_Int_Osucc(c_Int_Opred(X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1445]) ).

fof(i_0_2365,plain,
    ! [X3090,X3091] :
      ( ~ class_Orderings_Opreorder(X3091)
      | c_Orderings_Oord__class_Oless__eq(X3091,X3090,X3090) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_2366,plain,
    ! [X3320,X3321] :
      ( ~ class_Rings_Olinordered__idom(X3321)
      | c_Groups_Osgn__class_Osgn(X3321,c_Groups_Osgn__class_Osgn(X3321,X3320)) = c_Groups_Osgn__class_Osgn(X3321,X3320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_2367,plain,
    ! [X3824,X3825,X3826] :
      ( ( c_Int_Onumber__class_Onumber__of(X3826,X3825) != c_Int_Onumber__class_Onumber__of(X3826,X3824)
        | X3825 = X3824
        | ~ class_Int_Onumber__ring(X3826)
        | ~ class_Int_Oring__char__0(X3826) )
      & ( X3825 != X3824
        | c_Int_Onumber__class_Onumber__of(X3826,X3825) = c_Int_Onumber__class_Onumber__of(X3826,X3824)
        | ~ class_Int_Onumber__ring(X3826)
        | ~ class_Int_Oring__char__0(X3826) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_2368,plain,
    ! [X2852,X2853] :
      ( ~ class_Groups_Omonoid__mult(X2853)
      | hAPP(c_Groups_Otimes__class_Otimes(X2853,c_Groups_Oone__class_Oone(X2853)),X2852) = X2852 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_2369,plain,
    ! [X2850,X2851] :
      ( ~ class_Groups_Ocomm__monoid__mult(X2851)
      | hAPP(c_Groups_Otimes__class_Otimes(X2851,c_Groups_Oone__class_Oone(X2851)),X2850) = X2850 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_2370,plain,
    ! [X2584,X2585] :
      ( ~ class_Rings_Ocomm__semiring__1(X2585)
      | hAPP(c_Groups_Otimes__class_Otimes(X2585,c_Groups_Oone__class_Oone(X2585)),X2584) = X2584 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_2371,plain,
    ! [X4417] :
      ( X4417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4417) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_2372,plain,
    ! [X2856,X2857] :
      ( ~ class_RealVector_Oreal__normed__algebra(X2857)
      | hAPP(c_Groups_Otimes__class_Otimes(X2857,X2856),c_Groups_Ozero__class_Ozero(X2857)) = c_Groups_Ozero__class_Ozero(X2857) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).

fof(i_0_2373,plain,
    ! [X2854,X2855] :
      ( ~ class_RealVector_Oreal__normed__algebra(X2855)
      | hAPP(c_Groups_Otimes__class_Otimes(X2855,X2854),c_Groups_Ozero__class_Ozero(X2855)) = c_Groups_Ozero__class_Ozero(X2855) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).

fof(i_0_2374,plain,
    ! [X2767,X2768] :
      ( ~ class_Rings_Omult__zero(X2768)
      | hAPP(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_mult__zero__right])]) ).

fof(i_0_2375,plain,
    ! [X2586,X2587] :
      ( ~ class_Rings_Ocomm__semiring__1(X2587)
      | hAPP(c_Groups_Otimes__class_Otimes(X2587,X2586),c_Groups_Ozero__class_Ozero(X2587)) = c_Groups_Ozero__class_Ozero(X2587) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_2376,plain,
    ! [X4423] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4423) = X4423,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_2377,plain,
    ! [X4059] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4059) = X4059,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_2378,plain,
    ! [X4422] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4422,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4422,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_2379,plain,
    ! [X4060] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4060,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4060,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_2380,plain,
    ! [X4402,X4403] :
      ( X4403 != X4402
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4403,X4402) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_2381,plain,
    ! [X4424] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4424),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_2382,plain,
    ! [X4365] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4365),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_2383,plain,
    ! [X3920,X3921] :
      ( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3921) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3920)
        | X3921 = X3920 )
      & ( X3921 != X3920
        | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3921) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X3920) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__inj__iff])]) ).

cnf(i_0_2384,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_1442]) ).

cnf(i_0_2385,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1441]) ).

fof(i_0_2386,plain,
    ! [X2848,X2849] :
      ( ~ class_Groups_Omonoid__mult(X2849)
      | hAPP(c_Groups_Otimes__class_Otimes(X2849,X2848),c_Groups_Oone__class_Oone(X2849)) = X2848 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_2387,plain,
    ! [X2846,X2847] :
      ( ~ class_Groups_Ocomm__monoid__mult(X2847)
      | hAPP(c_Groups_Otimes__class_Otimes(X2847,X2846),c_Groups_Oone__class_Oone(X2847)) = X2846 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_2388,plain,
    ! [X2582,X2583] :
      ( ~ class_Rings_Ocomm__semiring__1(X2583)
      | hAPP(c_Groups_Otimes__class_Otimes(X2583,X2582),c_Groups_Oone__class_Oone(X2583)) = X2582 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_2389,plain,
    ! [X4017,X4018,X4019] :
      ( ( c_Groups_Ouminus__class_Ouminus(X4019,X4018) != c_Groups_Ouminus__class_Ouminus(X4019,X4017)
        | X4018 = X4017
        | ~ class_Lattices_Oboolean__algebra(X4019) )
      & ( X4018 != X4017
        | c_Groups_Ouminus__class_Ouminus(X4019,X4018) = c_Groups_Ouminus__class_Ouminus(X4019,X4017)
        | ~ class_Lattices_Oboolean__algebra(X4019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_2390,plain,
    ! [X4028,X4029,X4030] :
      ( ( c_Groups_Ouminus__class_Ouminus(X4030,X4029) != c_Groups_Ouminus__class_Ouminus(X4030,X4028)
        | X4029 = X4028
        | ~ class_Groups_Ogroup__add(X4030) )
      & ( X4029 != X4028
        | c_Groups_Ouminus__class_Ouminus(X4030,X4029) = c_Groups_Ouminus__class_Ouminus(X4030,X4028)
        | ~ class_Groups_Ogroup__add(X4030) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_2391,plain,
    ! [X3325,X3326,X3327] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X3327)
      | c_Rings_Oinverse__class_Oinverse(X3327,X3326) != c_Rings_Oinverse__class_Oinverse(X3327,X3325)
      | X3326 = X3325 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq])]) ).

fof(i_0_2392,plain,
    ! [X3322,X3323,X3324] :
      ( ( c_Rings_Oinverse__class_Oinverse(X3324,X3323) != c_Rings_Oinverse__class_Oinverse(X3324,X3322)
        | X3323 = X3322
        | ~ class_Rings_Odivision__ring__inverse__zero(X3324) )
      & ( X3323 != X3322
        | c_Rings_Oinverse__class_Oinverse(X3324,X3323) = c_Rings_Oinverse__class_Oinverse(X3324,X3322)
        | ~ class_Rings_Odivision__ring__inverse__zero(X3324) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq])])]) ).

fof(i_0_2393,plain,
    ! [X3388,X3389] :
      ( ~ class_Rings_Odivision__ring(X3389)
      | X3388 = c_Groups_Ozero__class_Ozero(X3389)
      | c_Rings_Oinverse__class_Oinverse(X3389,c_Rings_Oinverse__class_Oinverse(X3389,X3388)) = X3388 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).

fof(i_0_2394,plain,
    ! [X4406] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4406,X4406),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_2395,plain,
    ! [X4042] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4042,X4042),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_2396,plain,
    ! [X2862] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2862,X2862),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

fof(i_0_2397,plain,
    ! [X4103,X4104] :
      ( ~ class_RealVector_Oreal__normed__field(X4104)
      | ~ class_SEQ_Obanach(X4104)
      | hAPP(c_Transcendental_Oexp(X4104),X4103) != c_Groups_Ozero__class_Ozero(X4104) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__not__eq__zero])]) ).

fof(i_0_2398,plain,
    ! [X4283] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X4283) = X4283,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_2399,plain,
    ! [X4282] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4282,c_Int_OPls) = X4282,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

cnf(i_0_2400,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

fof(i_0_2401,plain,
    ! [X2570,X2571] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X2571)
      | hAPP(c_Groups_Otimes__class_Otimes(X2571,X2570),X2570) = X2570 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).

fof(i_0_2402,plain,
    ! [X2568,X2569] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X2569)
      | hAPP(c_Groups_Otimes__class_Otimes(X2569,X2568),X2568) = X2568 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).

fof(i_0_2403,plain,
    ! [X4011,X4012] :
      ( ~ class_Lattices_Oboolean__algebra(X4012)
      | c_Groups_Ouminus__class_Ouminus(X4012,c_Groups_Ouminus__class_Ouminus(X4012,X4011)) = X4011 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_2404,plain,
    ! [X4020,X4021] :
      ( ~ class_Groups_Ogroup__add(X4021)
      | c_Groups_Ouminus__class_Ouminus(X4021,c_Groups_Ouminus__class_Ouminus(X4021,X4020)) = X4020 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_2405,plain,
    ! [X3318,X3319] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X3319)
      | c_Rings_Oinverse__class_Oinverse(X3319,c_Rings_Oinverse__class_Oinverse(X3319,X3318)) = X3318 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).

fof(i_0_2406,plain,
    ! [X4025,X4026,X4027] :
      ( ( c_Groups_Ouminus__class_Ouminus(X4027,X4026) != X4025
        | c_Groups_Ouminus__class_Ouminus(X4027,X4025) = X4026
        | ~ class_Groups_Ogroup__add(X4027) )
      & ( c_Groups_Ouminus__class_Ouminus(X4027,X4025) != X4026
        | c_Groups_Ouminus__class_Ouminus(X4027,X4026) = X4025
        | ~ class_Groups_Ogroup__add(X4027) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_2407,plain,
    ! [X4022,X4023,X4024] :
      ( ( X4023 != c_Groups_Ouminus__class_Ouminus(X4024,X4022)
        | X4022 = c_Groups_Ouminus__class_Ouminus(X4024,X4023)
        | ~ class_Groups_Ogroup__add(X4024) )
      & ( X4022 != c_Groups_Ouminus__class_Ouminus(X4024,X4023)
        | X4023 = c_Groups_Ouminus__class_Ouminus(X4024,X4022)
        | ~ class_Groups_Ogroup__add(X4024) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_2408,plain,
    ! [X4435] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4435) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0]) ).

fof(i_0_2409,plain,
    ! [X4098] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4098)) = X4098,
    inference(variable_rename,[status(thm)],[fact_ln__exp]) ).

fof(i_0_2410,plain,
    ! [X4161] :
      ( ~ class_RealVector_Oreal__normed__field(X4161)
      | ~ class_SEQ_Obanach(X4161)
      | hAPP(c_Transcendental_Oexp(X4161),c_Groups_Ozero__class_Ozero(X4161)) = c_Groups_Oone__class_Oone(X4161) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__zero])]) ).

fof(i_0_2411,plain,
    ! [X4299] :
      ( ~ class_Int_Onumber__ring(X4299)
      | c_Int_Oiszero(X4299,c_Int_Onumber__class_Onumber__of(X4299,c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).

fof(i_0_2412,plain,
    ! [X4531] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4531) = X4531,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

fof(i_0_2413,plain,
    ! [X4043] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4043) = X4043,
    inference(variable_rename,[status(thm)],[fact_zmult__1]) ).

fof(i_0_2414,plain,
    ! [X2590] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X2590) = X2590,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

fof(i_0_2415,plain,
    ! [X4434] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4434),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_2416,plain,
    ! [X4101,X4102] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4102) != X4101
      | hAPP(c_Transcendental_Oln,X4101) = X4102 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ln__unique])]) ).

fof(i_0_2417,plain,
    ! [X4099,X4100] :
      ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4100) != X4099
      | hAPP(c_Transcendental_Oln,X4099) = X4100 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__ln__eq])]) ).

fof(i_0_2418,plain,
    ! [X4704,X4705] :
      ( ( hAPP(c_NthRoot_Osqrt,X4705) != hAPP(c_NthRoot_Osqrt,X4704)
        | X4705 = X4704 )
      & ( X4705 != X4704
        | hAPP(c_NthRoot_Osqrt,X4705) = hAPP(c_NthRoot_Osqrt,X4704) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__iff])]) ).

fof(i_0_2419,plain,
    ! [X3923,X3924] :
      ( ( c_Groups_Ozero__class_Ozero(X3924) != c_Groups_Ouminus__class_Ouminus(X3924,X3923)
        | c_Groups_Ozero__class_Ozero(X3924) = X3923
        | ~ class_Groups_Ogroup__add(X3924) )
      & ( c_Groups_Ozero__class_Ozero(X3924) != X3923
        | c_Groups_Ozero__class_Ozero(X3924) = c_Groups_Ouminus__class_Ouminus(X3924,X3923)
        | ~ class_Groups_Ogroup__add(X3924) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_2420,plain,
    ! [X3398,X3399] :
      ( ( c_Rings_Oinverse__class_Oinverse(X3399,X3398) != c_Groups_Oone__class_Oone(X3399)
        | X3398 = c_Groups_Oone__class_Oone(X3399)
        | ~ class_Fields_Ofield__inverse__zero(X3399) )
      & ( X3398 != c_Groups_Oone__class_Oone(X3399)
        | c_Rings_Oinverse__class_Oinverse(X3399,X3398) = c_Groups_Oone__class_Oone(X3399)
        | ~ class_Fields_Ofield__inverse__zero(X3399) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).

fof(i_0_2421,plain,
    ! [X3927,X3928] :
      ( ( c_Groups_Ouminus__class_Ouminus(X3928,X3927) != c_Groups_Ozero__class_Ozero(X3928)
        | X3927 = c_Groups_Ozero__class_Ozero(X3928)
        | ~ class_Groups_Ogroup__add(X3928) )
      & ( X3927 != c_Groups_Ozero__class_Ozero(X3928)
        | c_Groups_Ouminus__class_Ouminus(X3928,X3927) = c_Groups_Ozero__class_Ozero(X3928)
        | ~ class_Groups_Ogroup__add(X3928) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_2422,plain,
    ! [X3540,X3541] :
      ( ( c_Groups_Osgn__class_Osgn(X3541,X3540) != c_Groups_Ozero__class_Ozero(X3541)
        | X3540 = c_Groups_Ozero__class_Ozero(X3541)
        | ~ class_RealVector_Oreal__normed__vector(X3541) )
      & ( X3540 != c_Groups_Ozero__class_Ozero(X3541)
        | c_Groups_Osgn__class_Osgn(X3541,X3540) = c_Groups_Ozero__class_Ozero(X3541)
        | ~ class_RealVector_Oreal__normed__vector(X3541) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff])])]) ).

fof(i_0_2423,plain,
    ! [X3544,X3545] :
      ( ( c_Groups_Osgn__class_Osgn(X3545,X3544) != c_Groups_Ozero__class_Ozero(X3545)
        | X3544 = c_Groups_Ozero__class_Ozero(X3545)
        | ~ class_Rings_Olinordered__idom(X3545) )
      & ( X3544 != c_Groups_Ozero__class_Ozero(X3545)
        | c_Groups_Osgn__class_Osgn(X3545,X3544) = c_Groups_Ozero__class_Ozero(X3545)
        | ~ class_Rings_Olinordered__idom(X3545) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_2424,plain,
    ! [X3392,X3393] :
      ( ( c_Rings_Oinverse__class_Oinverse(X3393,X3392) != c_Groups_Ozero__class_Ozero(X3393)
        | X3392 = c_Groups_Ozero__class_Ozero(X3393)
        | ~ class_Rings_Odivision__ring__inverse__zero(X3393) )
      & ( X3392 != c_Groups_Ozero__class_Ozero(X3393)
        | c_Rings_Oinverse__class_Oinverse(X3393,X3392) = c_Groups_Ozero__class_Ozero(X3393)
        | ~ class_Rings_Odivision__ring__inverse__zero(X3393) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).

fof(i_0_2425,plain,
    ! [X3390,X3391] :
      ( ~ class_Rings_Odivision__ring(X3391)
      | X3390 = c_Groups_Ozero__class_Ozero(X3391)
      | c_Rings_Oinverse__class_Oinverse(X3391,X3390) != c_Groups_Ozero__class_Ozero(X3391) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).

fof(i_0_2426,plain,
    ! [X3386,X3387] :
      ( ~ class_Rings_Odivision__ring(X3387)
      | c_Rings_Oinverse__class_Oinverse(X3387,X3386) != c_Groups_Ozero__class_Ozero(X3387)
      | X3386 = c_Groups_Ozero__class_Ozero(X3387) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).

fof(i_0_2427,plain,
    ! [X4528] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4528),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4528,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).

fof(i_0_2428,plain,
    ! [X4044] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4044),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4044,
    inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).

fof(i_0_2429,plain,
    ! [X4268] :
      ( ~ class_Rings_Osemiring__1(X4268)
      | ~ c_Int_Oiszero(X4268,c_Groups_Oone__class_Oone(X4268)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])]) ).

fof(i_0_2430,plain,
    ! [X5046,X5047] :
      ( ~ class_Groups_Ouminus(X5047)
      | class_Groups_Ouminus(tc_fun(X5046,X5047)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_2431,plain,
    ! [X5038,X5039] :
      ( ~ class_Lattices_Oboolean__algebra(X5039)
      | class_Lattices_Oboolean__algebra(tc_fun(X5038,X5039)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_2432,plain,
    ! [X5044,X5045] :
      ( ~ class_Orderings_Oord(X5045)
      | class_Orderings_Oord(tc_fun(X5044,X5045)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_2433,plain,
    ! [X5042,X5043] :
      ( ~ class_Orderings_Oorder(X5043)
      | class_Orderings_Oorder(tc_fun(X5042,X5043)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_2434,plain,
    ! [X5040,X5041] :
      ( ~ class_Orderings_Opreorder(X5041)
      | class_Orderings_Opreorder(tc_fun(X5040,X5041)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_2435,plain,
    ! [X4228] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4228)) = X4228,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_2436,plain,
    ! [X3929,X3930] :
      ( ( c_Groups_Ouminus__class_Ouminus(X3930,X3929) != X3929
        | X3929 = c_Groups_Ozero__class_Ozero(X3930)
        | ~ class_Groups_Olinordered__ab__group__add(X3930) )
      & ( X3929 != c_Groups_Ozero__class_Ozero(X3930)
        | c_Groups_Ouminus__class_Ouminus(X3930,X3929) = X3929
        | ~ class_Groups_Olinordered__ab__group__add(X3930) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_2437,plain,
    ! [X3925,X3926] :
      ( ( X3925 != c_Groups_Ouminus__class_Ouminus(X3926,X3925)
        | X3925 = c_Groups_Ozero__class_Ozero(X3926)
        | ~ class_Groups_Olinordered__ab__group__add(X3926) )
      & ( X3925 != c_Groups_Ozero__class_Ozero(X3926)
        | X3925 = c_Groups_Ouminus__class_Ouminus(X3926,X3925)
        | ~ class_Groups_Olinordered__ab__group__add(X3926) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_2438,plain,
    ! [X4265,X4266] :
      ( ( ~ c_Int_Oiszero(X4266,X4265)
        | X4265 = c_Groups_Ozero__class_Ozero(X4266)
        | ~ class_Rings_Osemiring__1(X4266) )
      & ( X4265 != c_Groups_Ozero__class_Ozero(X4266)
        | c_Int_Oiszero(X4266,X4265)
        | ~ class_Rings_Osemiring__1(X4266) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).

fof(i_0_2439,plain,
    ! [X4160] :
      ( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4160) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X4160 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4160 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X4160) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exp__eq__one__iff])]) ).

fof(i_0_2440,plain,
    ! [X4284] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),X4284) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).

fof(i_0_2441,plain,
    ! [X5031] :
      ( ~ class_Rings_Olinordered__idom(X5031)
      | c_Groups_Oabs__class_Oabs(X5031,c_Groups_Oone__class_Oone(X5031)) = c_Groups_Oone__class_Oone(X5031) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_2442,plain,
    ! [X3922] :
      ( ~ class_Groups_Ogroup__add(X3922)
      | c_Groups_Ouminus__class_Ouminus(X3922,c_Groups_Ozero__class_Ozero(X3922)) = c_Groups_Ozero__class_Ozero(X3922) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_2443,plain,
    ! [X3552] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X3552)
      | c_Groups_Osgn__class_Osgn(X3552,c_Groups_Oone__class_Oone(X3552)) = c_Groups_Oone__class_Oone(X3552) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__one])]) ).

fof(i_0_2444,plain,
    ! [X3543] :
      ( ~ class_Groups_Osgn__if(X3543)
      | c_Groups_Osgn__class_Osgn(X3543,c_Groups_Ozero__class_Ozero(X3543)) = c_Groups_Ozero__class_Ozero(X3543) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_2445,plain,
    ! [X3542] :
      ( ~ class_RealVector_Oreal__normed__vector(X3542)
      | c_Groups_Osgn__class_Osgn(X3542,c_Groups_Ozero__class_Ozero(X3542)) = c_Groups_Ozero__class_Ozero(X3542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero])]) ).

fof(i_0_2446,plain,
    ! [X3400] :
      ( ~ class_Rings_Odivision__ring(X3400)
      | c_Rings_Oinverse__class_Oinverse(X3400,c_Groups_Oone__class_Oone(X3400)) = c_Groups_Oone__class_Oone(X3400) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).

fof(i_0_2447,plain,
    ! [X3394] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X3394)
      | c_Rings_Oinverse__class_Oinverse(X3394,c_Groups_Ozero__class_Ozero(X3394)) = c_Groups_Ozero__class_Ozero(X3394) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).

fof(i_0_2448,plain,
    ! [X3382] :
      ( ~ class_Fields_Ofield__inverse__zero(X3382)
      | c_Rings_Oinverse__class_Oinverse(X3382,c_Groups_Ozero__class_Ozero(X3382)) = c_Groups_Ozero__class_Ozero(X3382) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).

fof(i_0_2449,plain,
    ! [X4689] :
      ( ( hAPP(c_NthRoot_Osqrt,X4689) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X4689 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
      & ( X4689 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | hAPP(c_NthRoot_Osqrt,X4689) = 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_2450,plain,
    ! [X4714] :
      ( ( hAPP(c_NthRoot_Osqrt,X4714) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X4714 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4714 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | hAPP(c_NthRoot_Osqrt,X4714) = 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_2451,plain,
    ! [X4267] :
      ( ~ class_Rings_Osemiring__1(X4267)
      | c_Int_Oiszero(X4267,c_Groups_Ozero__class_Ozero(X4267)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).

fof(i_0_2452,plain,
    ! [X4287] :
      ( ~ class_Int_Onumber__ring(X4287)
      | c_Int_Onumber__class_Onumber__of(X4287,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X4287) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_2453,plain,
    ! [X4286] :
      ( ~ class_Int_Onumber__ring(X4286)
      | c_Groups_Ozero__class_Ozero(X4286) = c_Int_Onumber__class_Onumber__of(X4286,c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_2454,plain,
    ! [X2772] :
      ( ~ class_Rings_Ozero__neq__one(X2772)
      | c_Groups_Ozero__class_Ozero(X2772) != c_Groups_Oone__class_Oone(X2772) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_2455,plain,
    ! [X2771] :
      ( ~ class_Rings_Ozero__neq__one(X2771)
      | c_Groups_Oone__class_Oone(X2771) != c_Groups_Ozero__class_Ozero(X2771) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_2456,plain,
    ! [X4235] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4235) = X4235,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

cnf(i_0_2457,plain,
    c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[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)],[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_1447,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2458,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[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_1451,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2459,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[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_1452,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2460,plain,
    hAPP(c_Transcendental_Oarctan,X1) = hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(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),hAPP(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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1453,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2461,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,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1454,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2462,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),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,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
    | ~ 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,hAPP(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_Int_OPls,c_Int_OPls),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_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)],[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_1455,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2463,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[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_1456,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2464,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[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_1457,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2465,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1)
    | ~ c_Orderings_Oord__class_Oless(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),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,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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_Int_OPls,c_Int_OPls),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_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)],[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_1458,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2466,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1459,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2467,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1460,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2468,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1461,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2469,plain,
    hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),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_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[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_1462,c_0_1448]),c_0_1448]),c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2470,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1463,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2471,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1464,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2472,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1465,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2473,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1466,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2474,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) != 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)],[i_0_1467,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2475,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(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)],[inference(rw,[status(thm)],[i_0_1468,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2476,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,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3)),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)],[i_0_1469,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2477,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3)
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1470,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2478,plain,
    c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1471,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2479,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1472,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2480,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1473,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2481,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1474,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2482,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1475,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2483,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3)))
    | ~ 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)],[i_0_1476,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2484,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3)) = c_Power_Opower__class_Opower(X1,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3))
    | ~ class_Rings_Oring__1(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)],[i_0_1477,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2485,plain,
    ( X1 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3))
    | hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1478,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2486,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1479,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2487,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1480,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2488,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1481,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2489,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1482,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2490,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1483,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2491,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1484,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2492,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1485,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2493,plain,
    ( c_Power_Opower__class_Opower(X1,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1486,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2494,plain,
    ( c_Power_Opower__class_Opower(X1,X2,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X3)) = hAPP(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)],[inference(rw,[status(thm)],[i_0_1487,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2495,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1488,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2496,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1489,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2497,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1490,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2498,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(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)],[inference(rw,[status(thm)],[i_0_1491,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2499,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)),hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1(X1) ),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2500,plain,
    ( X1 = X2
    | hAPP(X3,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(X3,X1),hAPP(X3,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X3,esk12_4(X4,X3,X2,X1),X4) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1493,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2501,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X2,X1)
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1494,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2502,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) != 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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1495,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2503,plain,
    ( 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)
    | ~ 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_Int_OPls,c_Int_OPls),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_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)],[i_0_1496,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2504,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1497,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2505,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[i_0_1498,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2506,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1499,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2507,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_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2)),X2)
    | ~ 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_1500,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2508,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2509,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2510,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,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1503,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2511,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1504,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2512,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1505,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2513,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_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),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)],[inference(rw,[status(thm)],[i_0_1506,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2514,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ 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)],[i_0_1507,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2515,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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)],[i_0_1508,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2516,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | ~ 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)],[i_0_1509,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2517,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(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_1510,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2518,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ class_Rings_Oring__1(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)],[i_0_1511,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2519,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1512,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2520,plain,
    hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2521,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_Int_OPls,c_Int_OPls),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_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)],[i_0_1514,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2522,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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_Int_OPls,c_Int_OPls),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_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)],[i_0_1515,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2523,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_Int_OPls,c_Int_OPls),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_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)],[i_0_1516,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2524,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1517,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2525,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | X2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1518,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2526,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(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)],[i_0_1519,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2527,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1520,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2528,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1521,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2529,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,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(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_1522,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2530,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1523,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2531,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) != 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1524,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2532,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk4_4(X3,X2,X4,X1)),hAPP(X3,esk4_4(X3,X2,X4,X1)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_2533,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1526,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2534,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1527,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2535,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1528,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2536,plain,
    ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1529,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2537,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | c_Int_Onumber__class_Onumber__of(X1,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_1530,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2538,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1531,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2539,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1532,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2540,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1533,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2541,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1534,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2542,plain,
    hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1535,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2543,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2544,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1537,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2545,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    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_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2546,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1539,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2547,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(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_1540,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2548,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1541,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2549,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1542,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2550,plain,
    ( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1543,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2551,plain,
    ( hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3))))
    | ~ hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,esk11_3(X2,X1,X3),X3)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_2552,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))))
    | c_Groups_Oone__class_Oone(X1) != c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1545,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2553,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ 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)],[i_0_1546,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2554,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_Int_OPls,c_Int_OPls),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_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)],[i_0_1547,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2555,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1548,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2556,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1549,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2557,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_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1550]),
    [final] ).

cnf(i_0_2558,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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,hAPP(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_1551]),
    [final] ).

cnf(i_0_2559,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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,hAPP(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_1552]),
    [final] ).

cnf(i_0_2560,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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_1553]),
    [final] ).

cnf(i_0_2561,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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_1554]),
    [final] ).

cnf(i_0_2562,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),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_1555,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2563,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),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_1556,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2564,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),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_1557,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2565,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),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_1558,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2566,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1)),hAPP(X4,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,X1,esk8_3(X2,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1559]),
    [final] ).

cnf(i_0_2567,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(X4,X3),hAPP(X4,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,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,X1,esk7_3(X2,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1560]),
    [final] ).

cnf(i_0_2568,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1561,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2569,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(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_1562]),
    [final] ).

cnf(i_0_2570,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(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_1563]),
    [final] ).

cnf(i_0_2571,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1564]),
    [final] ).

cnf(i_0_2572,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1565]),
    [final] ).

cnf(i_0_2573,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1566,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2574,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),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)],[inference(rw,[status(thm)],[i_0_1567,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2575,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,X2,X2),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_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),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)],[inference(rw,[status(thm)],[i_0_1568,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2576,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3)),X2),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(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_1562]),
    [final] ).

cnf(i_0_2577,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3)),X2),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(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_1563]),
    [final] ).

cnf(i_0_2578,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4)),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1564]),
    [final] ).

cnf(i_0_2579,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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4)),X2))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1565]),
    [final] ).

cnf(i_0_2580,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_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)],[i_0_1569,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2581,plain,
    ( hBOOL(hAPP(X1,esk11_3(X2,X1,X3)))
    | hBOOL(hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1544]),
    [final] ).

cnf(i_0_2582,plain,
    ( c_Rings_Oinverse__class_Oinverse(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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ class_Fields_Ofield(X1)
    | ~ 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)],[i_0_1570,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2583,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_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1571]),
    [final] ).

cnf(i_0_2584,plain,
    ( c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(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_1572]),
    [final] ).

cnf(i_0_2585,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(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_1573]),
    [final] ).

cnf(i_0_2586,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(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_1574]),
    [final] ).

cnf(i_0_2587,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),c_Int_Onumber__class_Onumber__of(X1,X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1575]),
    [final] ).

cnf(i_0_2588,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),c_Int_Onumber__class_Onumber__of(X1,X2)))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1576]),
    [final] ).

cnf(i_0_2589,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,esk5_3(X2,X3,X1)),X3),X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_2590,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X5),X2),hAPP(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_1578]),
    [final] ).

cnf(i_0_2591,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X5),X2),hAPP(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_1579]),
    [final] ).

cnf(i_0_2592,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(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_1580]),
    [final] ).

cnf(i_0_2593,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(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_1573]),
    [final] ).

cnf(i_0_2594,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(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_1574]),
    [final] ).

cnf(i_0_2595,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1575]),
    [final] ).

cnf(i_0_2596,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1576]),
    [final] ).

cnf(i_0_2597,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),X4))
    | ~ 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)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1581]),
    [final] ).

cnf(i_0_2598,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_1582]),
    [final] ).

cnf(i_0_2599,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X2)))),
    inference(split_conjunct,[status(thm)],[i_0_1583]),
    [final] ).

cnf(i_0_2600,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,X1,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)],[i_0_1584,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2601,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X5),X2)),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1585]),
    [final] ).

cnf(i_0_2602,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1586,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2603,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1587,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2604,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1588,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2605,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1589,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2606,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1590,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2607,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1591,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2608,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1592,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2609,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1593,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2610,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1594,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2611,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1595,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2612,plain,
    ( X4 = X5
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ c_Deriv_Oderiv(X1,X2,X3,X4)
    | ~ c_Deriv_Oderiv(X1,X2,X3,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1596]),
    [final] ).

cnf(i_0_2613,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2),hAPP(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_1597]),
    [final] ).

cnf(i_0_2614,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4),c_Rings_Oinverse__class_Oinverse(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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_1598]),
    [final] ).

cnf(i_0_2615,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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_1599,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2616,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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_1600,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2617,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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_1601,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2618,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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_1602,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2619,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,hAPP(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_1562]),
    [final] ).

cnf(i_0_2620,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,hAPP(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_1563]),
    [final] ).

cnf(i_0_2621,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,hAPP(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_1564]),
    [final] ).

cnf(i_0_2622,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,hAPP(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_1565]),
    [final] ).

cnf(i_0_2623,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,hAPP(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_1562]),
    [final] ).

cnf(i_0_2624,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,hAPP(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_1563]),
    [final] ).

cnf(i_0_2625,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,hAPP(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_1564]),
    [final] ).

cnf(i_0_2626,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,hAPP(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_1565]),
    [final] ).

cnf(i_0_2627,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1),hAPP(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_1603]),
    [final] ).

cnf(i_0_2628,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X3),hAPP(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_1603]),
    [final] ).

cnf(i_0_2629,plain,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1604]),
    [final] ).

cnf(i_0_2630,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1573]),
    [final] ).

cnf(i_0_2631,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1574]),
    [final] ).

cnf(i_0_2632,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1575]),
    [final] ).

cnf(i_0_2633,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1576]),
    [final] ).

cnf(i_0_2634,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,hAPP(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_1573]),
    [final] ).

cnf(i_0_2635,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,hAPP(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_1574]),
    [final] ).

cnf(i_0_2636,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,hAPP(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_1575]),
    [final] ).

cnf(i_0_2637,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,hAPP(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_1576]),
    [final] ).

cnf(i_0_2638,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_1605]),
    [final] ).

cnf(i_0_2639,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_1606]),
    [final] ).

cnf(i_0_2640,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,hAPP(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_1562]),
    [final] ).

cnf(i_0_2641,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,hAPP(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_1563]),
    [final] ).

cnf(i_0_2642,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,hAPP(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_1564]),
    [final] ).

cnf(i_0_2643,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,hAPP(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_1565]),
    [final] ).

cnf(i_0_2644,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,hAPP(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_1607]),
    [final] ).

cnf(i_0_2645,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X4),hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1608]),
    [final] ).

cnf(i_0_2646,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1609,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2647,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1610,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2648,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,hAPP(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_1611]),
    [final] ).

cnf(i_0_2649,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1562]),
    [final] ).

cnf(i_0_2650,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1563]),
    [final] ).

cnf(i_0_2651,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1564]),
    [final] ).

cnf(i_0_2652,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1565]),
    [final] ).

cnf(i_0_2653,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,hAPP(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_1573]),
    [final] ).

cnf(i_0_2654,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,hAPP(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_1574]),
    [final] ).

cnf(i_0_2655,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,hAPP(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_1575]),
    [final] ).

cnf(i_0_2656,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,hAPP(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_1576]),
    [final] ).

cnf(i_0_2657,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,hAPP(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_1573]),
    [final] ).

cnf(i_0_2658,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,hAPP(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_1574]),
    [final] ).

cnf(i_0_2659,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,hAPP(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_1575]),
    [final] ).

cnf(i_0_2660,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,hAPP(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_1576]),
    [final] ).

cnf(i_0_2661,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),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_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))),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_1612,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2662,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1613,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2663,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2664,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2665,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2666,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2667,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),X3)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2668,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),X3)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2669,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),X3)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2670,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),X3)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2671,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1618]),
    [final] ).

cnf(i_0_2672,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1619]),
    [final] ).

cnf(i_0_2673,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1620]),
    [final] ).

cnf(i_0_2674,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1621]),
    [final] ).

cnf(i_0_2675,plain,
    ( X1 = X2
    | X3 = X4
    | c_Groups_Oplus__class_Oplus(X5,hAPP(c_Groups_Otimes__class_Otimes(X5,X1),X3),hAPP(c_Groups_Otimes__class_Otimes(X5,X2),X4)) != c_Groups_Oplus__class_Oplus(X5,hAPP(c_Groups_Otimes__class_Otimes(X5,X1),X4),hAPP(c_Groups_Otimes__class_Otimes(X5,X2),X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1622]),
    [final] ).

cnf(i_0_2676,plain,
    ( X2 = X4
    | X3 = X5
    | c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)) != c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X5),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1623]),
    [final] ).

cnf(i_0_2677,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1575]),
    [final] ).

cnf(i_0_2678,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1576]),
    [final] ).

cnf(i_0_2679,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1573]),
    [final] ).

cnf(i_0_2680,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1574]),
    [final] ).

cnf(i_0_2681,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,hAPP(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_1562]),
    [final] ).

cnf(i_0_2682,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,hAPP(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_1563]),
    [final] ).

cnf(i_0_2683,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,hAPP(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_1564]),
    [final] ).

cnf(i_0_2684,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,hAPP(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_1565]),
    [final] ).

cnf(i_0_2685,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)),X3)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2))),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1624]),
    [final] ).

cnf(i_0_2686,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(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_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)],[i_0_1625,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2687,plain,
    ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(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_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)],[i_0_1626,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2688,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1627,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2689,plain,
    ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
    | ~ class_Rings_Olinordered__idom(X2)
    | ~ class_Int_Onumber__ring(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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1628,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2690,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3))),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1629]),
    [final] ).

cnf(i_0_2691,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,hAPP(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_1573]),
    [final] ).

cnf(i_0_2692,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,hAPP(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_1574]),
    [final] ).

cnf(i_0_2693,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,hAPP(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_1575]),
    [final] ).

cnf(i_0_2694,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,hAPP(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_1576]),
    [final] ).

cnf(i_0_2695,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_1630]),
    [final] ).

cnf(i_0_2696,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1631]),
    [final] ).

cnf(i_0_2697,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,esk6_3(X3,X2,X1)))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_2698,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,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_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[i_0_1633,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2699,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1634,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2700,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1564]),
    [final] ).

cnf(i_0_2701,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1565]),
    [final] ).

cnf(i_0_2702,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1562]),
    [final] ).

cnf(i_0_2703,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1563]),
    [final] ).

cnf(i_0_2704,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_1635]),
    [final] ).

cnf(i_0_2705,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_1636]),
    [final] ).

cnf(i_0_2706,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_1637]),
    [final] ).

cnf(i_0_2707,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk7_3(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1560]),
    [final] ).

cnf(i_0_2708,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk8_3(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Deriv_Oderiv(tc_RealDef_Oreal,X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1559]),
    [final] ).

cnf(i_0_2709,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1638,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2710,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1639,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2711,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1640,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2712,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1641,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2713,plain,
    ( hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2)),X3),hAPP(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_1642]),
    [final] ).

cnf(i_0_2714,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X4)),hAPP(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_1643]),
    [final] ).

cnf(i_0_2715,plain,
    ( hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X4)),hAPP(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_1644]),
    [final] ).

cnf(i_0_2716,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)),X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1645]),
    [final] ).

cnf(i_0_2717,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1646,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2718,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_1573]),
    [final] ).

cnf(i_0_2719,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_1574]),
    [final] ).

cnf(i_0_2720,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_1575]),
    [final] ).

cnf(i_0_2721,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_1576]),
    [final] ).

cnf(i_0_2722,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1647]),
    [final] ).

cnf(i_0_2723,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1648]),
    [final] ).

cnf(i_0_2724,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1649]),
    [final] ).

cnf(i_0_2725,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1650]),
    [final] ).

cnf(i_0_2726,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1651]),
    [final] ).

cnf(i_0_2727,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1652]),
    [final] ).

cnf(i_0_2728,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_1653]),
    [final] ).

cnf(i_0_2729,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_1654]),
    [final] ).

cnf(i_0_2730,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_1655]),
    [final] ).

cnf(i_0_2731,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_1656]),
    [final] ).

cnf(i_0_2732,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_1657]),
    [final] ).

cnf(i_0_2733,plain,
    ( hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X5))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1658]),
    [final] ).

cnf(i_0_2734,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1659]),
    [final] ).

cnf(i_0_2735,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1660,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2736,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1661,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2737,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1662,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2738,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1663,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2739,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1664,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2740,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1665,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2741,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1666,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2742,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1667,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2743,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),hAPP(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_1668]),
    [final] ).

cnf(i_0_2744,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4)),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_2745,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_2746,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_1671]),
    [final] ).

cnf(i_0_2747,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_1672]),
    [final] ).

cnf(i_0_2748,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_1673]),
    [final] ).

cnf(i_0_2749,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1614]),
    [final] ).

cnf(i_0_2750,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1615]),
    [final] ).

cnf(i_0_2751,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1616]),
    [final] ).

cnf(i_0_2752,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1617]),
    [final] ).

cnf(i_0_2753,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_2754,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_1675]),
    [final] ).

cnf(i_0_2755,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_1676]),
    [final] ).

cnf(i_0_2756,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_2757,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2758,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2759,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2760,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2761,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2762,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2763,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2764,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2765,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2766,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2767,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2768,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2769,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_1678]),
    [final] ).

cnf(i_0_2770,plain,
    ( hAPP(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_1679]),
    [final] ).

cnf(i_0_2771,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) = hAPP(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_1680]),
    [final] ).

cnf(i_0_2772,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_1681,c_0_1449]),c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2773,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_1564]),
    [final] ).

cnf(i_0_2774,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_1565]),
    [final] ).

cnf(i_0_2775,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_1562]),
    [final] ).

cnf(i_0_2776,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_1563]),
    [final] ).

cnf(i_0_2777,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1682,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2778,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1683,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2779,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1684,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2780,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1685,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2781,plain,
    c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = hAPP(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_1686]),
    [final] ).

cnf(i_0_2782,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),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_1687,c_0_1448]),c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_2783,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1),hAPP(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_1603]),
    [final] ).

cnf(i_0_2784,plain,
    ( c_Power_Opower__class_Opower(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4) = hAPP(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_1688]),
    [final] ).

cnf(i_0_2785,plain,
    ( c_Power_Opower__class_Opower(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4) = hAPP(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_1689]),
    [final] ).

cnf(i_0_2786,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_1573]),
    [final] ).

cnf(i_0_2787,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_1574]),
    [final] ).

cnf(i_0_2788,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_1575]),
    [final] ).

cnf(i_0_2789,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_1576]),
    [final] ).

cnf(i_0_2790,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,hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1),hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1597]),
    [final] ).

cnf(i_0_2791,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,hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X3),hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1)))
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1597]),
    [final] ).

cnf(i_0_2792,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4)),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1690]),
    [final] ).

cnf(i_0_2793,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2)),X2)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1691]),
    [final] ).

cnf(i_0_2794,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1692]),
    [final] ).

cnf(i_0_2795,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)),X2)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1693]),
    [final] ).

cnf(i_0_2796,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1694]),
    [final] ).

cnf(i_0_2797,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1616]),
    [final] ).

cnf(i_0_2798,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1695]),
    [final] ).

cnf(i_0_2799,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1617]),
    [final] ).

cnf(i_0_2800,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1696]),
    [final] ).

cnf(i_0_2801,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1697]),
    [final] ).

cnf(i_0_2802,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(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_1698]),
    [final] ).

cnf(i_0_2803,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1614]),
    [final] ).

cnf(i_0_2804,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,hAPP(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_1699]),
    [final] ).

cnf(i_0_2805,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1615]),
    [final] ).

cnf(i_0_2806,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,hAPP(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_1700]),
    [final] ).

cnf(i_0_2807,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,hAPP(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_1701]),
    [final] ).

cnf(i_0_2808,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1702]),
    [final] ).

cnf(i_0_2809,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1703]),
    [final] ).

cnf(i_0_2810,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1704]),
    [final] ).

cnf(i_0_2811,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1705]),
    [final] ).

cnf(i_0_2812,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1706]),
    [final] ).

cnf(i_0_2813,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1707]),
    [final] ).

cnf(i_0_2814,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1708]),
    [final] ).

cnf(i_0_2815,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1709]),
    [final] ).

cnf(i_0_2816,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1710]),
    [final] ).

cnf(i_0_2817,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1711]),
    [final] ).

cnf(i_0_2818,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X3)))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_2819,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_1713]),
    [final] ).

cnf(i_0_2820,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_1714]),
    [final] ).

cnf(i_0_2821,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_1715]),
    [final] ).

cnf(i_0_2822,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_1716]),
    [final] ).

cnf(i_0_2823,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_1717]),
    [final] ).

cnf(i_0_2824,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_1718]),
    [final] ).

cnf(i_0_2825,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_1719]),
    [final] ).

cnf(i_0_2826,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_1720]),
    [final] ).

cnf(i_0_2827,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,hAPP(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_1698]),
    [final] ).

cnf(i_0_2828,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1614]),
    [final] ).

cnf(i_0_2829,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1721]),
    [final] ).

cnf(i_0_2830,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(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_1699]),
    [final] ).

cnf(i_0_2831,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2832,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1722]),
    [final] ).

cnf(i_0_2833,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1696]),
    [final] ).

cnf(i_0_2834,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1697]),
    [final] ).

cnf(i_0_2835,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1694]),
    [final] ).

cnf(i_0_2836,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2837,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1723]),
    [final] ).

cnf(i_0_2838,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(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_1695]),
    [final] ).

cnf(i_0_2839,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1617]),
    [final] ).

cnf(i_0_2840,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1724]),
    [final] ).

cnf(i_0_2841,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,hAPP(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_1700]),
    [final] ).

cnf(i_0_2842,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(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_1701]),
    [final] ).

cnf(i_0_2843,plain,
    ( c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3)) = hAPP(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_1725]),
    [final] ).

cnf(i_0_2844,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1726]),
    [final] ).

cnf(i_0_2845,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_2846,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_2847,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_2848,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_1630]),
    [final] ).

cnf(i_0_2849,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_1730]),
    [final] ).

cnf(i_0_2850,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_1731,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2851,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_1732,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2852,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_1733]),
    [final] ).

cnf(i_0_2853,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_1734,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2854,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_1735,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2855,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1736,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2856,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_1737]),
    [final] ).

cnf(i_0_2857,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_1562]),
    [final] ).

cnf(i_0_2858,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_1563]),
    [final] ).

cnf(i_0_2859,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_1564]),
    [final] ).

cnf(i_0_2860,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_1565]),
    [final] ).

cnf(i_0_2861,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_2862,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_2863,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_1740]),
    [final] ).

cnf(i_0_2864,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_1741]),
    [final] ).

cnf(i_0_2865,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_1742]),
    [final] ).

cnf(i_0_2866,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_1743]),
    [final] ).

cnf(i_0_2867,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_1744]),
    [final] ).

cnf(i_0_2868,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_1745]),
    [final] ).

cnf(i_0_2869,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_1655]),
    [final] ).

cnf(i_0_2870,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_1746]),
    [final] ).

cnf(i_0_2871,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_1657]),
    [final] ).

cnf(i_0_2872,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(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_1747]),
    [final] ).

cnf(i_0_2873,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_2874,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_2875,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_2876,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_2877,plain,
    ( hAPP(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_1748,c_0_1449]),
    [final] ).

cnf(i_0_2878,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(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_1749]),
    [final] ).

cnf(i_0_2879,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(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_1750]),
    [final] ).

cnf(i_0_2880,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(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_1751]),
    [final] ).

cnf(i_0_2881,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2),hAPP(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_1752]),
    [final] ).

cnf(i_0_2882,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2),hAPP(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_1753]),
    [final] ).

cnf(i_0_2883,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(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_1754]),
    [final] ).

cnf(i_0_2884,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2),hAPP(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_1755]),
    [final] ).

cnf(i_0_2885,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1756,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2886,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1757,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2887,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1758,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2888,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1759,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2889,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_1760]),
    [final] ).

cnf(i_0_2890,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_1761]),
    [final] ).

cnf(i_0_2891,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_1762]),
    [final] ).

cnf(i_0_2892,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_1763]),
    [final] ).

cnf(i_0_2893,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_2894,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1738]),
    [final] ).

cnf(i_0_2895,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))) ),
    inference(rw,[status(thm)],[i_0_1764,c_0_1449]),
    [final] ).

cnf(i_0_2896,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_1614]),
    [final] ).

cnf(i_0_2897,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_1615]),
    [final] ).

cnf(i_0_2898,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_1616]),
    [final] ).

cnf(i_0_2899,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_1617]),
    [final] ).

cnf(i_0_2900,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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_1765]),
    [final] ).

cnf(i_0_2901,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_1766]),
    [final] ).

cnf(i_0_2902,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1767]),
    [final] ).

cnf(i_0_2903,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1768,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_2904,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1769]),
    [final] ).

cnf(i_0_2905,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_2906,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_1771]),
    [final] ).

cnf(i_0_2907,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_1772]),
    [final] ).

cnf(i_0_2908,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_1773]),
    [final] ).

cnf(i_0_2909,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,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X5)) != c_Groups_Oplus__class_Oplus(X1,X4,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_2910,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,hAPP(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_1775]),
    [final] ).

cnf(i_0_2911,plain,
    ( c_Groups_Oplus__class_Oplus(X3,hAPP(c_Groups_Otimes__class_Otimes(X3,X1),X4),hAPP(c_Groups_Otimes__class_Otimes(X3,X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Groups_Otimes__class_Otimes(X3,X1),X5),hAPP(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_1623]),
    [final] ).

cnf(i_0_2912,plain,
    ( c_Groups_Oplus__class_Oplus(X3,hAPP(c_Groups_Otimes__class_Otimes(X3,X1),X4),hAPP(c_Groups_Otimes__class_Otimes(X3,X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(c_Groups_Otimes__class_Otimes(X3,X1),X5),hAPP(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_1622]),
    [final] ).

cnf(i_0_2913,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_1776]),
    [final] ).

cnf(i_0_2914,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_1777]),
    [final] ).

cnf(i_0_2915,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_1778]),
    [final] ).

cnf(i_0_2916,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1779]),
    [final] ).

cnf(i_0_2917,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1780]),
    [final] ).

cnf(i_0_2918,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,hAPP(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_1781]),
    [final] ).

cnf(i_0_2919,plain,
    ( c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X3) = hAPP(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_1782]),
    [final] ).

cnf(i_0_2920,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) = hAPP(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_1783]),
    [final] ).

cnf(i_0_2921,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_1784,c_0_1449]),
    [final] ).

cnf(i_0_2922,plain,
    ( c_Groups_Oabs__class_Oabs(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) = hAPP(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_1785]),
    [final] ).

cnf(i_0_2923,plain,
    ( c_Groups_Oabs__class_Oabs(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) = hAPP(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_1785]),
    [final] ).

cnf(i_0_2924,plain,
    ( c_Groups_Oabs__class_Oabs(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) = hAPP(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_1785]),
    [final] ).

cnf(i_0_2925,plain,
    ( c_Groups_Oabs__class_Oabs(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)) = hAPP(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_1785]),
    [final] ).

cnf(i_0_2926,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3)),X2) = hAPP(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_1786]),
    [final] ).

cnf(i_0_2927,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1787]),
    [final] ).

cnf(i_0_2928,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1788]),
    [final] ).

cnf(i_0_2929,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1789]),
    [final] ).

cnf(i_0_2930,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1704]),
    [final] ).

cnf(i_0_2931,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1738]),
    [final] ).

cnf(i_0_2932,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1790]),
    [final] ).

cnf(i_0_2933,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),hAPP(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_1739]),
    [final] ).

cnf(i_0_2934,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1791]),
    [final] ).

cnf(i_0_2935,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1792]),
    [final] ).

cnf(i_0_2936,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1709]),
    [final] ).

cnf(i_0_2937,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4),hAPP(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_1793]),
    [final] ).

cnf(i_0_2938,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(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_1794]),
    [final] ).

cnf(i_0_2939,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(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_1710]),
    [final] ).

cnf(i_0_2940,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(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_1738]),
    [final] ).

cnf(i_0_2941,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4),hAPP(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_1795]),
    [final] ).

cnf(i_0_2942,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2),hAPP(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_1739]),
    [final] ).

cnf(i_0_2943,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(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_1711]),
    [final] ).

cnf(i_0_2944,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X3),hAPP(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_1796]),
    [final] ).

cnf(i_0_2945,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),X4) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1797]),
    [final] ).

cnf(i_0_2946,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),hAPP(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_1798]),
    [final] ).

cnf(i_0_2947,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_1799]),
    [final] ).

cnf(i_0_2948,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_1800]),
    [final] ).

cnf(i_0_2949,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_1801]),
    [final] ).

cnf(i_0_2950,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_1800]),
    [final] ).

cnf(i_0_2951,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_1800]),
    [final] ).

cnf(i_0_2952,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_1801]),
    [final] ).

cnf(i_0_2953,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_1801]),
    [final] ).

cnf(i_0_2954,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_1802]),
    [final] ).

cnf(i_0_2955,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_1802]),
    [final] ).

cnf(i_0_2956,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_1802]),
    [final] ).

cnf(i_0_2957,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_1802]),
    [final] ).

cnf(i_0_2958,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_1803]),
    [final] ).

cnf(i_0_2959,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_1803]),
    [final] ).

cnf(i_0_2960,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_1803]),
    [final] ).

cnf(i_0_2961,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_1803]),
    [final] ).

cnf(i_0_2962,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_1800]),
    [final] ).

cnf(i_0_2963,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_1801]),
    [final] ).

cnf(i_0_2964,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3))))
    | 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_1659]),
    [final] ).

cnf(i_0_2965,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_1614]),
    [final] ).

cnf(i_0_2966,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_1615]),
    [final] ).

cnf(i_0_2967,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_1616]),
    [final] ).

cnf(i_0_2968,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_1617]),
    [final] ).

cnf(i_0_2969,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),hAPP(c_Transcendental_Oln,X2))
    | ~ c_Orderings_Oord__class_Oless(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) ),
    inference(split_conjunct,[status(thm)],[i_0_1804]),
    [final] ).

cnf(i_0_2970,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),hAPP(c_Transcendental_Oln,X2))
    | ~ c_Orderings_Oord__class_Oless(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) ),
    inference(split_conjunct,[status(thm)],[i_0_1805]),
    [final] ).

cnf(i_0_2971,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X2))),X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1806]),
    [final] ).

cnf(i_0_2972,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)),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_1807]),
    [final] ).

cnf(i_0_2973,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),hAPP(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_1808]),
    [final] ).

cnf(i_0_2974,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),hAPP(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_1809]),
    [final] ).

cnf(i_0_2975,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_1810,c_0_1449]),
    [final] ).

cnf(i_0_2976,plain,
    c_Int_Opred(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1811,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_2977,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(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_1750]),
    [final] ).

cnf(i_0_2978,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X3),hAPP(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_1752]),
    [final] ).

cnf(i_0_2979,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3),X1),hAPP(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_1753]),
    [final] ).

cnf(i_0_2980,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(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_1812]),
    [final] ).

cnf(i_0_2981,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(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_1813]),
    [final] ).

cnf(i_0_2982,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1),hAPP(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_1814]),
    [final] ).

cnf(i_0_2983,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(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_1754]),
    [final] ).

cnf(i_0_2984,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(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_1815]),
    [final] ).

cnf(i_0_2985,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3),X1),hAPP(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_1816]),
    [final] ).

cnf(i_0_2986,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2),hAPP(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_1817]),
    [final] ).

cnf(i_0_2987,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X3),hAPP(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_1755]),
    [final] ).

cnf(i_0_2988,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))))
    | c_Groups_Ozero__class_Ozero(X1) != c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_2989,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_1800]),
    [final] ).

cnf(i_0_2990,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_1800]),
    [final] ).

cnf(i_0_2991,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_1818]),
    [final] ).

cnf(i_0_2992,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_1819]),
    [final] ).

cnf(i_0_2993,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_1801]),
    [final] ).

cnf(i_0_2994,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_1801]),
    [final] ).

cnf(i_0_2995,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_1820]),
    [final] ).

cnf(i_0_2996,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_1821]),
    [final] ).

cnf(i_0_2997,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_1822]),
    [final] ).

cnf(i_0_2998,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_1823]),
    [final] ).

cnf(i_0_2999,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_1824]),
    [final] ).

cnf(i_0_3000,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_1825]),
    [final] ).

cnf(i_0_3001,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_1826]),
    [final] ).

cnf(i_0_3002,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_1802]),
    [final] ).

cnf(i_0_3003,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_1827]),
    [final] ).

cnf(i_0_3004,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_1828]),
    [final] ).

cnf(i_0_3005,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_1829]),
    [final] ).

cnf(i_0_3006,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_1830]),
    [final] ).

cnf(i_0_3007,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_1803]),
    [final] ).

cnf(i_0_3008,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_1831]),
    [final] ).

cnf(i_0_3009,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_1802]),
    [final] ).

cnf(i_0_3010,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_1832]),
    [final] ).

cnf(i_0_3011,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_1803]),
    [final] ).

cnf(i_0_3012,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_1833]),
    [final] ).

cnf(i_0_3013,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1812]),
    [final] ).

cnf(i_0_3014,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1814]),
    [final] ).

cnf(i_0_3015,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(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_1834]),
    [final] ).

cnf(i_0_3016,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_1835]),
    [final] ).

cnf(i_0_3017,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_1836]),
    [final] ).

cnf(i_0_3018,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_1836]),
    [final] ).

cnf(i_0_3019,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1837]),
    [final] ).

cnf(i_0_3020,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1838]),
    [final] ).

cnf(i_0_3021,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1839]),
    [final] ).

cnf(i_0_3022,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(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_1840]),
    [final] ).

cnf(i_0_3023,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_3024,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1814]),
    [final] ).

cnf(i_0_3025,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1812]),
    [final] ).

cnf(i_0_3026,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_1841]),
    [final] ).

cnf(i_0_3027,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_1713]),
    [final] ).

cnf(i_0_3028,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_1842]),
    [final] ).

cnf(i_0_3029,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_1715]),
    [final] ).

cnf(i_0_3030,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_1843]),
    [final] ).

cnf(i_0_3031,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_1718]),
    [final] ).

cnf(i_0_3032,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_1844]),
    [final] ).

cnf(i_0_3033,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_1720]),
    [final] ).

cnf(i_0_3034,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_1281]),
    [final] ).

cnf(i_0_3035,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),hAPP(c_Transcendental_Oln,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),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1804]),
    [final] ).

cnf(i_0_3036,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),hAPP(c_Transcendental_Oln,X2))
    | ~ 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),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1805]),
    [final] ).

cnf(i_0_3037,plain,
    ( hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),hAPP(c_Transcendental_Oln,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_1845]),
    [final] ).

cnf(i_0_3038,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_1846]),
    [final] ).

cnf(i_0_3039,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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_1847]),
    [final] ).

cnf(i_0_3040,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_1848]),
    [final] ).

cnf(i_0_3041,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_1849]),
    [final] ).

cnf(i_0_3042,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_1850]),
    [final] ).

cnf(i_0_3043,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_1851]),
    [final] ).

cnf(i_0_3044,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_1852]),
    [final] ).

cnf(i_0_3045,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_1853]),
    [final] ).

cnf(i_0_3046,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1),hAPP(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_1854]),
    [final] ).

cnf(i_0_3047,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X3),hAPP(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_1854]),
    [final] ).

cnf(i_0_3048,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_1855]),
    [final] ).

cnf(i_0_3049,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,hAPP(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_1856]),
    [final] ).

cnf(i_0_3050,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,hAPP(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_1856]),
    [final] ).

cnf(i_0_3051,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,hAPP(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_1856]),
    [final] ).

cnf(i_0_3052,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1857]),
    [final] ).

cnf(i_0_3053,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1857]),
    [final] ).

cnf(i_0_3054,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1857]),
    [final] ).

cnf(i_0_3055,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),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1857]),
    [final] ).

cnf(i_0_3056,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,hAPP(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_1856]),
    [final] ).

cnf(i_0_3057,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_1858]),
    [final] ).

cnf(i_0_3058,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_1730]),
    [final] ).

cnf(i_0_3059,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_1859,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3060,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_1860,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3061,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_1861]),
    [final] ).

cnf(i_0_3062,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_1862]),
    [final] ).

cnf(i_0_3063,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_1863]),
    [final] ).

cnf(i_0_3064,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_1733]),
    [final] ).

cnf(i_0_3065,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_1864,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3066,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_1865,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3067,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_1866]),
    [final] ).

cnf(i_0_3068,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1867]),
    [final] ).

cnf(i_0_3069,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1868]),
    [final] ).

cnf(i_0_3070,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1869]),
    [final] ).

cnf(i_0_3071,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1868]),
    [final] ).

cnf(i_0_3072,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1856]),
    [final] ).

cnf(i_0_3073,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1856]),
    [final] ).

cnf(i_0_3074,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(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_1870]),
    [final] ).

cnf(i_0_3075,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1871]),
    [final] ).

cnf(i_0_3076,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1872]),
    [final] ).

cnf(i_0_3077,plain,
    ( c_Orderings_Oord__class_Oless(X1,hAPP(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_1873]),
    [final] ).

cnf(i_0_3078,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1874]),
    [final] ).

cnf(i_0_3079,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1875]),
    [final] ).

cnf(i_0_3080,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1857]),
    [final] ).

cnf(i_0_3081,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(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_1876]),
    [final] ).

cnf(i_0_3082,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1877]),
    [final] ).

cnf(i_0_3083,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1878]),
    [final] ).

cnf(i_0_3084,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1874]),
    [final] ).

cnf(i_0_3085,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1857]),
    [final] ).

cnf(i_0_3086,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(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_1879]),
    [final] ).

cnf(i_0_3087,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_1880]),
    [final] ).

cnf(i_0_3088,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_1836]),
    [final] ).

cnf(i_0_3089,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_1836]),
    [final] ).

cnf(i_0_3090,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_1836]),
    [final] ).

cnf(i_0_3091,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_1836]),
    [final] ).

cnf(i_0_3092,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1881]),
    [final] ).

cnf(i_0_3093,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1882]),
    [final] ).

cnf(i_0_3094,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,X2,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1883,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3095,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,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1884,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3096,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_1885]),
    [final] ).

cnf(i_0_3097,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_1886]),
    [final] ).

cnf(i_0_3098,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_1887]),
    [final] ).

cnf(i_0_3099,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_1888]),
    [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,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_1889]),
    [final] ).

cnf(i_0_3101,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) = 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_1890,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3102,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1891,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3103,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),hAPP(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_1624]),
    [final] ).

cnf(i_0_3104,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_1892]),
    [final] ).

cnf(i_0_3105,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_1893]),
    [final] ).

cnf(i_0_3106,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_1894]),
    [final] ).

cnf(i_0_3107,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_1895]),
    [final] ).

cnf(i_0_3108,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_1896]),
    [final] ).

cnf(i_0_3109,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1897]),
    [final] ).

cnf(i_0_3110,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1898]),
    [final] ).

cnf(i_0_3111,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_1899]),
    [final] ).

cnf(i_0_3112,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_1900]),
    [final] ).

cnf(i_0_3113,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1901]),
    [final] ).

cnf(i_0_3114,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1902]),
    [final] ).

cnf(i_0_3115,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1903]),
    [final] ).

cnf(i_0_3116,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1904]),
    [final] ).

cnf(i_0_3117,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_1905,c_0_1449]),
    [final] ).

cnf(i_0_3118,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),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),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1906,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3119,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),X4) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1907]),
    [final] ).

cnf(i_0_3120,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),X4) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3121,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4)) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1909]),
    [final] ).

cnf(i_0_3122,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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1910,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3123,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(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)],[i_0_1911,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3124,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_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)],[i_0_1912,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3125,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_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)],[i_0_1913,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3126,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_1914]),
    [final] ).

cnf(i_0_3127,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1),hAPP(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_1915]),
    [final] ).

cnf(i_0_3128,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X2),hAPP(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_1915]),
    [final] ).

cnf(i_0_3129,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_1916]),
    [final] ).

cnf(i_0_3130,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_1917]),
    [final] ).

cnf(i_0_3131,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_1918]),
    [final] ).

cnf(i_0_3132,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_1919]),
    [final] ).

cnf(i_0_3133,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_1920]),
    [final] ).

cnf(i_0_3134,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_1921]),
    [final] ).

cnf(i_0_3135,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_1922]),
    [final] ).

cnf(i_0_3136,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_1923]),
    [final] ).

cnf(i_0_3137,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_1924]),
    [final] ).

cnf(i_0_3138,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_1925,c_0_1449]),
    [final] ).

cnf(i_0_3139,plain,
    ( c_Deriv_Oderiv(X1,c_Transcendental_Oexp(X1),X2,hAPP(c_Transcendental_Oexp(X1),X2))
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1926]),
    [final] ).

cnf(i_0_3140,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(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_1927]),
    [final] ).

cnf(i_0_3141,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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_1928]),
    [final] ).

cnf(i_0_3142,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_1929]),
    [final] ).

cnf(i_0_3143,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_1930]),
    [final] ).

cnf(i_0_3144,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_1931]),
    [final] ).

cnf(i_0_3145,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = c_Groups_Oabs__class_Oabs(X1,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1932]),
    [final] ).

cnf(i_0_3146,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_1933]),
    [final] ).

cnf(i_0_3147,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_1933]),
    [final] ).

cnf(i_0_3148,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_1934]),
    [final] ).

cnf(i_0_3149,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_1935]),
    [final] ).

cnf(i_0_3150,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_1936]),
    [final] ).

cnf(i_0_3151,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_1937]),
    [final] ).

cnf(i_0_3152,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_1937]),
    [final] ).

cnf(i_0_3153,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_1938,c_0_1449]),
    [final] ).

cnf(i_0_3154,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_1939,c_0_1449]),
    [final] ).

cnf(i_0_3155,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_1940,c_0_1449]),
    [final] ).

cnf(i_0_3156,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_1941,c_0_1449]),
    [final] ).

cnf(i_0_3157,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1942]),
    [final] ).

cnf(i_0_3158,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,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),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1943]),
    [final] ).

cnf(i_0_3159,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3160,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1945]),
    [final] ).

cnf(i_0_3161,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_1946]),
    [final] ).

cnf(i_0_3162,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Transcendental_Oexp(X1),X2)),hAPP(c_Transcendental_Oexp(X1),X3)) = hAPP(c_Transcendental_Oexp(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1947]),
    [final] ).

cnf(i_0_3163,plain,
    ( hAPP(c_Transcendental_Oexp(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,hAPP(c_Transcendental_Oexp(X1),X2)),hAPP(c_Transcendental_Oexp(X1),X3))
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1948]),
    [final] ).

cnf(i_0_3164,plain,
    ( c_Power_Opower__class_Opower(X1,X2,hAPP(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_1949]),
    [final] ).

cnf(i_0_3165,plain,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1950]),
    [final] ).

cnf(i_0_3166,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_1799]),
    [final] ).

cnf(i_0_3167,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Opred(X1),c_Int_Opred(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_Opred(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1951,c_0_1448]),c_0_1449]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3168,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_1952]),
    [final] ).

cnf(i_0_3169,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1953]),
    [final] ).

cnf(i_0_3170,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2)),X3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1954]),
    [final] ).

cnf(i_0_3171,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),X3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1955]),
    [final] ).

cnf(i_0_3172,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2)),X3) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1956]),
    [final] ).

cnf(i_0_3173,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3)),X2) = c_Groups_Oabs__class_Oabs(X1,hAPP(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_1957]),
    [final] ).

cnf(i_0_3174,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4)) = c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),X4)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1958]),
    [final] ).

cnf(i_0_3175,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1959]),
    [final] ).

cnf(i_0_3176,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,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,X2,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1960]),
    [final] ).

cnf(i_0_3177,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ 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))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1961]),
    [final] ).

cnf(i_0_3178,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,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,X2,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1962]),
    [final] ).

cnf(i_0_3179,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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_1963]),
    [final] ).

cnf(i_0_3180,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_1964]),
    [final] ).

cnf(i_0_3181,plain,
    ( c_Deriv_Oderiv(X1,c_Groups_Otimes__class_Otimes(X1,X2),X3,X2)
    | ~ class_RealVector_Oreal__normed__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1965]),
    [final] ).

cnf(i_0_3182,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(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_1749]),
    [final] ).

cnf(i_0_3183,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3),hAPP(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_1966]),
    [final] ).

cnf(i_0_3184,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(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_1967]),
    [final] ).

cnf(i_0_3185,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1),hAPP(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_1751]),
    [final] ).

cnf(i_0_3186,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1899]),
    [final] ).

cnf(i_0_3187,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1900]),
    [final] ).

cnf(i_0_3188,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1897]),
    [final] ).

cnf(i_0_3189,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,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1898]),
    [final] ).

cnf(i_0_3190,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(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_1968]),
    [final] ).

cnf(i_0_3191,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),hAPP(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_1969]),
    [final] ).

cnf(i_0_3192,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_1970]),
    [final] ).

cnf(i_0_3193,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_1937]),
    [final] ).

cnf(i_0_3194,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_1887]),
    [final] ).

cnf(i_0_3195,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_1888]),
    [final] ).

cnf(i_0_3196,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_1889]),
    [final] ).

cnf(i_0_3197,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_1971]),
    [final] ).

cnf(i_0_3198,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_1972]),
    [final] ).

cnf(i_0_3199,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_1885]),
    [final] ).

cnf(i_0_3200,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_1973]),
    [final] ).

cnf(i_0_3201,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_1886]),
    [final] ).

cnf(i_0_3202,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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_1974]),
    [final] ).

cnf(i_0_3203,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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_1975]),
    [final] ).

cnf(i_0_3204,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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_1976]),
    [final] ).

cnf(i_0_3205,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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_1977]),
    [final] ).

cnf(i_0_3206,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,hAPP(c_Transcendental_Oln,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),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1978]),
    [final] ).

cnf(i_0_3207,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X5) = hAPP(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_1979]),
    [final] ).

cnf(i_0_3208,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X1))),
    inference(split_conjunct,[status(thm)],[i_0_1980]),
    [final] ).

cnf(i_0_3209,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1981]),
    [final] ).

cnf(i_0_3210,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1982]),
    [final] ).

cnf(i_0_3211,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_1952]),
    [final] ).

cnf(i_0_3212,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_1946]),
    [final] ).

cnf(i_0_3213,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_1983]),
    [final] ).

cnf(i_0_3214,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_1984]),
    [final] ).

cnf(i_0_3215,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 != hAPP(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_1985]),
    [final] ).

cnf(i_0_3216,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)
    | hAPP(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_1986]),
    [final] ).

cnf(i_0_3217,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),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1928]),
    [final] ).

cnf(i_0_3218,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),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1928]),
    [final] ).

cnf(i_0_3219,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ 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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1978]),
    [final] ).

cnf(i_0_3220,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,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),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_1987]),
    [final] ).

cnf(i_0_3221,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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_1974]),
    [final] ).

cnf(i_0_3222,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X1))
    | ~ 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_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1976]),
    [final] ).

cnf(i_0_3223,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_1988]),
    [final] ).

cnf(i_0_3224,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),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,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1989,c_0_1450]),
    [final] ).

cnf(i_0_3225,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1990,c_0_1450]),
    [final] ).

cnf(i_0_3226,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1751]),
    [final] ).

cnf(i_0_3227,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1749]),
    [final] ).

cnf(i_0_3228,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)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) != hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X5)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1979]),
    [final] ).

cnf(i_0_3229,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) != c_Int_OPls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1991,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3230,plain,
    c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1992,c_0_1448]),c_0_1449]),c_0_1450]),
    [final] ).

cnf(i_0_3231,plain,
    c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2),hAPP(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_1993]),
    [final] ).

cnf(i_0_3232,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_1994,c_0_1449]),
    [final] ).

cnf(i_0_3233,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_1995]),
    [final] ).

cnf(i_0_3234,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_1921]),
    [final] ).

cnf(i_0_3235,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_1922]),
    [final] ).

cnf(i_0_3236,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_1835]),
    [final] ).

cnf(i_0_3237,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_1835]),
    [final] ).

cnf(i_0_3238,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_1996]),
    [final] ).

cnf(i_0_3239,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_1923]),
    [final] ).

cnf(i_0_3240,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_1924]),
    [final] ).

cnf(i_0_3241,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_1920]),
    [final] ).

cnf(i_0_3242,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_1997]),
    [final] ).

cnf(i_0_3243,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_1998]),
    [final] ).

cnf(i_0_3244,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_1914]),
    [final] ).

cnf(i_0_3245,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X4)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1999]),
    [final] ).

cnf(i_0_3246,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2000]),
    [final] ).

cnf(i_0_3247,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_2001]),
    [final] ).

cnf(i_0_3248,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_2002]),
    [final] ).

cnf(i_0_3249,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_1525]),
    [final] ).

cnf(i_0_3250,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_2003]),
    [final] ).

cnf(i_0_3251,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_2004]),
    [final] ).

cnf(i_0_3252,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_2005]),
    [final] ).

cnf(i_0_3253,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_2006]),
    [final] ).

cnf(i_0_3254,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_2007]),
    [final] ).

cnf(i_0_3255,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_2008]),
    [final] ).

cnf(i_0_3256,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_2009]),
    [final] ).

cnf(i_0_3257,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_2010]),
    [final] ).

cnf(i_0_3258,plain,
    ( c_Groups_Oplus__class_Oplus(X2,hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1),hAPP(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_1854]),
    [final] ).

cnf(i_0_3259,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2011]),
    [final] ).

cnf(i_0_3260,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2012]),
    [final] ).

cnf(i_0_3261,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2013]),
    [final] ).

cnf(i_0_3262,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_2014,c_0_1449]),
    [final] ).

cnf(i_0_3263,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_2015,c_0_1449]),
    [final] ).

cnf(i_0_3264,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_2016,c_0_1449]),
    [final] ).

cnf(i_0_3265,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_2017,c_0_1449]),
    [final] ).

cnf(i_0_3266,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_2018]),
    [final] ).

cnf(i_0_3267,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_2019]),
    [final] ).

cnf(i_0_3268,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_2020]),
    [final] ).

cnf(i_0_3269,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_2021]),
    [final] ).

cnf(i_0_3270,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_2022]),
    [final] ).

cnf(i_0_3271,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_2023]),
    [final] ).

cnf(i_0_3272,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_2024]),
    [final] ).

cnf(i_0_3273,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_2025]),
    [final] ).

cnf(i_0_3274,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_2026]),
    [final] ).

cnf(i_0_3275,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_2027]),
    [final] ).

cnf(i_0_3276,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 != hAPP(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_1985]),
    [final] ).

cnf(i_0_3277,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Int_Onumber__class_Onumber__of(X2,X3) = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
    | hAPP(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_1986]),
    [final] ).

cnf(i_0_3278,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2028]),
    [final] ).

cnf(i_0_3279,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2029]),
    [final] ).

cnf(i_0_3280,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_2030]),
    [final] ).

cnf(i_0_3281,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_2031]),
    [final] ).

cnf(i_0_3282,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2032]),
    [final] ).

cnf(i_0_3283,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2033]),
    [final] ).

cnf(i_0_3284,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2034]),
    [final] ).

cnf(i_0_3285,plain,
    ( c_Orderings_Oord__class_Oless(X1,esk5_3(X2,X3,X1),c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_3286,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk6_3(X2,X3,X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_3287,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),esk5_3(X2,X3,X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1577]),
    [final] ).

cnf(i_0_3288,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_1799]),
    [final] ).

cnf(i_0_3289,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(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_2035]),
    [final] ).

cnf(i_0_3290,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(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_2036]),
    [final] ).

cnf(i_0_3291,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_1853]),
    [final] ).

cnf(i_0_3292,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2037]),
    [final] ).

cnf(i_0_3293,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_2038]),
    [final] ).

cnf(i_0_3294,plain,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2039]),
    [final] ).

cnf(i_0_3295,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)) = X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2040]),
    [final] ).

cnf(i_0_3296,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_2041]),
    [final] ).

cnf(i_0_3297,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_2042]),
    [final] ).

cnf(i_0_3298,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_2043]),
    [final] ).

cnf(i_0_3299,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(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_1986]),
    [final] ).

cnf(i_0_3300,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = hAPP(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_1985]),
    [final] ).

cnf(i_0_3301,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 != hAPP(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_2036]),
    [final] ).

cnf(i_0_3302,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))
    | hAPP(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_2035]),
    [final] ).

cnf(i_0_3303,plain,
    ( X1 = X2
    | hAPP(c_Transcendental_Oln,X1) != hAPP(c_Transcendental_Oln,X2)
    | ~ c_Orderings_Oord__class_Oless(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) ),
    inference(split_conjunct,[status(thm)],[i_0_2044]),
    [final] ).

cnf(i_0_3304,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_2045,c_0_1450]),
    [final] ).

cnf(i_0_3305,plain,
    ( c_Groups_Osgn__class_Osgn(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
    | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2046]),
    [final] ).

cnf(i_0_3306,plain,
    ( c_Groups_Osgn__class_Osgn(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2047]),
    [final] ).

cnf(i_0_3307,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2048]),
    [final] ).

cnf(i_0_3308,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_1946]),
    [final] ).

cnf(i_0_3309,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2049]),
    [final] ).

cnf(i_0_3310,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2049]),
    [final] ).

cnf(i_0_3311,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2050]),
    [final] ).

cnf(i_0_3312,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2050]),
    [final] ).

cnf(i_0_3313,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2051]),
    [final] ).

cnf(i_0_3314,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2051]),
    [final] ).

cnf(i_0_3315,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3316,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3317,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_2053]),
    [final] ).

cnf(i_0_3318,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2054,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3319,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2055]),
    [final] ).

cnf(i_0_3320,plain,
    hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2056]),
    [final] ).

cnf(i_0_3321,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),X3)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2057]),
    [final] ).

cnf(i_0_3322,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2058]),
    [final] ).

cnf(i_0_3323,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1),hAPP(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_1915]),
    [final] ).

cnf(i_0_3324,plain,
    ( hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3325,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3)) = hAPP(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_2060]),
    [final] ).

cnf(i_0_3326,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2061]),
    [final] ).

cnf(i_0_3327,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2062]),
    [final] ).

cnf(i_0_3328,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 != hAPP(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_2036]),
    [final] ).

cnf(i_0_3329,plain,
    ( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,c_Int_Onumber__class_Onumber__of(X2,X3))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(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_2035]),
    [final] ).

cnf(i_0_3330,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_2063]),
    [final] ).

cnf(i_0_3331,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2064]),
    [final] ).

cnf(i_0_3332,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_1952]),
    [final] ).

cnf(i_0_3333,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_2065]),
    [final] ).

cnf(i_0_3334,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2066]),
    [final] ).

cnf(i_0_3335,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2067]),
    [final] ).

cnf(i_0_3336,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_2068]),
    [final] ).

cnf(i_0_3337,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2069]),
    [final] ).

cnf(i_0_3338,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),X3)
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2070]),
    [final] ).

cnf(i_0_3339,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2071]),
    [final] ).

cnf(i_0_3340,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)],[i_0_2072,c_0_1448]),c_0_1449]),c_0_1450]),c_0_1450]),
    [final] ).

cnf(i_0_3341,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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2073]),
    [final] ).

cnf(i_0_3342,plain,
    ( X2 = X3
    | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) != hAPP(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_2074]),
    [final] ).

cnf(i_0_3343,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_2018]),
    [final] ).

cnf(i_0_3344,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_2019]),
    [final] ).

cnf(i_0_3345,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2075]),
    [final] ).

cnf(i_0_3346,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2076]),
    [final] ).

cnf(i_0_3347,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_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2077]),
    [final] ).

cnf(i_0_3348,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_Osgn__class_Osgn(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3349,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1959]),
    [final] ).

cnf(i_0_3350,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1961]),
    [final] ).

cnf(i_0_3351,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_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2079]),
    [final] ).

cnf(i_0_3352,plain,
    ( 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_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2080]),
    [final] ).

cnf(i_0_3353,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2081]),
    [final] ).

cnf(i_0_3354,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2082]),
    [final] ).

cnf(i_0_3355,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1959]),
    [final] ).

cnf(i_0_3356,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),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2083]),
    [final] ).

cnf(i_0_3357,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1961]),
    [final] ).

cnf(i_0_3358,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_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2084]),
    [final] ).

cnf(i_0_3359,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_2085]),
    [final] ).

cnf(i_0_3360,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_2086]),
    [final] ).

cnf(i_0_3361,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_2087]),
    [final] ).

cnf(i_0_3362,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_2088]),
    [final] ).

cnf(i_0_3363,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_2089]),
    [final] ).

cnf(i_0_3364,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2011]),
    [final] ).

cnf(i_0_3365,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2013]),
    [final] ).

cnf(i_0_3366,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2090]),
    [final] ).

cnf(i_0_3367,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2032]),
    [final] ).

cnf(i_0_3368,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Lattices_Oboolean__algebra(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2091]),
    [final] ).

cnf(i_0_3369,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2092]),
    [final] ).

cnf(i_0_3370,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2033]),
    [final] ).

cnf(i_0_3371,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2034]),
    [final] ).

cnf(i_0_3372,plain,
    ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),X1) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(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_2093]),
    [final] ).

cnf(i_0_3373,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_2094]),
    [final] ).

cnf(i_0_3374,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oplus__class_Oplus(X1,X2,X3)) = X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2095]),
    [final] ).

cnf(i_0_3375,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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2096]),
    [final] ).

cnf(i_0_3376,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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2097]),
    [final] ).

cnf(i_0_3377,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,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2098]),
    [final] ).

cnf(i_0_3378,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,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2099]),
    [final] ).

cnf(i_0_3379,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2100]),
    [final] ).

cnf(i_0_3380,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2101]),
    [final] ).

cnf(i_0_3381,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3382,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2103]),
    [final] ).

cnf(i_0_3383,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_1914]),
    [final] ).

cnf(i_0_3384,plain,
    hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2104]),
    [final] ).

cnf(i_0_3385,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_2105]),
    [final] ).

cnf(i_0_3386,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2106]),
    [final] ).

cnf(i_0_3387,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2107]),
    [final] ).

cnf(i_0_3388,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2108]),
    [final] ).

cnf(i_0_3389,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2075]),
    [final] ).

cnf(i_0_3390,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1981]),
    [final] ).

cnf(i_0_3391,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2076]),
    [final] ).

cnf(i_0_3392,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1982]),
    [final] ).

cnf(i_0_3393,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ 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_1981]),
    [final] ).

cnf(i_0_3394,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ 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_2080]),
    [final] ).

cnf(i_0_3395,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,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_2081]),
    [final] ).

cnf(i_0_3396,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ 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_1982]),
    [final] ).

cnf(i_0_3397,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ 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_2082]),
    [final] ).

cnf(i_0_3398,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2109]),
    [final] ).

cnf(i_0_3399,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,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_2077]),
    [final] ).

cnf(i_0_3400,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2078]),
    [final] ).

cnf(i_0_3401,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,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_2079]),
    [final] ).

cnf(i_0_3402,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Fields_Olinordered__field(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2110]),
    [final] ).

cnf(i_0_3403,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2083]),
    [final] ).

cnf(i_0_3404,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2084]),
    [final] ).

cnf(i_0_3405,plain,
    hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2111]),
    [final] ).

cnf(i_0_3406,plain,
    hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1)),hAPP(c_NthRoot_Osqrt,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2112]),
    [final] ).

cnf(i_0_3407,plain,
    ( hAPP(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_2000]),
    [final] ).

cnf(i_0_3408,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(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_2100]),
    [final] ).

cnf(i_0_3409,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(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_2101]),
    [final] ).

cnf(i_0_3410,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ 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_2102]),
    [final] ).

cnf(i_0_3411,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2))
    | ~ 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_2103]),
    [final] ).

cnf(i_0_3412,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_2113]),
    [final] ).

cnf(i_0_3413,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_1983]),
    [final] ).

cnf(i_0_3414,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_2063]),
    [final] ).

cnf(i_0_3415,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X1),hAPP(c_Transcendental_Oarctan,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2114]),
    [final] ).

cnf(i_0_3416,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2064]),
    [final] ).

cnf(i_0_3417,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2115]),
    [final] ).

cnf(i_0_3418,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_2065]),
    [final] ).

cnf(i_0_3419,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X1),hAPP(c_Transcendental_Oarctan,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2116]),
    [final] ).

cnf(i_0_3420,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2066]),
    [final] ).

cnf(i_0_3421,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1),hAPP(c_NthRoot_Osqrt,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2117]),
    [final] ).

cnf(i_0_3422,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_2088]),
    [final] ).

cnf(i_0_3423,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_2089]),
    [final] ).

cnf(i_0_3424,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_2086]),
    [final] ).

cnf(i_0_3425,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_2087]),
    [final] ).

cnf(i_0_3426,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,X3,X2)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2118]),
    [final] ).

cnf(i_0_3427,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_2119]),
    [final] ).

cnf(i_0_3428,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_2120]),
    [final] ).

cnf(i_0_3429,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_2121]),
    [final] ).

cnf(i_0_3430,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_2122]),
    [final] ).

cnf(i_0_3431,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),hAPP(c_NthRoot_Osqrt,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2123]),
    [final] ).

cnf(i_0_3432,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),hAPP(c_NthRoot_Osqrt,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2124]),
    [final] ).

cnf(i_0_3433,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),hAPP(c_NthRoot_Osqrt,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2125]),
    [final] ).

cnf(i_0_3434,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),hAPP(c_NthRoot_Osqrt,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2126]),
    [final] ).

cnf(i_0_3435,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,hAPP(c_NthRoot_Osqrt,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2127]),
    [final] ).

cnf(i_0_3436,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,hAPP(c_NthRoot_Osqrt,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2128]),
    [final] ).

cnf(i_0_3437,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,hAPP(c_NthRoot_Osqrt,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2129]),
    [final] ).

cnf(i_0_3438,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,hAPP(c_NthRoot_Osqrt,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2130]),
    [final] ).

cnf(i_0_3439,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_2131]),
    [final] ).

cnf(i_0_3440,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_2132]),
    [final] ).

cnf(i_0_3441,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_2133]),
    [final] ).

cnf(i_0_3442,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_2134]),
    [final] ).

cnf(i_0_3443,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_2135]),
    [final] ).

cnf(i_0_3444,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_2136]),
    [final] ).

cnf(i_0_3445,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_2137]),
    [final] ).

cnf(i_0_3446,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_1983]),
    [final] ).

cnf(i_0_3447,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_2138]),
    [final] ).

cnf(i_0_3448,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_2139]),
    [final] ).

cnf(i_0_3449,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_2140]),
    [final] ).

cnf(i_0_3450,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_2141]),
    [final] ).

cnf(i_0_3451,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_2142]),
    [final] ).

cnf(i_0_3452,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_2085]),
    [final] ).

cnf(i_0_3453,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_2143]),
    [final] ).

cnf(i_0_3454,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_2144]),
    [final] ).

cnf(i_0_3455,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_2145]),
    [final] ).

cnf(i_0_3456,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_2146]),
    [final] ).

cnf(i_0_3457,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
    inference(split_conjunct,[status(thm)],[i_0_2147]),
    [final] ).

cnf(i_0_3458,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(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_2098]),
    [final] ).

cnf(i_0_3459,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(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_2099]),
    [final] ).

cnf(i_0_3460,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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_2096]),
    [final] ).

cnf(i_0_3461,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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_2097]),
    [final] ).

cnf(i_0_3462,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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_2148]),
    [final] ).

cnf(i_0_3463,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_2036]),
    [final] ).

cnf(i_0_3464,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_2035]),
    [final] ).

cnf(i_0_3465,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_2149]),
    [final] ).

cnf(i_0_3466,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,X2)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2150]),
    [final] ).

cnf(i_0_3467,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_2151]),
    [final] ).

cnf(i_0_3468,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_2152]),
    [final] ).

cnf(i_0_3469,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_2153]),
    [final] ).

cnf(i_0_3470,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_2154,c_0_1449]),c_0_1449]),
    [final] ).

cnf(i_0_3471,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_2155]),
    [final] ).

cnf(i_0_3472,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_2156]),
    [final] ).

cnf(i_0_3473,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Rings_Oinverse__class_Odivide(X1,X2,X3)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2157]),
    [final] ).

cnf(i_0_3474,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_2127]),
    [final] ).

cnf(i_0_3475,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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_2128]),
    [final] ).

cnf(i_0_3476,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_2129]),
    [final] ).

cnf(i_0_3477,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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_2130]),
    [final] ).

cnf(i_0_3478,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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_2158]),
    [final] ).

cnf(i_0_3479,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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_2123]),
    [final] ).

cnf(i_0_3480,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2159]),
    [final] ).

cnf(i_0_3481,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2124]),
    [final] ).

cnf(i_0_3482,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_2160]),
    [final] ).

cnf(i_0_3483,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(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_2125]),
    [final] ).

cnf(i_0_3484,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2126]),
    [final] ).

cnf(i_0_3485,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2161]),
    [final] ).

cnf(i_0_3486,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_2162]),
    [final] ).

cnf(i_0_3487,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_2163]),
    [final] ).

cnf(i_0_3488,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_1920]),
    [final] ).

cnf(i_0_3489,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_1921]),
    [final] ).

cnf(i_0_3490,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_1922]),
    [final] ).

cnf(i_0_3491,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2164]),
    [final] ).

cnf(i_0_3492,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2165]),
    [final] ).

cnf(i_0_3493,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2166]),
    [final] ).

cnf(i_0_3494,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2167]),
    [final] ).

cnf(i_0_3495,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_3496,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2169]),
    [final] ).

cnf(i_0_3497,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,X1),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_2170]),
    [final] ).

cnf(i_0_3498,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_2171]),
    [final] ).

cnf(i_0_3499,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk9_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_3500,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[i_0_1395]),
    [final] ).

cnf(i_0_3501,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[i_0_1396]),
    [final] ).

cnf(i_0_3502,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_2132]),
    [final] ).

cnf(i_0_3503,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_2149]),
    [final] ).

cnf(i_0_3504,plain,
    ( hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,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_2173]),
    [final] ).

cnf(i_0_3505,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_2174]),
    [final] ).

cnf(i_0_3506,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_2175]),
    [final] ).

cnf(i_0_3507,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(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_2176]),
    [final] ).

cnf(i_0_3508,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(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_2176]),
    [final] ).

cnf(i_0_3509,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    inference(split_conjunct,[status(thm)],[fact_em0]),
    [final] ).

cnf(i_0_3510,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_2177]),
    [final] ).

cnf(i_0_3511,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_2178]),
    [final] ).

cnf(i_0_3512,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_2179]),
    [final] ).

cnf(i_0_3513,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_2180]),
    [final] ).

cnf(i_0_3514,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_2181]),
    [final] ).

cnf(i_0_3515,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_2182]),
    [final] ).

cnf(i_0_3516,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_2183]),
    [final] ).

cnf(i_0_3517,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_2113]),
    [final] ).

cnf(i_0_3518,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_2184]),
    [final] ).

cnf(i_0_3519,plain,
    ( X2 = X3
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2) != hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X3)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2185]),
    [final] ).

cnf(i_0_3520,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    inference(split_conjunct,[status(thm)],[i_0_2186]),
    [final] ).

cnf(i_0_3521,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    inference(split_conjunct,[status(thm)],[i_0_2187]),
    [final] ).

cnf(i_0_3522,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    inference(split_conjunct,[status(thm)],[fact_d_I3_J]),
    [final] ).

cnf(i_0_3523,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
    inference(split_conjunct,[status(thm)],[fact_H_I3_J]),
    [final] ).

cnf(i_0_3524,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_1985]),
    [final] ).

cnf(i_0_3525,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_1986]),
    [final] ).

cnf(i_0_3526,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_2181]),
    [final] ).

cnf(i_0_3527,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_2182]),
    [final] ).

cnf(i_0_3528,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_2188]),
    [final] ).

cnf(i_0_3529,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_2085]),
    [final] ).

cnf(i_0_3530,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2189]),
    [final] ).

cnf(i_0_3531,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_Opred(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2190]),
    [final] ).

cnf(i_0_3532,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(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_2191]),
    [final] ).

cnf(i_0_3533,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2192]),
    [final] ).

cnf(i_0_3534,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_2193]),
    [final] ).

cnf(i_0_3535,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_2193]),
    [final] ).

cnf(i_0_3536,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2189]),
    [final] ).

cnf(i_0_3537,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(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_2194]),
    [final] ).

cnf(i_0_3538,plain,
    ( hAPP(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_2195]),
    [final] ).

cnf(i_0_3539,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = hAPP(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_2196]),
    [final] ).

cnf(i_0_3540,plain,
    ( X2 = hAPP(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_2197]),
    [final] ).

cnf(i_0_3541,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2198]),
    [final] ).

cnf(i_0_3542,plain,
    ( hAPP(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_2176]),
    [final] ).

cnf(i_0_3543,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_2199]),
    [final] ).

cnf(i_0_3544,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_2200]),
    [final] ).

cnf(i_0_3545,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_2201]),
    [final] ).

cnf(i_0_3546,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_2202]),
    [final] ).

cnf(i_0_3547,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_2203]),
    [final] ).

cnf(i_0_3548,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_2204]),
    [final] ).

cnf(i_0_3549,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1),X3),X4) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(X3,X4))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2205]),
    [final] ).

cnf(i_0_3550,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_2206]),
    [final] ).

cnf(i_0_3551,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_2207]),
    [final] ).

cnf(i_0_3552,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_2171]),
    [final] ).

cnf(i_0_3553,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_2172]),
    [final] ).

cnf(i_0_3554,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2208]),
    [final] ).

cnf(i_0_3555,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(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_2209]),
    [final] ).

cnf(i_0_3556,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(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_2210]),
    [final] ).

cnf(i_0_3557,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_2211]),
    [final] ).

cnf(i_0_3558,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_2199]),
    [final] ).

cnf(i_0_3559,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_2200]),
    [final] ).

cnf(i_0_3560,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_2212]),
    [final] ).

cnf(i_0_3561,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_2213]),
    [final] ).

cnf(i_0_3562,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_2202]),
    [final] ).

cnf(i_0_3563,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_2203]),
    [final] ).

cnf(i_0_3564,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_2204]),
    [final] ).

cnf(i_0_3565,plain,
    ( c_Rings_Oinverse__class_Odivide(X2,X3,X4) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X4)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2196]),
    [final] ).

cnf(i_0_3566,plain,
    ( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X3) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3567,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_2132]),
    [final] ).

cnf(i_0_3568,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_2036]),
    [final] ).

cnf(i_0_3569,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_2035]),
    [final] ).

cnf(i_0_3570,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Rings_Oinverse__class_Odivide(X2,X3,X1) = X4
    | X3 != hAPP(c_Groups_Otimes__class_Otimes(X2,X4),X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2196]),
    [final] ).

cnf(i_0_3571,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,X3,X2) = X4
    | ~ class_Rings_Odivision__ring(X1)
    | X3 != hAPP(c_Groups_Otimes__class_Otimes(X1,X4),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2214]),
    [final] ).

cnf(i_0_3572,plain,
    ( c_Rings_Oinverse__class_Odivide(X2,X1,X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X4)
    | ~ class_Rings_Odivision__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2197]),
    [final] ).

cnf(i_0_3573,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3574,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,X4,X2)
    | ~ class_Rings_Odivision__ring(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_2215]),
    [final] ).

cnf(i_0_3575,plain,
    ( X2 = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) != X4
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_3576,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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_2073]),
    [final] ).

cnf(i_0_3577,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oabs__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2216]),
    [final] ).

cnf(i_0_3578,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2217]),
    [final] ).

cnf(i_0_3579,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2218]),
    [final] ).

cnf(i_0_3580,plain,
    ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X1)) = 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_2219]),
    [final] ).

cnf(i_0_3581,plain,
    ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X1)) = 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_2220]),
    [final] ).

cnf(i_0_3582,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2221]),
    [final] ).

cnf(i_0_3583,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,X2,X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2222]),
    [final] ).

cnf(i_0_3584,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,X2,X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2223]),
    [final] ).

cnf(i_0_3585,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_2224]),
    [final] ).

cnf(i_0_3586,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_3587,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_2224]),
    [final] ).

cnf(i_0_3588,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_2226]),
    [final] ).

cnf(i_0_3589,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2227]),
    [final] ).

cnf(i_0_3590,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2228]),
    [final] ).

cnf(i_0_3591,plain,
    ( X1 = X3
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2229]),
    [final] ).

cnf(i_0_3592,plain,
    ( X1 = X3
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2230]),
    [final] ).

cnf(i_0_3593,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2231]),
    [final] ).

cnf(i_0_3594,plain,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2232]),
    [final] ).

cnf(i_0_3595,plain,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2233]),
    [final] ).

cnf(i_0_3596,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2209]),
    [final] ).

cnf(i_0_3597,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2234]),
    [final] ).

cnf(i_0_3598,plain,
    ( c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2235]),
    [final] ).

cnf(i_0_3599,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,X1)) != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2219]),
    [final] ).

cnf(i_0_3600,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_2183]),
    [final] ).

cnf(i_0_3601,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_1985]),
    [final] ).

cnf(i_0_3602,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_1986]),
    [final] ).

cnf(i_0_3603,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_2236]),
    [final] ).

cnf(i_0_3604,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_2142]),
    [final] ).

cnf(i_0_3605,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_2237]),
    [final] ).

cnf(i_0_3606,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_2238]),
    [final] ).

cnf(i_0_3607,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_2239]),
    [final] ).

cnf(i_0_3608,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_2240]),
    [final] ).

cnf(i_0_3609,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_2241]),
    [final] ).

cnf(i_0_3610,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)),
    inference(split_conjunct,[status(thm)],[fact_dm_I1_J]),
    [final] ).

cnf(i_0_3611,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_2226]),
    [final] ).

cnf(i_0_3612,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_2242]),
    [final] ).

cnf(i_0_3613,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_2243]),
    [final] ).

cnf(i_0_3614,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_2244]),
    [final] ).

cnf(i_0_3615,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_2141]),
    [final] ).

cnf(i_0_3616,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_2245]),
    [final] ).

cnf(i_0_3617,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_2246]),
    [final] ).

cnf(i_0_3618,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_2139]),
    [final] ).

cnf(i_0_3619,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | hAPP(c_Transcendental_Oln,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),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2247]),
    [final] ).

cnf(i_0_3620,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)
    | hAPP(c_NthRoot_Osqrt,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_3621,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_2249]),
    [final] ).

cnf(i_0_3622,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
    | ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2250]),
    [final] ).

cnf(i_0_3623,plain,
    ( X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2251]),
    [final] ).

cnf(i_0_3624,plain,
    ( X3 = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2252]),
    [final] ).

cnf(i_0_3625,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e),
    inference(split_conjunct,[status(thm)],[fact_dm_I2_J]),
    [final] ).

cnf(i_0_3626,plain,
    c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2253]),
    [final] ).

cnf(i_0_3627,plain,
    c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_3628,plain,
    ( hAPP(c_Transcendental_Oexp(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,hAPP(c_Transcendental_Oexp(X1),X2))
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2255]),
    [final] ).

cnf(i_0_3629,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | hAPP(c_NthRoot_Osqrt,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2256]),
    [final] ).

cnf(i_0_3630,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_2257]),
    [final] ).

cnf(i_0_3631,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_2258]),
    [final] ).

cnf(i_0_3632,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1) = hAPP(c_Groups_Otimes__class_Otimes(X2,X3),X3)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2185]),
    [final] ).

cnf(i_0_3633,plain,
    ( hAPP(c_Transcendental_Oln,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2247]),
    [final] ).

cnf(i_0_3634,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_2259]),
    [final] ).

cnf(i_0_3635,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_2260]),
    [final] ).

cnf(i_0_3636,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_2261]),
    [final] ).

cnf(i_0_3637,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2262]),
    [final] ).

cnf(i_0_3638,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2263]),
    [final] ).

cnf(i_0_3639,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_2196]),
    [final] ).

cnf(i_0_3640,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_2194]),
    [final] ).

cnf(i_0_3641,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Groups_Osgn__class_Osgn(X1,X2) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_3642,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(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) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_3643,plain,
    ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | 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),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2265]),
    [final] ).

cnf(i_0_3644,plain,
    ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | 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),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_3645,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_2267]),
    [final] ).

cnf(i_0_3646,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_2268]),
    [final] ).

cnf(i_0_3647,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_2269]),
    [final] ).

cnf(i_0_3648,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_2270]),
    [final] ).

cnf(i_0_3649,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_2271]),
    [final] ).

cnf(i_0_3650,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_2272]),
    [final] ).

cnf(i_0_3651,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_2273]),
    [final] ).

cnf(i_0_3652,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_2274]),
    [final] ).

cnf(i_0_3653,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_2275]),
    [final] ).

cnf(i_0_3654,plain,
    ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2276]),
    [final] ).

cnf(i_0_3655,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2277]),
    [final] ).

cnf(i_0_3656,plain,
    ( X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2278]),
    [final] ).

cnf(i_0_3657,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_2279]),
    [final] ).

cnf(i_0_3658,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_2224]),
    [final] ).

cnf(i_0_3659,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2182]),
    [final] ).

cnf(i_0_3660,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2142]),
    [final] ).

cnf(i_0_3661,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2280]),
    [final] ).

cnf(i_0_3662,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2281]),
    [final] ).

cnf(i_0_3663,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2282]),
    [final] ).

cnf(i_0_3664,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_3665,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_3666,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2235]),
    [final] ).

cnf(i_0_3667,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_2283]),
    [final] ).

cnf(i_0_3668,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_2284]),
    [final] ).

cnf(i_0_3669,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_2285]),
    [final] ).

cnf(i_0_3670,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_2286]),
    [final] ).

cnf(i_0_3671,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2287]),
    [final] ).

cnf(i_0_3672,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2288]),
    [final] ).

cnf(i_0_3673,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_2289]),
    [final] ).

cnf(i_0_3674,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
    | ~ class_Rings_Odivision__ring(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2290]),
    [final] ).

cnf(i_0_3675,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_3676,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2292]),
    [final] ).

cnf(i_0_3677,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_3678,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_2294]),
    [final] ).

cnf(i_0_3679,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_2294]),
    [final] ).

cnf(i_0_3680,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_2295]),
    [final] ).

cnf(i_0_3681,plain,
    ( c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2251]),
    [final] ).

cnf(i_0_3682,plain,
    ( c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2252]),
    [final] ).

cnf(i_0_3683,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2296]),
    [final] ).

cnf(i_0_3684,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_2297]),
    [final] ).

cnf(i_0_3685,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_2298]),
    [final] ).

cnf(i_0_3686,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_2299]),
    [final] ).

cnf(i_0_3687,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_2300]),
    [final] ).

cnf(i_0_3688,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_3689,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2265]),
    [final] ).

cnf(i_0_3690,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_3691,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2301]),
    [final] ).

cnf(i_0_3692,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)),
    inference(split_conjunct,[status(thm)],[i_0_2302]),
    [final] ).

cnf(i_0_3693,plain,
    c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2303]),
    [final] ).

cnf(i_0_3694,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2199]),
    [final] ).

cnf(i_0_3695,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2304]),
    [final] ).

cnf(i_0_3696,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2305]),
    [final] ).

cnf(i_0_3697,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2260]),
    [final] ).

cnf(i_0_3698,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2260]),
    [final] ).

cnf(i_0_3699,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2202]),
    [final] ).

cnf(i_0_3700,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2204]),
    [final] ).

cnf(i_0_3701,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(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_2306]),
    [final] ).

cnf(i_0_3702,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2307]),
    [final] ).

cnf(i_0_3703,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2308]),
    [final] ).

cnf(i_0_3704,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2309]),
    [final] ).

cnf(i_0_3705,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3) = hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2310]),
    [final] ).

cnf(i_0_3706,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Osgn__class_Osgn(X1,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_3707,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2312]),
    [final] ).

cnf(i_0_3708,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_2313]),
    [final] ).

cnf(i_0_3709,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_2314]),
    [final] ).

cnf(i_0_3710,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_2315]),
    [final] ).

cnf(i_0_3711,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) ),
    inference(rw,[status(thm)],[i_0_2316,c_0_1449]),
    [final] ).

cnf(i_0_3712,plain,
    ( X1 = c_Int_OPls
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_2317,c_0_1449]),
    [final] ).

cnf(i_0_3713,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_2318]),
    [final] ).

cnf(i_0_3714,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2277]),
    [final] ).

cnf(i_0_3715,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2319]),
    [final] ).

cnf(i_0_3716,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2320]),
    [final] ).

cnf(i_0_3717,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2321]),
    [final] ).

cnf(i_0_3718,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2322]),
    [final] ).

cnf(i_0_3719,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ class_Groups_Oabs__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2216]),
    [final] ).

cnf(i_0_3720,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_2318]),
    [final] ).

cnf(i_0_3721,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2323]),
    [final] ).

cnf(i_0_3722,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2227]),
    [final] ).

cnf(i_0_3723,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2324]),
    [final] ).

cnf(i_0_3724,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2325]),
    [final] ).

cnf(i_0_3725,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) = hAPP(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_2231]),
    [final] ).

cnf(i_0_3726,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) = hAPP(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_2232]),
    [final] ).

cnf(i_0_3727,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1) = hAPP(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_2229]),
    [final] ).

cnf(i_0_3728,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_2196]),
    [final] ).

cnf(i_0_3729,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_2194]),
    [final] ).

cnf(i_0_3730,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[i_0_2326]),
    [final] ).

cnf(i_0_3731,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_2327]),
    [final] ).

cnf(i_0_3732,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2278]),
    [final] ).

cnf(i_0_3733,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_3734,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_2283]),
    [final] ).

cnf(i_0_3735,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_2284]),
    [final] ).

cnf(i_0_3736,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_2267]),
    [final] ).

cnf(i_0_3737,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_2274]),
    [final] ).

cnf(i_0_3738,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_2328]),
    [final] ).

cnf(i_0_3739,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_2275]),
    [final] ).

cnf(i_0_3740,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_2329]),
    [final] ).

cnf(i_0_3741,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_2330]),
    [final] ).

cnf(i_0_3742,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2331]),
    [final] ).

cnf(i_0_3743,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1),X2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2332]),
    [final] ).

cnf(i_0_3744,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1),X2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2333]),
    [final] ).

cnf(i_0_3745,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_2334]),
    [final] ).

cnf(i_0_3746,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_2335]),
    [final] ).

cnf(i_0_3747,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_2336]),
    [final] ).

cnf(i_0_3748,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_2337]),
    [final] ).

cnf(i_0_3749,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_2279]),
    [final] ).

cnf(i_0_3750,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_2328]),
    [final] ).

cnf(i_0_3751,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_2338]),
    [final] ).

cnf(i_0_3752,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2339]),
    [final] ).

cnf(i_0_3753,plain,
    hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2340]),
    [final] ).

cnf(i_0_3754,plain,
    hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2341]),
    [final] ).

cnf(i_0_3755,plain,
    hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2342]),
    [final] ).

cnf(i_0_3756,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(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_2343]),
    [final] ).

cnf(i_0_3757,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_2344]),
    [final] ).

cnf(i_0_3758,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_2345]),
    [final] ).

cnf(i_0_3759,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_2346]),
    [final] ).

cnf(i_0_3760,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_2347]),
    [final] ).

cnf(i_0_3761,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_2348]),
    [final] ).

cnf(i_0_3762,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_2349]),
    [final] ).

cnf(i_0_3763,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_2350]),
    [final] ).

cnf(i_0_3764,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_2351]),
    [final] ).

cnf(i_0_3765,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_2352]),
    [final] ).

cnf(i_0_3766,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_2294]),
    [final] ).

cnf(i_0_3767,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2353]),
    [final] ).

cnf(i_0_3768,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(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_2354]),
    [final] ).

cnf(i_0_3769,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(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_2354]),
    [final] ).

cnf(i_0_3770,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2355]),
    [final] ).

cnf(i_0_3771,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2355]),
    [final] ).

cnf(i_0_3772,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_2356]),
    [final] ).

cnf(i_0_3773,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_2357]),
    [final] ).

cnf(i_0_3774,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_3775,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_3776,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2358]),
    [final] ).

cnf(i_0_3777,plain,
    ( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
    | X1 != X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2181]),
    [final] ).

cnf(i_0_3778,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = X3
    | ~ class_Rings_Odivision__ring(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2359]),
    [final] ).

cnf(i_0_3779,plain,
    ( hAPP(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_2360]),
    [final] ).

cnf(i_0_3780,plain,
    ( hAPP(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_2361]),
    [final] ).

cnf(i_0_3781,plain,
    ( hAPP(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_2362]),
    [final] ).

cnf(i_0_3782,plain,
    ( hAPP(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_2363]),
    [final] ).

cnf(i_0_3783,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Opred(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
    inference(rw,[status(thm)],[i_0_2364,c_0_1450]),
    [final] ).

cnf(i_0_3784,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_2289]),
    [final] ).

cnf(i_0_3785,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2365]),
    [final] ).

cnf(i_0_3786,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2)) = c_Groups_Osgn__class_Osgn(X1,X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2366]),
    [final] ).

cnf(i_0_3787,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_2367]),
    [final] ).

cnf(i_0_3788,plain,
    ( hAPP(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_2368]),
    [final] ).

cnf(i_0_3789,plain,
    ( hAPP(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_2369]),
    [final] ).

cnf(i_0_3790,plain,
    ( hAPP(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_2370]),
    [final] ).

cnf(i_0_3791,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_2371]),
    [final] ).

cnf(i_0_3792,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_2286]),
    [final] ).

cnf(i_0_3793,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X2,X1),X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2277]),
    [final] ).

cnf(i_0_3794,plain,
    ( hAPP(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_2306]),
    [final] ).

cnf(i_0_3795,plain,
    ( hAPP(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_2306]),
    [final] ).

cnf(i_0_3796,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_3797,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_3798,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_3799,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[fact_one0]),
    [final] ).

cnf(i_0_3800,plain,
    ( hAPP(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_2372]),
    [final] ).

cnf(i_0_3801,plain,
    ( hAPP(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_2373]),
    [final] ).

cnf(i_0_3802,plain,
    ( hAPP(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_2374]),
    [final] ).

cnf(i_0_3803,plain,
    ( hAPP(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_2375]),
    [final] ).

cnf(i_0_3804,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_2376]),
    [final] ).

cnf(i_0_3805,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_2377]),
    [final] ).

cnf(i_0_3806,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_2378]),
    [final] ).

cnf(i_0_3807,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_2379]),
    [final] ).

cnf(i_0_3808,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2200]),
    [final] ).

cnf(i_0_3809,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2213]),
    [final] ).

cnf(i_0_3810,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2380]),
    [final] ).

cnf(i_0_3811,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2203]),
    [final] ).

cnf(i_0_3812,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_2381]),
    [final] ).

cnf(i_0_3813,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_2382]),
    [final] ).

cnf(i_0_3814,plain,
    ( X1 = X2
    | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2383]),
    [final] ).

cnf(i_0_3815,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_2384,c_0_1449]),
    [final] ).

cnf(i_0_3816,plain,
    ( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)
    | c_Int_OPls != X1 ),
    inference(rw,[status(thm)],[i_0_2385,c_0_1449]),
    [final] ).

cnf(i_0_3817,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
    inference(split_conjunct,[status(thm)],[fact_d1_I2_J]),
    [final] ).

cnf(i_0_3818,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_0),
    inference(split_conjunct,[status(thm)],[i_0_2186]),
    [final] ).

cnf(i_0_3819,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0),
    inference(split_conjunct,[status(thm)],[i_0_2187]),
    [final] ).

cnf(i_0_3820,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
    inference(split_conjunct,[status(thm)],[fact_d_I1_J]),
    [final] ).

cnf(i_0_3821,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
    inference(split_conjunct,[status(thm)],[fact_assms]),
    [final] ).

cnf(i_0_3822,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
    inference(split_conjunct,[status(thm)],[fact_H_I1_J]),
    [final] ).

cnf(i_0_3823,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(split_conjunct,[status(thm)],[fact_m_I1_J]),
    [final] ).

cnf(i_0_3824,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_2186]),
    [final] ).

cnf(i_0_3825,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_2187]),
    [final] ).

cnf(i_0_3826,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[fact_d_I2_J]),
    [final] ).

cnf(i_0_3827,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[fact_H_I2_J]),
    [final] ).

cnf(i_0_3828,plain,
    ( hAPP(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_2386]),
    [final] ).

cnf(i_0_3829,plain,
    ( hAPP(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_2387]),
    [final] ).

cnf(i_0_3830,plain,
    ( hAPP(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_2388]),
    [final] ).

cnf(i_0_3831,plain,
    ( X2 = X3
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2389]),
    [final] ).

cnf(i_0_3832,plain,
    ( X2 = X3
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ouminus__class_Ouminus(X1,X3)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2390]),
    [final] ).

cnf(i_0_3833,plain,
    ( X2 = X3
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2391]),
    [final] ).

cnf(i_0_3834,plain,
    ( X2 = X3
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3)
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2392]),
    [final] ).

cnf(i_0_3835,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2393]),
    [final] ).

cnf(i_0_3836,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2394]),
    [final] ).

cnf(i_0_3837,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2395]),
    [final] ).

cnf(i_0_3838,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2396]),
    [final] ).

cnf(i_0_3839,plain,
    ( ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1)
    | hAPP(c_Transcendental_Oexp(X1),X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2397]),
    [final] ).

cnf(i_0_3840,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2398]),
    [final] ).

cnf(i_0_3841,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_3842,plain,
    ( hAPP(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_2354]),
    [final] ).

cnf(i_0_3843,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(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_2355]),
    [final] ).

cnf(i_0_3844,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_3845,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
    inference(rw,[status(thm)],[i_0_2400,c_0_1449]),
    [final] ).

cnf(i_0_3846,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2) = X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2401]),
    [final] ).

cnf(i_0_3847,plain,
    ( hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2) = X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2402]),
    [final] ).

cnf(i_0_3848,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2403]),
    [final] ).

cnf(i_0_3849,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2404]),
    [final] ).

cnf(i_0_3850,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2405]),
    [final] ).

cnf(i_0_3851,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2406]),
    [final] ).

cnf(i_0_3852,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2406]),
    [final] ).

cnf(i_0_3853,plain,
    ( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2407]),
    [final] ).

cnf(i_0_3854,plain,
    ( X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2407]),
    [final] ).

cnf(i_0_3855,plain,
    hAPP(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_2408]),
    [final] ).

cnf(i_0_3856,plain,
    hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2409]),
    [final] ).

cnf(i_0_3857,plain,
    ( hAPP(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_2343]),
    [final] ).

cnf(i_0_3858,plain,
    ( hAPP(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_2343]),
    [final] ).

cnf(i_0_3859,plain,
    ( hAPP(c_Transcendental_Oexp(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_RealVector_Oreal__normed__field(X1)
    | ~ class_SEQ_Obanach(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2410]),
    [final] ).

cnf(i_0_3860,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2411]),
    [final] ).

cnf(i_0_3861,plain,
    hAPP(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_2412]),
    [final] ).

cnf(i_0_3862,plain,
    hAPP(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_2413]),
    [final] ).

cnf(i_0_3863,plain,
    hAPP(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_2414]),
    [final] ).

cnf(i_0_3864,plain,
    hAPP(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_2415]),
    [final] ).

cnf(i_0_3865,plain,
    ( hAPP(c_Transcendental_Oln,X2) = X1
    | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2416]),
    [final] ).

cnf(i_0_3866,plain,
    ( hAPP(c_Transcendental_Oln,X2) = X1
    | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2417]),
    [final] ).

cnf(i_0_3867,plain,
    ( X1 = X2
    | hAPP(c_NthRoot_Osqrt,X1) != hAPP(c_NthRoot_Osqrt,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2418]),
    [final] ).

cnf(i_0_3868,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Ouminus__class_Ouminus(X1,X2)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2419]),
    [final] ).

cnf(i_0_3869,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2420]),
    [final] ).

cnf(i_0_3870,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2421]),
    [final] ).

cnf(i_0_3871,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2422]),
    [final] ).

cnf(i_0_3872,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Osgn__class_Osgn(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2423]),
    [final] ).

cnf(i_0_3873,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2424]),
    [final] ).

cnf(i_0_3874,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Odivision__ring(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2425]),
    [final] ).

cnf(i_0_3875,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Odivision__ring(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2426]),
    [final] ).

cnf(i_0_3876,plain,
    hAPP(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_2427]),
    [final] ).

cnf(i_0_3877,plain,
    hAPP(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_2428]),
    [final] ).

cnf(i_0_3878,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2429]),
    [final] ).

cnf(i_0_3879,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2430]),
    [final] ).

cnf(i_0_3880,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2431]),
    [final] ).

cnf(i_0_3881,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2432]),
    [final] ).

cnf(i_0_3882,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2433]),
    [final] ).

cnf(i_0_3883,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2434]),
    [final] ).

cnf(i_0_3884,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2435]),
    [final] ).

cnf(i_0_3885,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,X2) != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2436]),
    [final] ).

cnf(i_0_3886,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ouminus__class_Ouminus(X2,X1)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2437]),
    [final] ).

cnf(i_0_3887,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2438]),
    [final] ).

cnf(i_0_3888,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2439]),
    [final] ).

cnf(i_0_3889,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),X1) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_2440]),
    [final] ).

cnf(i_0_3890,plain,
    ( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2421]),
    [final] ).

cnf(i_0_3891,plain,
    ( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Osgn__if(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_3892,plain,
    ( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2422]),
    [final] ).

cnf(i_0_3893,plain,
    ( c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2423]),
    [final] ).

cnf(i_0_3894,plain,
    ( c_Rings_Oinverse__class_Oinverse(X2,X1) = c_Groups_Oone__class_Oone(X2)
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2420]),
    [final] ).

cnf(i_0_3895,plain,
    ( c_Rings_Oinverse__class_Oinverse(X2,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_2424]),
    [final] ).

cnf(i_0_3896,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | c_Groups_Ozero__class_Ozero(X1) != X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2419]),
    [final] ).

cnf(i_0_3897,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_2441]),
    [final] ).

cnf(i_0_3898,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2442]),
    [final] ).

cnf(i_0_3899,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2443]),
    [final] ).

cnf(i_0_3900,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Osgn__if(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2444]),
    [final] ).

cnf(i_0_3901,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2445]),
    [final] ).

cnf(i_0_3902,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2446]),
    [final] ).

cnf(i_0_3903,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,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_2447]),
    [final] ).

cnf(i_0_3904,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2448]),
    [final] ).

cnf(i_0_3905,plain,
    ( c_Groups_Ouminus__class_Ouminus(X2,X1) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2436]),
    [final] ).

cnf(i_0_3906,plain,
    ( X1 = c_Groups_Ouminus__class_Ouminus(X2,X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Olinordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2437]),
    [final] ).

cnf(i_0_3907,plain,
    ( c_Int_Oiszero(X2,X1)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Osemiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2438]),
    [final] ).

cnf(i_0_3908,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | hAPP(c_NthRoot_Osqrt,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2449]),
    [final] ).

cnf(i_0_3909,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | hAPP(c_NthRoot_Osqrt,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2450]),
    [final] ).

cnf(i_0_3910,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2451]),
    [final] ).

cnf(i_0_3911,plain,
    ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2439]),
    [final] ).

cnf(i_0_3912,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_2452]),
    [final] ).

cnf(i_0_3913,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_2453]),
    [final] ).

cnf(i_0_3914,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2264]),
    [final] ).

cnf(i_0_3915,plain,
    ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,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_2265]),
    [final] ).

cnf(i_0_3916,plain,
    ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,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_2266]),
    [final] ).

cnf(i_0_3917,plain,
    ( hAPP(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_2449]),
    [final] ).

cnf(i_0_3918,plain,
    ( hAPP(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_2450]),
    [final] ).

cnf(i_0_3919,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_2454]),
    [final] ).

cnf(i_0_3920,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_2455]),
    [final] ).

cnf(i_0_3921,plain,
    c_Groups_Ouminus__class_Ouminus(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_zminus__0]),
    [final] ).

cnf(i_0_3922,plain,
    c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_INVERSE__ZERO]),
    [final] ).

cnf(i_0_3923,plain,
    hAPP(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_3924,plain,
    hAPP(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_3925,plain,
    hAPP(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_3926,plain,
    hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_ln__one]),
    [final] ).

cnf(i_0_3927,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_3928,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__code]),
    [final] ).

cnf(i_0_3929,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_3930,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_3931,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2456]),
    [final] ).

cnf(i_0_3932,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_minus__Pls]),
    [final] ).

cnf(i_0_3933,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_3934,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_3935,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_3936,plain,
    class_Groups_Oabs__if(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]),
    [final] ).

cnf(i_0_3937,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_3938,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_3939,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_3940,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_3941,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
    [final] ).

cnf(i_0_3942,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
    [final] ).

cnf(i_0_3943,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
    [final] ).

cnf(i_0_3944,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_3945,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_3946,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_3947,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_3948,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_3949,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
    [final] ).

cnf(i_0_3950,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]),
    [final] ).

cnf(i_0_3951,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
    [final] ).

cnf(i_0_3952,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
    [final] ).

cnf(i_0_3953,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
    [final] ).

cnf(i_0_3954,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_3955,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_3956,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_3957,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_3958,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_3959,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_3960,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_3961,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_3962,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]),
    [final] ).

cnf(i_0_3963,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
    [final] ).

cnf(i_0_3964,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]),
    [final] ).

cnf(i_0_3965,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_3966,plain,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
    [final] ).

cnf(i_0_3967,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_3968,plain,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
    [final] ).

cnf(i_0_3969,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]),
    [final] ).

cnf(i_0_3970,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
    [final] ).

cnf(i_0_3971,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]),
    [final] ).

cnf(i_0_3972,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
    [final] ).

cnf(i_0_3973,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_3974,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
    [final] ).

cnf(i_0_3975,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
    [final] ).

cnf(i_0_3976,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_3977,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
    [final] ).

cnf(i_0_3978,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_3979,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
    [final] ).

cnf(i_0_3980,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]),
    [final] ).

cnf(i_0_3981,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_3982,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_3983,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_3984,plain,
    class_SEQ_Obanach(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__SEQ_Obanach]),
    [final] ).

cnf(i_0_3985,plain,
    class_SEQ_Obanach(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__SEQ_Obanach]),
    [final] ).

cnf(i_0_3986,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_3987,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_3988,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_3989,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]),
    [final] ).

cnf(i_0_3990,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_3991,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]),
    [final] ).

cnf(i_0_3992,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]),
    [final] ).

cnf(i_0_3993,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]),
    [final] ).

cnf(i_0_3994,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_3995,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_3996,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]),
    [final] ).

cnf(i_0_3997,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]),
    [final] ).

cnf(i_0_3998,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_3999,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_4000,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_4001,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_4002,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_4003,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_4004,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_4005,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_4006,plain,
    class_Groups_Osgn__if(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]),
    [final] ).

cnf(i_0_4007,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_4008,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_4009,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
    [final] ).

cnf(i_0_4010,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]),
    [final] ).

cnf(i_0_4011,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
    [final] ).

cnf(i_0_4012,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
    [final] ).

cnf(i_0_4013,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
    [final] ).

cnf(i_0_4014,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4015,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4016,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4017,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4018,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4019,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_4020,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_4021,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_4022,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_4023,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]),
    [final] ).

cnf(i_0_4024,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_4025,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_4026,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_4027,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]),
    [final] ).

cnf(i_0_4028,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_4029,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_4030,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_4031,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_4032,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_4033,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_4034,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_4035,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_4036,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_4037,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4038,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4039,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4040,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4041,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4042,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_4043,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_4044,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_4045,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_4046,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]),
    [final] ).

cnf(i_0_4047,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_4048,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]),
    [final] ).

cnf(i_0_4049,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_4050,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_4051,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_4052,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_4053,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]),
    [final] ).

cnf(i_0_4054,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_4055,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_4056,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_4057,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_4058,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]),
    [final] ).

cnf(i_0_4059,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_4060,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_4061,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_4062,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_4063,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_4064,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_4065,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_4066,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_4067,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]),
    [final] ).

cnf(i_0_4068,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_4069,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_4070,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
    [final] ).

cnf(i_0_4071,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_4072,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]),
    [final] ).

cnf(i_0_4073,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_4074,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_4075,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
    [final] ).

cnf(i_0_4076,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4077,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4078,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4079,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4080,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4081,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4082,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4083,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4084,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4085,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
    [final] ).

cnf(i_0_4086,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]),
    [final] ).

cnf(i_0_4087,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_4088,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_4089,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
    [final] ).

cnf(i_0_4090,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_4091,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]),
    [final] ).

cnf(i_0_4092,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_4093,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_4094,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_4095,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
    [final] ).

cnf(i_0_4096,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]),
    [final] ).

cnf(i_0_4097,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_4098,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_4099,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
    [final] ).

cnf(i_0_4100,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_4101,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_4102,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_4103,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_4104,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]),
    [final] ).

cnf(i_0_4105,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_4106,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_4107,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_4108,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_4109,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_4110,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_4111,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_4112,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_4113,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_4114,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]),
    [final] ).

cnf(i_0_4115,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_4116,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_4117,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_4118,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_4119,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_4120,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4121,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4122,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4123,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4124,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4125,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_4126,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]),
    [final] ).

cnf(i_0_4127,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_4128,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_4129,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_4130,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_4131,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_4132,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_4133,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_4134,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]),
    [final] ).

cnf(i_0_4135,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_4136,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_4137,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_4138,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]),
    [final] ).

cnf(i_0_4139,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_4140,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_4141,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_4142,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_4143,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_4144,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_4145,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]),
    [final] ).

cnf(i_0_4146,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_4147,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_4148,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_4149,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4150,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4151,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4152,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4153,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4154,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_4155,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_4156,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_4157,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_4158,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]),
    [final] ).

cnf(i_0_4159,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_4160,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_4161,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_4162,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_4163,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_4164,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4165,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4166,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4167,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4168,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_4169,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_4170,plain,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
    [final] ).

cnf(i_0_4171,plain,
    class_Rings_Odivision__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
    [final] ).

cnf(i_0_4172,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
    [final] ).

cnf(i_0_4173,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
    [final] ).

cnf(i_0_4174,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_4175,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_4176,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_4177,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
    [final] ).

cnf(i_0_4178,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_4179,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]),
    [final] ).

cnf(i_0_4180,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_4181,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_4182,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_4183,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_4184,axiom,
    X1 = X1 ).

cnf(i_0_4185,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4186,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4187,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).

cnf(i_0_4188,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).

cnf(i_0_4189,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).

cnf(i_0_4190,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).

cnf(i_0_4191,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).

cnf(i_0_4192,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_4193,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_4194,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_4195,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_4196,axiom,
    ( X1 != X2
    | c_Int_Opred(X1) = c_Int_Opred(X2) ) ).

cnf(i_0_4197,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_4198,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_4199,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_4200,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_4201,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_4202,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_4203,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_4204,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_4205,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_4206,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).

cnf(i_0_4207,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).

cnf(i_0_4208,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).

cnf(i_0_4209,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).

cnf(i_0_4210,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).

cnf(i_0_4211,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).

cnf(i_0_4212,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
    | c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).

cnf(i_0_4213,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).

cnf(i_0_4214,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_4215,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_4216,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_4217,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_4218,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_4219,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_4220,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_4221,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4222,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_4223,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_4224,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_4225,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_4226,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
    | c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_4227,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
    | c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_4228,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_4229,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_4230,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_4231,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__field(X1)
    | class_RealVector_Oreal__normed__field(X2) ) ).

cnf(i_0_4232,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_4233,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_4234,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_4235,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_4236,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_4237,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_4238,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_4239,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_4240,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_4241,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_4242,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_4243,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_4244,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | class_RealVector_Oreal__normed__algebra(X2) ) ).

cnf(i_0_4245,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_4246,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4247,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_4248,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_4249,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_4250,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_4251,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_4252,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_4253,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_4254,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_4255,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_4256,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_4257,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_4258,axiom,
    ( X1 != X2
    | ~ class_SEQ_Obanach(X1)
    | class_SEQ_Obanach(X2) ) ).

cnf(i_0_4259,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_4260,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X1,X3,X4,X5)
    | c_Deriv_Oderiv(X2,X3,X4,X5) ) ).

cnf(i_0_4261,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X1,X4,X5)
    | c_Deriv_Oderiv(X3,X2,X4,X5) ) ).

cnf(i_0_4262,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X4,X1,X5)
    | c_Deriv_Oderiv(X3,X4,X2,X5) ) ).

cnf(i_0_4263,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X4,X5,X1)
    | c_Deriv_Oderiv(X3,X4,X5,X2) ) ).

cnf(i_0_4264,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_4265,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_4266,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_4267,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_4268,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_4269,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__div__algebra(X1)
    | class_RealVector_Oreal__normed__div__algebra(X2) ) ).

cnf(i_0_4270,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_4271,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_4272,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_4273,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_4274,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_4275,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_4276,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_4277,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_4278,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4279,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_4280,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_4281,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_4282,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_4283,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_4284,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_4285,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_4286,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_4287,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_4288,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_4289,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | class_RealVector_Oreal__normed__vector(X2) ) ).

cnf(i_0_4290,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_4291,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_4292,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra__1(X1)
    | class_RealVector_Oreal__normed__algebra__1(X2) ) ).

cnf(i_0_4293,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_4294,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_4295,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_4296,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_4184_001,axiom,
    X1 = X1 ).

cnf(i_0_4185_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4186_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4187_004,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).

cnf(i_0_4188_005,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).

cnf(i_0_4189_006,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).

cnf(i_0_4190_007,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).

cnf(i_0_4191_008,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).

cnf(i_0_4192_009,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_4193_010,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_4194_011,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_4195_012,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_4196_013,axiom,
    ( X1 != X2
    | c_Int_Opred(X1) = c_Int_Opred(X2) ) ).

cnf(i_0_4197_014,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_4198_015,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_4199_016,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_4200_017,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_4201_018,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_4202_019,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_4203_020,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_4204_021,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_4205_022,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_4206_023,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).

cnf(i_0_4207_024,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).

cnf(i_0_4208_025,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).

cnf(i_0_4209_026,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).

cnf(i_0_4210_027,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).

cnf(i_0_4211_028,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).

cnf(i_0_4212_029,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
    | c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).

cnf(i_0_4213_030,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).

cnf(i_0_4214_031,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_4215_032,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_4216_033,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_4217_034,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_4218_035,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_4219_036,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_4220_037,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_4221_038,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4222_039,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_4223_040,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_4224_041,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_4225_042,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_4226_043,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
    | c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_4227_044,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
    | c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_4228_045,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_4229_046,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_4230_047,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_4231_048,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__field(X1)
    | class_RealVector_Oreal__normed__field(X2) ) ).

cnf(i_0_4232_049,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_4233_050,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_4234_051,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_4235_052,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_4236_053,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_4237_054,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_4238_055,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_4239_056,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_4240_057,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_4241_058,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_4242_059,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_4243_060,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_4244_061,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | class_RealVector_Oreal__normed__algebra(X2) ) ).

cnf(i_0_4245_062,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_4246_063,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4247_064,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_4248_065,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_4249_066,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_4250_067,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_4251_068,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_4252_069,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_4253_070,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_4254_071,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_4255_072,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_4256_073,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_4257_074,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_4258_075,axiom,
    ( X1 != X2
    | ~ class_SEQ_Obanach(X1)
    | class_SEQ_Obanach(X2) ) ).

cnf(i_0_4259_076,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_4260_077,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X1,X3,X4,X5)
    | c_Deriv_Oderiv(X2,X3,X4,X5) ) ).

cnf(i_0_4261_078,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X1,X4,X5)
    | c_Deriv_Oderiv(X3,X2,X4,X5) ) ).

cnf(i_0_4262_079,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X4,X1,X5)
    | c_Deriv_Oderiv(X3,X4,X2,X5) ) ).

cnf(i_0_4263_080,axiom,
    ( X1 != X2
    | ~ c_Deriv_Oderiv(X3,X4,X5,X1)
    | c_Deriv_Oderiv(X3,X4,X5,X2) ) ).

cnf(i_0_4264_081,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_4265_082,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_4266_083,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_4267_084,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_4268_085,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_4269_086,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__div__algebra(X1)
    | class_RealVector_Oreal__normed__div__algebra(X2) ) ).

cnf(i_0_4270_087,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_4271_088,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_4272_089,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_4273_090,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_4274_091,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_4275_092,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_4276_093,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_4277_094,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_4278_095,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4279_096,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_4280_097,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_4281_098,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_4282_099,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_4283_100,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_4284_101,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_4285_102,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_4286_103,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_4287_104,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_4288_105,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_4289_106,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | class_RealVector_Oreal__normed__vector(X2) ) ).

cnf(i_0_4290_107,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_4291_108,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_4292_109,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra__1(X1)
    | class_RealVector_Oreal__normed__algebra__1(X2) ) ).

cnf(i_0_4293_110,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_4294_111,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_4295_112,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_4296_113,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_4297,plain,
    hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2),
    inference(equality_inference,[],[2477]) ).

cnf(i_0_4298,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,[],[2502]) ).

cnf(i_0_4299,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
    inference(equality_inference,[],[2504]) ).

cnf(i_0_4300,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | 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),X1) ),
    inference(equality_inference,[],[2524]) ).

cnf(i_0_4301,plain,
    ( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
    | 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(equality_inference,[],[2525]) ).

cnf(i_0_4302,plain,
    ( hAPP(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(equality_inference,[],[2527]) ).

cnf(i_0_4303,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ouminus__class_Ouminus(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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[2541]) ).

cnf(i_0_4304,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | 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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[2543]) ).

cnf(i_0_4305,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_Int_OPls,c_Int_OPls),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_Int_OPls,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[2544]) ).

cnf(i_0_4306,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(equality_inference,[],[2558]) ).

cnf(i_0_4307,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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2),X3),X1)) ),
    inference(equality_inference,[],[2559]) ).

cnf(i_0_4308,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[2676]) ).

cnf(i_0_4309,plain,
    X1 = X1,
    inference(equality_inference,[],[2782]) ).

cnf(i_0_4310,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,[],[2856]) ).

cnf(i_0_4311,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X4),hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X3)) ),
    inference(equality_inference,[],[2912]) ).

cnf(i_0_4312,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))) ),
    inference(equality_inference,[],[2964]) ).

cnf(i_0_4313,plain,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | X2 = X2
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
    inference(equality_inference,[],[3192]) ).

cnf(i_0_4314,plain,
    ( ~ class_Fields_Ofield(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2) = hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2) ),
    inference(equality_inference,[],[3207]) ).

cnf(i_0_4315,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,[],[3228]) ).

cnf(i_0_4316,plain,
    ( X1 = 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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(equality_inference,[],[3303]) ).

cnf(i_0_4317,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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,[],[3341]) ).

cnf(i_0_4318,plain,
    ( X1 = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(equality_inference,[],[3342]) ).

cnf(i_0_4319,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3442]) ).

cnf(i_0_4320,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[3443]) ).

cnf(i_0_4321,plain,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3445]) ).

cnf(i_0_4322,plain,
    X1 = X1,
    inference(equality_inference,[],[3470]) ).

cnf(i_0_4323,plain,
    X1 = X1,
    inference(equality_inference,[],[3471]) ).

cnf(i_0_4324,plain,
    X1 = X1,
    inference(equality_inference,[],[3472]) ).

cnf(i_0_4325,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,[],[3488]) ).

cnf(i_0_4326,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,[],[3490]) ).

cnf(i_0_4327,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
    inference(equality_inference,[],[3519]) ).

cnf(i_0_4328,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) = X3 ),
    inference(equality_inference,[],[3537]) ).

cnf(i_0_4329,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) = X3 ),
    inference(equality_inference,[],[3538]) ).

cnf(i_0_4330,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) ),
    inference(equality_inference,[],[3539]) ).

cnf(i_0_4331,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)),X2) ),
    inference(equality_inference,[],[3540]) ).

cnf(i_0_4332,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(equality_inference,[],[3553]) ).

cnf(i_0_4333,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X2) = X3 ),
    inference(equality_inference,[],[3570]) ).

cnf(i_0_4334,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X2) = X3 ),
    inference(equality_inference,[],[3572]) ).

cnf(i_0_4335,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X2) ),
    inference(equality_inference,[],[3573]) ).

cnf(i_0_4336,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,hAPP(c_Groups_Otimes__class_Otimes(X1,X3),X2),X2) ),
    inference(equality_inference,[],[3575]) ).

cnf(i_0_4337,plain,
    X1 = X1,
    inference(equality_inference,[],[3582]) ).

cnf(i_0_4338,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[3591]) ).

cnf(i_0_4339,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3592]) ).

cnf(i_0_4340,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[3594]) ).

cnf(i_0_4341,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3595]) ).

cnf(i_0_4342,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,[],[3600]) ).

cnf(i_0_4343,plain,
    ( ~ class_Rings_Oidom(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X2)) = hAPP(c_Groups_Otimes__class_Otimes(X1,X2),X2) ),
    inference(equality_inference,[],[3632]) ).

cnf(i_0_4344,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3633]) ).

cnf(i_0_4345,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,[],[3658]) ).

cnf(i_0_4346,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3662]) ).

cnf(i_0_4347,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3663]) ).

cnf(i_0_4348,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3664]) ).

cnf(i_0_4349,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3665]) ).

cnf(i_0_4350,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[3680]) ).

cnf(i_0_4351,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3681]) ).

cnf(i_0_4352,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3682]) ).

cnf(i_0_4353,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3697]) ).

cnf(i_0_4354,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3698]) ).

cnf(i_0_4355,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_inference,[],[3699]) ).

cnf(i_0_4356,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
    inference(equality_inference,[],[3700]) ).

cnf(i_0_4357,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,[],[3713]) ).

cnf(i_0_4358,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[3714]) ).

cnf(i_0_4359,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(equality_inference,[],[3722]) ).

cnf(i_0_4360,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
    inference(equality_inference,[],[3726]) ).

cnf(i_0_4361,plain,
    hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[3727]) ).

cnf(i_0_4362,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(equality_inference,[],[3732]) ).

cnf(i_0_4363,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,[],[3736]) ).

cnf(i_0_4364,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,[],[3737]) ).

cnf(i_0_4365,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,[],[3738]) ).

cnf(i_0_4366,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,[],[3739]) ).

cnf(i_0_4367,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,[],[3749]) ).

cnf(i_0_4368,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3775]) ).

cnf(i_0_4369,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3776]) ).

cnf(i_0_4370,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3777]) ).

cnf(i_0_4371,plain,
    ( X1 = X1
    | ~ class_Rings_Odivision__ring(X2)
    | X1 = c_Groups_Ozero__class_Ozero(X2)
    | X1 = c_Groups_Ozero__class_Ozero(X2) ),
    inference(equality_inference,[],[3778]) ).

cnf(i_0_4372,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3787]) ).

cnf(i_0_4373,plain,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[3793]) ).

cnf(i_0_4374,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3794]) ).

cnf(i_0_4375,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | hAPP(c_Groups_Otimes__class_Otimes(X1,X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3795]) ).

cnf(i_0_4376,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3810]) ).

cnf(i_0_4377,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(equality_inference,[],[3811]) ).

cnf(i_0_4378,plain,
    X1 = X1,
    inference(equality_inference,[],[3814]) ).

cnf(i_0_4379,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
    inference(equality_inference,[],[3815]) ).

cnf(i_0_4380,plain,
    c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(equality_inference,[],[3816]) ).

cnf(i_0_4381,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3831]) ).

cnf(i_0_4382,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3832]) ).

cnf(i_0_4383,plain,
    ( ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3834]) ).

cnf(i_0_4384,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
    inference(equality_inference,[],[3852]) ).

cnf(i_0_4385,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
    inference(equality_inference,[],[3854]) ).

cnf(i_0_4386,plain,
    hAPP(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,[],[3857]) ).

cnf(i_0_4387,plain,
    hAPP(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,[],[3858]) ).

cnf(i_0_4388,plain,
    hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),X1)) = X1,
    inference(equality_inference,[],[3866]) ).

cnf(i_0_4389,plain,
    X1 = X1,
    inference(equality_inference,[],[3867]) ).

cnf(i_0_4390,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3890]) ).

cnf(i_0_4391,plain,
    ( ~ class_Groups_Osgn__if(X1)
    | c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3891]) ).

cnf(i_0_4392,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3892]) ).

cnf(i_0_4393,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3893]) ).

cnf(i_0_4394,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
    inference(equality_inference,[],[3894]) ).

cnf(i_0_4395,plain,
    ( ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3895]) ).

cnf(i_0_4396,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[3896]) ).

cnf(i_0_4397,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3905]) ).

cnf(i_0_4398,plain,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[3906]) ).

cnf(i_0_4399,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[3907]) ).

cnf(i_0_4400,plain,
    hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(equality_inference,[],[3911]) ).

cnf(i_0_4401,plain,
    c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[3914]) ).

cnf(i_0_4402,plain,
    c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(equality_inference,[],[3916]) ).

cnf(i_0_4403,plain,
    hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(equality_inference,[],[3917]) ).

cnf(i_0_4404,plain,
    hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(equality_inference,[],[3918]) ).

cnf(i_0_4405,plain,
    $false,
    inference(scs_inference,[],[i_0_3457,i_0_3523,i_0_3823,i_0_4177,i_0_2798]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW216+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n001.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 06:27:18 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 0.97/5.79  % Version  : CSE_E---1.7
% 0.97/5.79  % Problem  : theBenchmark.p
% 0.97/5.79  % SZS status Theorem for theBenchmark.p
% 0.97/5.79  % SZS output start CNFRefutation
% See solution above
% 5.23/5.93  % Total time : 5.449s
%------------------------------------------------------------------------------