CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW229+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 : n020.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 05:30:36 PM UTC 2026

% Result   : Theorem 5.95s 5.80s
% Output   : CNFRefutation 6.16s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1479)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_th0,axiom,
    ! [X42,X18,X85,X17] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X85)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X42)),X85)
       => ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X85),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X42)),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th0) ).

fof(fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X74] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X74)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [X70,X15] :
      ( ( 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,X15))
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X70)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X15))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) )
      & ( ~ 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,X15))
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X70)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X15))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_div__if,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).

fof(fact_le__SucE,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Nat_OSuc(X30))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
       => X12 = c_Nat_OSuc(X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_not__less__eq__eq,axiom,
    ! [X21,X42] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_not__less__eq,axiom,
    ! [X21,X42] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X42,X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X42))
      <=> X21 = X42 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [X12,X30] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X12)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Nat_OSuc(X12))
       => X12 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucE,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Nat_OSuc(X30))
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
       => X12 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
   => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).

fof(fact_Bit0__def,axiom,
    ! [X26] : c_Int_OBit0(X26) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X30] : c_Nat_OSuc(X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_Bit1__def,axiom,
    ! [X26] : c_Int_OBit1(X26) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

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_Suc__div__eq__add3__div__number__of,axiom,
    ! [X70,X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X12))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X12),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [X30,X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X12))),X30) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X12),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [X30,X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X30)))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
    ? [X51] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51)
      & ! [X47] :
          ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,v_z____)))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,v_z____)),X51) )
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X47),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

fof(fact_d_I2_J,axiom,
    ! [X47] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,v_z____)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,v_z____)),v_d____) )
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X47),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_d_I2_J) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X38,X7] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X7)
        & class_Int_Onumber__ring(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X38,c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(X12)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,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_div2__Suc__Suc) ).

fof(fact_real__average__minus__first,axiom,
    ! [X5,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X5),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X6),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__average__minus__first) ).

fof(fact_real__average__minus__second,axiom,
    ! [X6,X5] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,X6),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X6) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X6),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__average__minus__second) ).

fof(fact_th1,axiom,
    ! [X69] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X69,v_z____)),v_d____)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X69),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_th1) ).

fof(fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096,axiom,
    ? [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,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_Suc__n__div__2__gt__zero) ).

fof(fact_real__gt__half__sum,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X10)
     => 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,X10),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).

fof(fact_real__less__half__sum,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,X10)
     => 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,X10),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_half__gt__zero,axiom,
    ! [X13,X7] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X7)
        & class_Int_Onumber__ring(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X13)
       => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X13,c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).

fof(fact_div__2__gt__zero,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,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_div__2__gt__zero) ).

fof(fact_half,axiom,
    ! [X7] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X7)
        & class_Int_Onumber__ring(X7) )
     => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [X30] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X30))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

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_less__2__cases,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
     => ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__2__cases) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [X30] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X30) = c_Nat_OSuc(c_Nat_OSuc(X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [X30] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_add__self__div__2,axiom,
    ! [X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X12),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__self__div__2) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X30)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X12),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_AALL_An_O_Acmod_A_Ig_An_J_A_060_061_Ar_059_AALL_An_O_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X65] :
        ( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X65,X4)),v_r)
       => ~ ! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X65,X4))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_AALL_An_O_Acmod_A_Ig_An_J_A_060_061_Ar_059_AALL_An_O_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096,axiom,
    ? [X64] :
    ! [X3] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X64,X3)),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X64,X3))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).

fof(fact_th,axiom,
    ! [X4] :
    ? [X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th) ).

fof(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096,axiom,
    ! [X21] :
    ? [X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X21))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).

fof(fact_g_I2_J,axiom,
    ! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X4))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I2_J) ).

fof(fact_diff__special_I2_J,axiom,
    ! [X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Oone__class_Oone(X7)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).

fof(fact_lemma__NBseq__def2,axiom,
    ! [X54,X41] :
      ( class_RealVector_Oreal__normed__vector(X41)
     => ( ? [X63] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
            & ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X4)),X63) )
      <=> ? [X35] :
          ! [X4] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).

fof(fact_lemma__NBseq__def,axiom,
    ! [X54,X41] :
      ( class_RealVector_Oreal__normed__vector(X41)
     => ( ? [X63] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
            & ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X4)),X63) )
      <=> ? [X35] :
          ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).

fof(fact_one__add__one__is__two,axiom,
    ! [X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7)) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OBit1(X66))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X72),c_Int_OBit1(X71))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OBit1(X66))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X72),c_Int_OBit1(X71))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [X40,X26] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X26),c_Int_OBit1(X40)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [X40,X26] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X26),c_Int_OBit0(X40)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X40,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X26),c_Int_OBit0(X40)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X40,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X26),c_Int_OBit1(X40)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_diff__special_I1_J,axiom,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_add__special_I3_J,axiom,
    ! [X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Oone__class_Oone(X7)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,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,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OBit0(X66))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X72),c_Int_OBit0(X71))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X72),c_Int_OBit0(X71))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OBit0(X66))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X72),c_Int_OBit1(X71))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OBit1(X66))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OBit1(X66))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X72),c_Int_OBit1(X71))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_divide__Numeral1,axiom,
    ! [X11,X7] :
      ( ( class_Fields_Ofield(X7)
        & class_Int_Onumber__ring(X7) )
     => c_Rings_Oinverse__class_Odivide(X7,X11,c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(c_Int_OPls))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_divide__numeral__1,axiom,
    ! [X6,X7] :
      ( ( class_Fields_Ofield(X7)
        & class_Int_Onumber__ring(X7) )
     => c_Rings_Oinverse__class_Odivide(X7,X6,c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(c_Int_OPls))) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [X12,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26)),X12) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X25),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [X12,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),c_Nat_OSuc(X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_nat__lt__two__imp__zero__or__one,axiom,
    ! [X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X11 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

fof(fact_less__special_I4_J,axiom,
    ! [X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Groups_Oone__class_Oone(X7))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,c_Int_OBit1(c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_le__special_I4_J,axiom,
    ! [X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Groups_Oone__class_Oone(X7))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,c_Int_OBit1(c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [X37,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [X37,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [X18,X17,X50] :
      ( hBOOL(hAPP(X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18)))
    <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
            & ~ hBOOL(hAPP(X50,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X51] :
              ( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X51)
              & ~ hBOOL(hAPP(X50,X51)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X69] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X69),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_Suc__diff__diff,axiom,
    ! [X26,X30,X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X12),X30),c_Nat_OSuc(X26)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X28))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X28))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X28),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [X15,X70] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X70)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X15))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_number__of__Bit1,axiom,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(X15)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Int_Onumber__class_Onumber__of(X7,X15)),c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_le__div__geq,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).

fof(fact_subseq__Suc__iff,axiom,
    ! [X2] :
      ( c_SEQ_Osubseq(X2)
    <=> ! [X4] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X4),hAPP(X2,c_Nat_OSuc(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).

fof(fact_calculation,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
   => ? [X33] :
      ! [X47] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X47),v_r)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X47))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [X40,X26] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X26),c_Int_OBit0(X40)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X40,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X26),c_Int_OBit0(X40)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X66,X28] :
      ( c_Int_OBit1(X28) = c_Int_OBit1(X66)
    <=> X28 = X66 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_Suc__less__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X42),c_Nat_OSuc(X21))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X12),c_Nat_OSuc(X30))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_Suc__le__mono,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),c_Nat_OSuc(X42))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_Suc__pred,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

fof(fact_diff__Suc__less,axiom,
    ! [X24,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Nat_OSuc(X24)),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OBit0(X66))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X72),c_Int_OBit0(X71))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OBit0(X66))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X71,X72] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X72),c_Int_OBit0(X71))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_add__eq__if,axiom,
    ! [X30,X12] :
      ( ( X12 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30) = X30 )
      & ( X12 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [X40] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X40)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_Suc__diff__le,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X12),X30) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_number__of__Bit0,axiom,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit0(X15)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),c_Int_Onumber__class_Onumber__of(X7,X15)),c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_less__add__Suc1,axiom,
    ! [X12,X24] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X12,X24] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_le__Suc__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,c_Nat_OSuc(X21))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
        | X42 = c_Nat_OSuc(X21) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_Suc__mono,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X12),c_Nat_OSuc(X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [X69,X73,X7] :
      ( ( class_Int_Onumber(X7)
        & class_Orderings_Olinorder(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Int_Onumber__class_Onumber__of(X7,X73),c_Int_Onumber__class_Onumber__of(X7,X69))
      <=> ~ c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X69),c_Int_Onumber__class_Onumber__of(X7,X73)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_expand__Suc,axiom,
    ! [X70] :
      ( 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,X70))
     => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,c_Nat_OSuc(X21))
    <=> ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X57] :
            ( X42 = c_Nat_OSuc(X57)
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X42))
      <=> X21 = X42 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oone__class_Oone(X7) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X40,X26] : c_Int_OBit0(X26) != c_Int_OBit1(X40),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X40,X26] : c_Int_OBit1(X26) != c_Int_OBit0(X40),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_less__trans__Suc,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X26)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X24),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_abs__add__one__not__less__self,axiom,
    ! [X11] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [X30,X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X12),c_Nat_OSuc(X30)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [X30,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X12),X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Nat_OSuc(X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [X30,X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Nat_OSuc(X30)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_add__Suc,axiom,
    ! [X30,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X12),X30) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_add__Suc__right,axiom,
    ! [X30,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Nat_OSuc(X30)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_add__nat__number__of,axiom,
    ! [X84,X70] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X84)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_less__Suc__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,c_Nat_OSuc(X21))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
        | X42 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Suc__lessD,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X12),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X12),X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__le__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X42),X21)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__leD,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X12),X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,c_Nat_OSuc(X21))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X69] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X69),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
    <=> ? [X45] : X21 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_Suc__lessI,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => ( c_Nat_OSuc(X12) != X30
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X12),X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_add__leE,axiom,
    ! [X30,X26,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),X30)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_real__of__nat__Suc__gt__zero,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).

fof(fact_one__is__add,axiom,
    ! [X21,X42] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X21)
    <=> ( ( X42 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X21 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(fact_add__is__1,axiom,
    ! [X21,X42] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X42 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X21 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X28))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X28))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X28) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X28),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_less__fun__def,axiom,
    ! [X1,X2,X7,X41] :
      ( class_Orderings_Oord(X41)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X7,X41),X2,X1)
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X2,X1)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_not__square__less__zero,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__ring(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X6),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_less__Suc0,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_diff__less__Suc,axiom,
    ! [X30,X12] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),c_Nat_OSuc(X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_le__nat__number__of,axiom,
    ! [X83,X73] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X73),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X83))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,X83)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X26] : c_Int_OBit1(X26) != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X40] : c_Int_OPls != c_Int_OBit1(X40),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_Suc__diff__1,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_Suc__pred_H,axiom,
    ! [X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => X30 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_Suc__leI,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X12),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_less__SucI,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Nat_OSuc(X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Nat_OSuc(X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_le__SucI,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Nat_OSuc(X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_not__add__less1,axiom,
    ! [X25,X24] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X24,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_abs__number__of,axiom,
    ! [X11,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( ( c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X11),c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) = c_Groups_Ouminus__class_Ouminus(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) )
        & ( ~ c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X11),c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) = c_Int_Onumber__class_Onumber__of(X7,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__number__of) ).

fof(fact_minus__Bit0,axiom,
    ! [X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X26)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_add__diff__inverse,axiom,
    ! [X30,X12] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_less__le__not__le,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
          & ~ c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_real__of__nat__Suc,axiom,
    ! [X30] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X30)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
       => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_xt1_I9_J,axiom,
    ! [X6,X5,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X6)
       => ~ c_Orderings_Oord__class_Oless(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless(X7,X37,X36)
          | X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_leD,axiom,
    ! [X11,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => ~ c_Orderings_Oord__class_Oless(X7,X11,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_linorder__not__le,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
      <=> c_Orderings_Oord__class_Oless(X7,X37,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_order__less__not__sym,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__asym_H,axiom,
    ! [X5,X6,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ~ c_Orderings_Oord__class_Oless(X7,X5,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__asym,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_Suc__inject,axiom,
    ! [X10,X11] :
      ( c_Nat_OSuc(X11) = c_Nat_OSuc(X10)
     => X11 = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(fact_nat_Oinject,axiom,
    ! [X60,X61] :
      ( c_Nat_OSuc(X61) = c_Nat_OSuc(X60)
    <=> X61 = X60 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

fof(fact_sgn__poly__def,axiom,
    ! [X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
         => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) )
        & ( X11 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
         => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X11)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7)) )
            & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X11)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).

fof(fact_abs__poly__def,axiom,
    ! [X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))
         => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X11) )
        & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))
         => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X11) = X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).

fof(fact_div__1,axiom,
    ! [X12] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [X66,X28] :
      ( c_Int_OBit0(X28) = c_Int_OBit0(X66)
    <=> X28 = X66 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_diff__Suc__1,axiom,
    ! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_zero__less__Suc,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_lessI,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Nat_OSuc(X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
    <=> ? [X52] : X21 = c_Nat_OSuc(X52) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_abs__not__less__zero,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_norm__not__less__zero,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

fof(fact_abs__if,axiom,
    ! [X6,X7] :
      ( class_Groups_Oabs__if(X7)
     => ( ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) )
        & ( ~ c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,X6) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_sgn__if,axiom,
    ! [X11,X7] :
      ( class_Groups_Osgn__if(X7)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Ozero__class_Ozero(X7) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X7)
         => ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
             => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Oone__class_Oone(X7) )
            & ( ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
             => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_not__real__of__nat__less__zero,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X10,X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( X11 != X10
       => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X36,X37,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X37,X36)
       => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( X11 != X10
       => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__cases,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ( X11 != X10
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_not__leE,axiom,
    ! [X11,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => c_Orderings_Oord__class_Oless(X7,X11,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_linorder__le__cases,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_zabs__def,axiom,
    ! [X24] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Groups_Oabs__class_Oabs(tc_Int_Oint,X24) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Groups_Oabs__class_Oabs(tc_Int_Oint,X24) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

fof(fact_real__abs__def,axiom,
    ! [X13] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13) = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).

fof(fact_abs__real__def,axiom,
    ! [X6] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).

fof(fact_not__one__less__zero,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_not__one__le__zero,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X30] : c_Nat_OSuc(X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

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

fof(fact_zsgn__def,axiom,
    ! [X24] :
      ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = 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_sgn__real__def,axiom,
    ! [X6] :
      ( ( X6 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X6 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = 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_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_order__less__irrefl,axiom,
    ! [X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,X11,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_Suc__not__Zero,axiom,
    ! [X12] : c_Nat_OSuc(X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X58] : c_Nat_OSuc(X58) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X12] : c_Nat_OSuc(X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X59] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X30] : c_Nat_OSuc(X30) != X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X30] : X30 != c_Nat_OSuc(X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_not__less0,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_less__zeroE,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,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,
    ! [X66] :
      ( c_Int_OPls = c_Int_OBit0(X66)
    <=> c_Int_OPls = X66 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X28] :
      ( c_Int_OBit0(X28) = c_Int_OPls
    <=> X28 = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_less__not__refl,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_thc1,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_thc1) ).

fof(fact_th2,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_th2) ).

fof(fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

fof(fact__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

fof(fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

fof(fact_th00,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th00) ).

fof(fact_lemmaCauchy,axiom,
    ! [X54,X55,X7,X41] :
      ( ( class_RealVector_Oreal__normed__vector(X41)
        & class_Orderings_Oord(X7) )
     => ( ! [X4] :
            ( c_Orderings_Oord__class_Oless__eq(X7,X55,X4)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,c_Groups_Ominus__class_Ominus(X41,hAPP(X54,X55),hAPP(X54,X4))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
       => ! [X4] :
            ( c_Orderings_Oord__class_Oless__eq(X7,X55,X4)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X41,hAPP(X54,X55)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).

fof(fact_N2,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_N2) ).

fof(fact_e2,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,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_e2) ).

fof(fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096) ).

fof(fact_th32,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th32) ).

fof(fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X7,X41] :
      ( class_Orderings_Oord(X41)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X2,X1)
      <=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X41,hAPP(X2,X3),hAPP(X1,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_abs__sum__triangle__ineq,axiom,
    ! [X12,X40,X10,X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X10),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X40),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X40))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).

fof(fact_numeral__3__eq__3,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).

fof(fact_mult_Oprod__diff__prod,axiom,
    ! [X5,X6,X10,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10),c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X11,X6),c_Groups_Ominus__class_Ominus(X7,X10,X5)),c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X11,X6),X5)),c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ominus__class_Ominus(X7,X10,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Oplus__class_Oplus(X7,X9,X8))),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X9)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X5,X8)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_norm__diff__triangle__ineq,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Oplus__class_Oplus(X7,X9,X8))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X9)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X5,X8)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).

fof(fact_DERIV__inverse__lemma,axiom,
    ! [X86,X5,X6,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ominus__class_Ominus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5)),X86) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5),X86)),c_Rings_Oinverse__class_Oinverse(X7,X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).

fof(fact_poly__cont,axiom,
    ! [X23,X14,X20] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
     => ? [X51] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X51)
          & ! [X47] :
              ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,X14)))
                & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X47,X14)),X51) )
             => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X23),X47),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X23),X14))),X20) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).

fof(fact_numeral__2__eq__2,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).

fof(fact_semiring__norm_I115_J,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

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__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096,axiom,
    ! [X37] :
      ( ? [X33] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)))),X37) )
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).

fof(fact_ath2,axiom,
    ! [X12,X9,X5,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X5)),X9)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5,X12)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X12)),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath2) ).

fof(fact_unimodular__reduce__norm,axiom,
    ! [X14] :
      ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X14,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X14,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).

fof(fact_Deriv_Oinverse__diff__inverse,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Ominus__class_Ominus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5)) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Groups_Ominus__class_Ominus(X7,X6,X5)),c_Rings_Oinverse__class_Oinverse(X7,X5))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).

fof(fact_real__of__nat__div3,axiom,
    ! [X11,X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_RealDef_Oreal(tc_Nat_Onat,X11)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X11))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div3) ).

fof(fact_real__of__nat__div2,axiom,
    ! [X11,X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_RealDef_Oreal(tc_Nat_Onat,X11)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div2) ).

fof(fact_mult__diff__mult,axiom,
    ! [X5,X6,X10,X11,X7] :
      ( class_Rings_Oring(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10),c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X11,c_Groups_Ominus__class_Ominus(X7,X10,X5)),c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X11,X6),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).

fof(fact_eq__add__iff1,axiom,
    ! [X19,X18,X16,X88,X17,X7] :
      ( class_Rings_Oring(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X17,X88),X16) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X18,X88),X19)
      <=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X17,X18),X88),X16) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [X19,X18,X16,X88,X17,X7] :
      ( class_Rings_Oring(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X17,X88),X16) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X18,X88),X19)
      <=> X16 = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X18,X17),X88),X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_combine__common__factor,axiom,
    ! [X9,X5,X20,X6,X7] :
      ( class_Rings_Osemiring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X20),c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X5,X20),X9)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X20),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X19,X16,X18,X17,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( ( X17 != X18
          & X16 != X19 )
      <=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X17,X16),c_Groups_Otimes__class_Otimes(X7,X18,X19)) != c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X17,X19),c_Groups_Otimes__class_Otimes(X7,X18,X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X77,X36,X37,X69,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X69,X37),c_Groups_Otimes__class_Otimes(X7,X36,X77)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X69,X77),c_Groups_Otimes__class_Otimes(X7,X36,X37))
      <=> ( X69 = X36
          | X37 = X77 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_abs__diff__less__iff,axiom,
    ! [X38,X17,X36,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X36,X17)),X38)
      <=> ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X17,X38),X36)
          & c_Orderings_Oord__class_Oless(X7,X36,c_Groups_Oplus__class_Oplus(X7,X17,X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5))),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_norm__triangle__ineq3,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5))),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).

fof(fact_gt__half__sum,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7))),X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_less__half__sum,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => c_Orderings_Oord__class_Oless(X7,X6,c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_th000_I3_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th000_I3_J) ).

fof(fact_complex__mod__triangle__ineq2,axiom,
    ! [X6,X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X5,X6)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).

fof(fact_complex__mod__triangle__sub,axiom,
    ! [X14,X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X15),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X15,X14)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).

fof(fact_nat__diff__split,axiom,
    ! [X18,X17,X50] :
      ( hBOOL(hAPP(X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
         => hBOOL(hAPP(X50,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X51] :
            ( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X51)
           => hBOOL(hAPP(X50,X51)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(fact_fz_I2_J,axiom,
    ! [X34] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X34)
     => ? [X35] :
        ! [X4] :
          ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X4)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X4)),v_z____)),X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I2_J) ).

fof(fact_odd__less__0,axiom,
    ! [X77] :
      ( 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),X77),X77),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X77,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(fact_norm__mult__less,axiom,
    ! [X39,X10,X13,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),X13)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X10),X39)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X39)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).

fof(fact_norm__add__less,axiom,
    ! [X39,X10,X13,X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),X13)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X10),X39)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X11,X10)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X39)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).

fof(fact_frac__less2,axiom,
    ! [X14,X15,X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
         => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X15)
           => ( c_Orderings_Oord__class_Oless(X7,X15,X14)
             => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X14),c_Rings_Oinverse__class_Odivide(X7,X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_frac__less,axiom,
    ! [X14,X15,X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
         => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X15)
           => ( c_Orderings_Oord__class_Oless__eq(X7,X15,X14)
             => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X14),c_Rings_Oinverse__class_Odivide(X7,X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_mult__mono_H,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Rings_Oordered__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,X8)
         => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
           => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
             => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X8)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Rings_Oordered__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,X8)
         => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5)
           => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
             => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X8)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_frac__le,axiom,
    ! [X14,X15,X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
         => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X15)
           => ( c_Orderings_Oord__class_Oless__eq(X7,X15,X14)
             => c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X14),c_Rings_Oinverse__class_Odivide(X7,X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_less__diff__iff,axiom,
    ! [X21,X42,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X42)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X21)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X28))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).

fof(fact_le__diff__iff,axiom,
    ! [X21,X42,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X42)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X21)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X28))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).

fof(fact_add__number__of__diff2,axiom,
    ! [X15,X9,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Ominus__class_Ominus(X7,X9,c_Int_Onumber__class_Onumber__of(X7,X15))) = c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15))),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_ath,axiom,
    ! [X20,X11,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X20))
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X12)),X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X18,X17,X16,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X16)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X16,X17),c_Groups_Otimes__class_Otimes(X7,X16,X18))
        <=> c_Orderings_Oord__class_Oless(X7,X17,X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X18,X17,X16,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X16,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X16,X17),c_Groups_Otimes__class_Otimes(X7,X16,X18))
        <=> c_Orderings_Oord__class_Oless(X7,X18,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_inverse__add,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Ofield(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Oplus__class_Oplus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Rings_Oinverse__class_Oinverse(X7,X6)),c_Rings_Oinverse__class_Oinverse(X7,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).

fof(fact_division__ring__inverse__diff,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Ominus__class_Ominus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Groups_Ominus__class_Ominus(X7,X5,X6)),c_Rings_Oinverse__class_Oinverse(X7,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).

fof(fact_division__ring__inverse__add,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Oplus__class_Oplus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Groups_Oplus__class_Oplus(X7,X6,X5)),c_Rings_Oinverse__class_Oinverse(X7,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [X70,X5,X6,X41] :
      ( ( class_Int_Onumber(X41)
        & class_Rings_Oring(X41) )
     => c_Groups_Otimes__class_Otimes(X41,c_Groups_Ominus__class_Ominus(X41,X6,X5),c_Int_Onumber__class_Onumber__of(X41,X70)) = c_Groups_Ominus__class_Ominus(X41,c_Groups_Otimes__class_Otimes(X41,X6,c_Int_Onumber__class_Onumber__of(X41,X70)),c_Groups_Otimes__class_Otimes(X41,X5,c_Int_Onumber__class_Onumber__of(X41,X70))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X70,X5,X6,X41] :
      ( ( class_Int_Onumber(X41)
        & class_Rings_Osemiring(X41) )
     => c_Groups_Otimes__class_Otimes(X41,c_Groups_Oplus__class_Oplus(X41,X6,X5),c_Int_Onumber__class_Onumber__of(X41,X70)) = c_Groups_Oplus__class_Oplus(X41,c_Groups_Otimes__class_Otimes(X41,X6,c_Int_Onumber__class_Onumber__of(X41,X70)),c_Groups_Otimes__class_Otimes(X41,X5,c_Int_Onumber__class_Onumber__of(X41,X70))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [X9,X5,X70,X41] :
      ( ( class_Int_Onumber(X41)
        & class_Rings_Oring(X41) )
     => c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),c_Groups_Ominus__class_Ominus(X41,X5,X9)) = c_Groups_Ominus__class_Ominus(X41,c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),X5),c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X9,X5,X70,X41] :
      ( ( class_Int_Onumber(X41)
        & class_Rings_Osemiring(X41) )
     => c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),c_Groups_Oplus__class_Oplus(X41,X5,X9)) = c_Groups_Oplus__class_Oplus(X41,c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),X5),c_Groups_Otimes__class_Otimes(X41,c_Int_Onumber__class_Onumber__of(X41,X70),X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096,axiom,
    ( ? [X33] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
  <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).

fof(fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
    ~ ! [X49] :
        ~ ! [X4] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49,X4)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X4)),v_z____)),v_d____) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

fof(fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096,axiom,
    ? [X35] :
    ! [X4] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X4)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X4)),v_z____)),v_d____) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096) ).

fof(fact_N1,axiom,
    ! [X4] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X4)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X4)),v_z____)),v_d____) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_N1) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X18,X17,X16,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X16,X17),c_Groups_Otimes__class_Otimes(X7,X16,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X16)
            & c_Orderings_Oord__class_Oless(X7,X17,X18) )
          | ( c_Orderings_Oord__class_Oless(X7,X16,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless(X7,X18,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X18,X16,X17,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X17,X16),c_Groups_Otimes__class_Otimes(X7,X18,X16))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X16)
            & c_Orderings_Oord__class_Oless(X7,X17,X18) )
          | ( c_Orderings_Oord__class_Oless(X7,X16,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless(X7,X18,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_Deriv_Oadd__diff__add,axiom,
    ! [X8,X5,X9,X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5),c_Groups_Ominus__class_Ominus(X7,X9,X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Oplus__class_Oplus(X7,X9,X8)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_mult__number__of__left,axiom,
    ! [X14,X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(X7,X15),X14)) = c_Groups_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(X7,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X70,X15)),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_add__number__of__diff1,axiom,
    ! [X9,X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Ominus__class_Ominus(X7,c_Int_Onumber__class_Onumber__of(X7,X15),X9)) = c_Groups_Ominus__class_Ominus(X7,c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X15)),X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_add__number__of__left,axiom,
    ! [X14,X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X15),X14)) = c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X15)),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X8,X9,X5,X6,X13,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( X13 != c_Groups_Ozero__class_Ozero(X7)
       => ( ( X6 = X5
            & X9 != X8 )
         => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Otimes__class_Otimes(X7,X13,X9)) != c_Groups_Oplus__class_Oplus(X7,X5,c_Groups_Otimes__class_Otimes(X7,X13,X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_zdiv__mono2,axiom,
    ! [X5,X76,X6] :
      ( 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),X76)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X5)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X76)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [X5,X76,X6] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X76)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X5)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X76),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_s1,axiom,
    ! [X37] :
      ( ? [X33] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),X37) )
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5)),c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X5,X6))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5)),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_natceiling__eq,axiom,
    ! [X11,X30] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),X11)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
       => c_RComplete_Onatceiling(X11) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).

fof(fact_norm__triangle__ineq2,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).

fof(fact_norm__diff__ineq,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5)),c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).

fof(fact_norm__mult__ineq,axiom,
    ! [X10,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),c_RealVector_Onorm__class_Onorm(X7,X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).

fof(fact_norm__triangle__ineq4,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).

fof(fact_norm__triangle__ineq,axiom,
    ! [X10,X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oplus__class_Oplus(X7,X11,X10)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),c_RealVector_Onorm__class_Onorm(X7,X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).

fof(fact_poly__diff,axiom,
    ! [X11,X22,X23,X7] :
      ( class_Rings_Ocomm__ring(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X23,X22)),X11) = c_Groups_Ominus__class_Ominus(X7,hAPP(c_Polynomial_Opoly(X7,X23),X11),hAPP(c_Polynomial_Opoly(X7,X22),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).

fof(fact_poly__add,axiom,
    ! [X11,X22,X23,X7] :
      ( class_Rings_Ocomm__semiring__0(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X23,X22)),X11) = c_Groups_Oplus__class_Oplus(X7,hAPP(c_Polynomial_Opoly(X7,X23),X11),hAPP(c_Polynomial_Opoly(X7,X22),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).

fof(fact_le__diff__conv2,axiom,
    ! [X27,X29,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X29)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X28),X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X5,X9,X6,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X9))
       => c_Orderings_Oord__class_Oless(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X18,X16,X17,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X17,X16),c_Groups_Oplus__class_Oplus(X7,X18,X16))
      <=> c_Orderings_Oord__class_Oless(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X5,X6,X9,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X9,X6),c_Groups_Oplus__class_Oplus(X7,X9,X5))
       => c_Orderings_Oord__class_Oless(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X18,X17,X16,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X16,X17),c_Groups_Oplus__class_Oplus(X7,X16,X18))
      <=> c_Orderings_Oord__class_Oless(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X18,X16,X17,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X17,X16),c_Groups_Oplus__class_Oplus(X7,X18,X16))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X5,X9,X6,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X9))
       => c_Orderings_Oord__class_Oless__eq(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X18,X17,X16,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X16,X17),c_Groups_Oplus__class_Oplus(X7,X16,X18))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X5,X6,X9,X7] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X9,X6),c_Groups_Oplus__class_Oplus(X7,X9,X5))
       => c_Orderings_Oord__class_Oless__eq(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [X30,X12,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X12)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X30)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X26),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X26)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_real__of__nat__div4,axiom,
    ! [X11,X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X11)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_RealDef_Oreal(tc_Nat_Onat,X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div4) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X21,X42,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X42),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X21,X42,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X42),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Olinordered__comm__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X9),c_Rings_Oinverse__class_Odivide(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Oordered__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Oordered__comm__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Oordered__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_divide__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X9),c_Rings_Oinverse__class_Odivide(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X6)
       => ( c_Orderings_Oord__class_Oless(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X6)
       => ( c_Orderings_Oord__class_Oless(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X6)
       => ( c_Orderings_Oord__class_Oless(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X9),c_Rings_Oinverse__class_Odivide(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Rings_Oordered__ring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Rings_Oordered__ring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X5,X9),c_Rings_Oinverse__class_Odivide(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_natfloor__eq,axiom,
    ! [X11,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
       => c_RComplete_Onatfloor(X11) = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).

fof(fact_le__add__diff,axiom,
    ! [X12,X30,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X12),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(fact_add__strict__mono,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,X9,X8)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,X9,X8)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,X8)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_add__mono,axiom,
    ! [X8,X9,X5,X6,X7] :
      ( class_Groups_Oordered__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X9,X8)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X8)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X36,X36),c_Groups_Otimes__class_Otimes(X7,X37,X37)) = c_Groups_Ozero__class_Ozero(X7)
      <=> ( X36 = c_Groups_Ozero__class_Ozero(X7)
          & X37 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X5,X12,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X12),c_Groups_Otimes__class_Otimes(X7,X5,X12)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_mult__left_Odiff,axiom,
    ! [X62,X10,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X11,X10),X62) = c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X62),c_Groups_Otimes__class_Otimes(X7,X10,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).

fof(fact_mult_Odiff__left,axiom,
    ! [X5,X75,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ominus__class_Ominus(X7,X6,X75),X5) = c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Otimes__class_Otimes(X7,X75,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Ocomm__semiring(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_mult_Oadd__left,axiom,
    ! [X5,X75,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X75),X5) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Otimes__class_Otimes(X7,X75,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

fof(fact_mult__left_Oadd,axiom,
    ! [X62,X10,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X11,X10),X62) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X62),c_Groups_Otimes__class_Otimes(X7,X10,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_diff__divide__distrib,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5),X9) = c_Groups_Ominus__class_Ominus(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X9),c_Rings_Oinverse__class_Odivide(X7,X5,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_divide_Odiff,axiom,
    ! [X62,X10,X11,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ominus__class_Ominus(X7,X11,X10),X62) = c_Groups_Ominus__class_Ominus(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X62),c_Rings_Oinverse__class_Odivide(X7,X10,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).

fof(fact_add__divide__distrib,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X9),c_Rings_Oinverse__class_Odivide(X7,X5,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_divide_Oadd,axiom,
    ! [X62,X10,X11,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oplus__class_Oplus(X7,X11,X10),X62) = c_Groups_Oplus__class_Oplus(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X62),c_Rings_Oinverse__class_Odivide(X7,X10,X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).

fof(fact_mult__right_Odiff,axiom,
    ! [X10,X11,X87,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X87,c_Groups_Ominus__class_Ominus(X7,X11,X10)) = c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X87,X11),c_Groups_Otimes__class_Otimes(X7,X87,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).

fof(fact_mult_Odiff__right,axiom,
    ! [X76,X5,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ominus__class_Ominus(X7,X5,X76)) = c_Groups_Ominus__class_Ominus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Otimes__class_Otimes(X7,X6,X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).

fof(fact_mult_Oadd__right,axiom,
    ! [X76,X5,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X76)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Otimes__class_Otimes(X7,X6,X76)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

fof(fact_mult__right_Oadd,axiom,
    ! [X10,X11,X87,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X87,c_Groups_Oplus__class_Oplus(X7,X11,X10)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X87,X11),c_Groups_Otimes__class_Otimes(X7,X87,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X14,X10,X11,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,X11,c_Groups_Oplus__class_Oplus(X7,X10,X14)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10),c_Groups_Otimes__class_Otimes(X7,X11,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_zdiv__mono1,axiom,
    ! [X5,X75,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,X75)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X75,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__le__mono2,axiom,
    ! [X26,X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X30),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X26,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [X5,X75,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,X75)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X75,X5),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X14,X81,X15,X82] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,X14)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X82,X81),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_diff__less__mono,axiom,
    ! [X9,X5,X6] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X6)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__less__mono2,axiom,
    ! [X40,X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X40)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_add__less__mono,axiom,
    ! [X40,X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X40)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X40)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_add__le__mono,axiom,
    ! [X40,X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X40)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X40)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X6,X5,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X5,X6))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X18))
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,X17)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_nat__less__real__le,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).

fof(fact_nat__le__real__less,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X42)
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X42),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).

fof(fact_real__add__mult__distrib,axiom,
    ! [X15,X79,X80] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X80,X79),X15) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X80,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X79,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

fof(fact_reals__Archimedean6,axiom,
    ! [X13] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
     => ? [X4] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X13)
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_RealDef_Oreal(tc_Nat_Onat,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).

fof(fact_less__diff__conv,axiom,
    ! [X28,X29,X27] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X28),X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(fact_le__diff__conv,axiom,
    ! [X27,X28,X29] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X28),X27)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(fact_add__diff__assoc2,axiom,
    ! [X24,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26),X24) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [X24,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X26) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_diff__add__assoc,axiom,
    ! [X24,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X26) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_diff__diff__right,axiom,
    ! [X24,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X26),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(fact_add__diff__assoc,axiom,
    ! [X24,X25,X26] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X26)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X18))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X17,X18))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
    ? [X53] :
    ! [X32] :
      ( ? [X3] :
          ( ? [X33] :
              ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
              & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X32,X3) )
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X32,X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).

fof(fact_s,axiom,
    ! [X32] :
      ( ? [X3] :
          ( ? [X33] :
              ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
              & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X32,X3) )
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X32,v_s____) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [X27,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X28)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X28))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X17,X18),c_Groups_Ozero__class_Ozero(X7))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless(X7,X18,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X18) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X17,X18),c_Groups_Ozero__class_Ozero(X7))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless__eq(X7,X18,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X18) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X17,X18),c_Groups_Ozero__class_Ozero(X7))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless__eq(X7,X18,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X18) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X17,X18))
      <=> ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X18) )
          | ( c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless(X7,X18,c_Groups_Ozero__class_Ozero(X7)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X17,X18))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X18) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,X18,c_Groups_Ozero__class_Ozero(X7)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X17,X18))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17)
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X18) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,X18,c_Groups_Ozero__class_Ozero(X7)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_natfloor__div__nat,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
       => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X10))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X11),X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__div__nat) ).

fof(fact_numeral__1__eq__Suc__0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_Bseq__inverse__lemma,axiom,
    ! [X11,X13,X7] :
      ( class_RealVector_Oreal__normed__div__algebra(X7)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_RealVector_Onorm__class_Onorm(X7,X11))
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
         => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,c_Rings_Oinverse__class_Oinverse(X7,X11)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).

fof(fact_mult__neg__pos,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X5,X6),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_divide__neg__pos,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X10)
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless(X7,X10,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__cancel__semiring(X7)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
            & c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7)) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5) ) )
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__cancel__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__cancel__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__cancel__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Otimes__class_Otimes(X7,X5,X6),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless(X7,X10,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X10)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_add__neg__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_less__1__mult,axiom,
    ! [X30,X12,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X12)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),X30)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Otimes__class_Otimes(X7,X12,X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_mult__pos__pos,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__semiring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_divide__pos__pos,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X10)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__ring(X7)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
            & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5) )
          | ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
            & c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7)) ) )
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__cancel__semiring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X11)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X10)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X5)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_mult__neg__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__ring__strict(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_divide__neg__neg,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,X10,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oordered__ring(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,c_Groups_Ozero__class_Ozero(X7))
       => ( c_Orderings_Oord__class_Oless(X7,X10,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_add__gr__0,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X21))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
        | 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_add__gr__0) ).

fof(fact_real__0__le__divide__iff,axiom,
    ! [X37,X36] :
      ( 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,X36,X37))
    <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,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),X37) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
          | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X9,X6),c_Groups_Oplus__class_Oplus(X7,X9,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__right__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),c_Groups_Oplus__class_Oplus(X7,X5,X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__ab__semigroup__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X9,X6),c_Groups_Oplus__class_Oplus(X7,X9,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_decseq__def,axiom,
    ! [X54,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_SEQ_Odecseq(X7,X54)
      <=> ! [X52,X4] :
            ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52,X4)
           => c_Orderings_Oord__class_Oless__eq(X7,hAPP(X54,X4),hAPP(X54,X52)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).

fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
    ! [X30,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X14),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X30)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_RealDef_Oreal(tc_Nat_Onat,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).

fof(fact_pos__add__strict,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,X5,X9)
         => c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Oplus__class_Oplus(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless(X7,X5,X9)
         => c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Oplus__class_Oplus(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X9)
         => c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Oplus__class_Oplus(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__increasing,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X9)
         => c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Oplus__class_Oplus(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X6,X5,X9,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X9)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X6)
         => c_Orderings_Oord__class_Oless__eq(X7,X5,c_Groups_Oplus__class_Oplus(X7,X6,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_s1m,axiom,
    ! [X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X14),v_r)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1m) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X25)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X26),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_zadd__left__mono,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X24),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_div__le__mono,axiom,
    ! [X26,X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X26),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X30,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).

fof(fact_diff__le__mono,axiom,
    ! [X40,X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X40),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X40)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [X40,X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_add__le__mono1,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_real__add__left__mono,axiom,
    ! [X14,X10,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X11),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X14,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X12,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X12),X12) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7)),X12) ),
    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,
    ! [X6,X12,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X12,c_Groups_Otimes__class_Otimes(X7,X6,X12)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_div__add__self1,axiom,
    ! [X6,X5,X7] :
      ( class_Divides_Osemiring__div(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X5,X6),X5) = c_Groups_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Odiv(X7,X6,X5),c_Groups_Oone__class_Oone(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [X6,X5,X7] :
      ( class_Divides_Osemiring__div(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_Divides_Odiv__class_Odiv(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X5) = c_Groups_Oplus__class_Oplus(X7,c_Divides_Odiv__class_Odiv(X7,X6,X5),c_Groups_Oone__class_Oone(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).

fof(fact_abs__add__abs,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5))) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [X5,X6] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [X5,X6] :
      ( 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,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [X5,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X10,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),X10)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_eq__diff__iff,axiom,
    ! [X21,X42,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X42)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X21)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X28) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X28)
        <=> X42 = X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X5,X6,X9,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => ( X9 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Otimes__class_Otimes(X7,X9,X6),c_Groups_Otimes__class_Otimes(X7,X9,X5)) = c_Rings_Oinverse__class_Odivide(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X5,X6,X9,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => ( X9 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Otimes__class_Otimes(X7,X6,X9),c_Groups_Otimes__class_Otimes(X7,X5,X9)) = c_Rings_Oinverse__class_Odivide(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_int__div__less__self,axiom,
    ! [X26,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X26),X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).

fof(fact_div__less__dividend,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X30)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).

fof(fact_diff__less,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).

fof(fact_natfloor__subtract,axiom,
    ! [X11,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6),X11)
     => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X6))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X11),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).

fof(fact_natceiling__subtract,axiom,
    ! [X11,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6),X11)
     => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X6))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X11),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X17,X17))
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,X17,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_even__less__0__iff,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X17,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oplus__class_Oplus(X7,X17,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oplus__class_Oplus(X7,X17,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Oab__semigroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X9) = c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,X5,X9)) ),
    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_I25_J,axiom,
    ! [X8,X9,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,X9,X8)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X9),X8) ),
    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,
    ! [X8,X9,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,X9,X8)) = c_Groups_Oplus__class_Oplus(X7,X9,c_Groups_Oplus__class_Oplus(X7,X6,X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_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__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_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_real__0__less__add__iff,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X37))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

fof(fact_real__0__le__add__iff,axiom,
    ! [X37,X36] :
      ( 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,X36,X37))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

fof(fact_real__add__less__0__iff,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X37),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X37,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

fof(fact_real__add__le__0__iff,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X37),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

fof(fact_inverse__less__imp__less,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5))
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
         => c_Orderings_Oord__class_Oless(X7,X5,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).

fof(fact_inverse__less__imp__less__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Rings_Oinverse__class_Oinverse(X7,X5))
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,X5,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X17,X18)
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ominus__class_Ominus(X7,X17,X18),c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X17,X18)
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ominus__class_Ominus(X7,X17,X18),c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_abs__minus__add__cancel,axiom,
    ! [X10,X11] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [X19,X16,X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Groups_Ominus__class_Ominus(X7,X17,X18) = c_Groups_Ominus__class_Ominus(X7,X16,X19)
       => ( c_Orderings_Oord__class_Oless(X7,X17,X18)
        <=> c_Orderings_Oord__class_Oless(X7,X16,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [X19,X16,X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Groups_Ominus__class_Ominus(X7,X17,X18) = c_Groups_Ominus__class_Ominus(X7,X16,X19)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X17,X18)
        <=> c_Orderings_Oord__class_Oless__eq(X7,X16,X19) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096,axiom,
    ! [X36,X48] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X48),v_r)
     => ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X48)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X36,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).

fof(fact_diff__cancel,axiom,
    ! [X30,X12,X26] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X30)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [X30,X26,X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X26)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(fact_diff__commute,axiom,
    ! [X26,X25,X24] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X25),X26) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X26),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).

fof(fact_diff__diff__left,axiom,
    ! [X26,X25,X24] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X25),X26) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(fact_zadd__assoc,axiom,
    ! [X78,X79,X80] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X80,X79),X78) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X80,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X79,X78)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [X26,X30,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30),X26) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_zadd__left__commute,axiom,
    ! [X14,X10,X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X14,X10,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_zless__add1__eq,axiom,
    ! [X77,X69] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X77,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,X77)
        | X69 = X77 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_mth2,axiom,
    ? [X33] :
    ! [X3] :
      ( ? [X46] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X46),v_r)
          & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X46)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mth2) ).

fof(fact_add1__zle__eq,axiom,
    ! [X77,X69] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X69,c_Groups_Oone__class_Oone(tc_Int_Oint)),X77)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,X77) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_zle__diff1__eq,axiom,
    ! [X77,X69] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X77,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,X77) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X77,X69] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X77,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X77) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_less__bin__lemma,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X28,X66),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_real__le__eq__diff,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X37)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X36,X37),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).

fof(fact_zero__less__diff,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X42))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(fact_abs__div__pos,axiom,
    ! [X11,X10,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X10)
       => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oabs__class_Oabs(X7,X11),X10) = c_Groups_Oabs__class_Oabs(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_less__add__eq__less,axiom,
    ! [X30,X12,X40,X26] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X40)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X40) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X30)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_natfloor__add,axiom,
    ! [X6,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X11),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).

fof(fact_natceiling__add,axiom,
    ! [X6,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X6))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X11),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).

fof(fact_abs__less__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X17),X18)
      <=> ( c_Orderings_Oord__class_Oless(X7,X17,X18)
          & c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

fof(fact_abs__leI,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5)
         => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X6),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X17),X18)
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X17,X18)
          & c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

fof(fact_add__lessD1,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X26)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__leD1,axiom,
    ! [X30,X26,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X30,X26,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_real__of__nat__diff,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
     => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X12),c_RealDef_Oreal(tc_Nat_Onat,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).

fof(fact_frac__eq__eq,axiom,
    ! [X69,X36,X77,X37,X7] :
      ( class_Fields_Ofield(X7)
     => ( X37 != c_Groups_Ozero__class_Ozero(X7)
       => ( X77 != c_Groups_Ozero__class_Ozero(X7)
         => ( c_Rings_Oinverse__class_Odivide(X7,X36,X37) = c_Rings_Oinverse__class_Odivide(X7,X69,X77)
          <=> c_Groups_Otimes__class_Otimes(X7,X36,X77) = c_Groups_Otimes__class_Otimes(X7,X69,X37) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Groups_Oordered__comm__monoid__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X36)
       => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X37)
         => ( c_Groups_Oplus__class_Oplus(X7,X36,X37) = c_Groups_Ozero__class_Ozero(X7)
          <=> ( X36 = c_Groups_Ozero__class_Ozero(X7)
              & X37 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_less__imp__inverse__less,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X5),c_Rings_Oinverse__class_Oinverse(X7,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).

fof(fact_less__imp__inverse__less__neg,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ( c_Orderings_Oord__class_Oless(X7,X5,c_Groups_Ozero__class_Ozero(X7))
         => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X5),c_Rings_Oinverse__class_Oinverse(X7,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).

fof(fact_less__nat__number__of,axiom,
    ! [X83,X73] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X73),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X83))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X83)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X83) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X83) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_minus__apply,axiom,
    ! [X36,X67,X68,X41,X7] :
      ( class_Groups_Ominus(X7)
     => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X41,X7),X68,X67),X36) = c_Groups_Ominus__class_Ominus(X7,hAPP(X68,X36),hAPP(X67,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(fact_abs__le__interval__iff,axiom,
    ! [X38,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X36),X38)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X38),X36)
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).

fof(fact_diff__number__of__eq,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_less__natfloor,axiom,
    ! [X30,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X30))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X11),X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).

fof(fact_natceiling__le__eq,axiom,
    ! [X17,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X36),X17)
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,c_RealDef_Oreal(tc_Nat_Onat,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).

fof(fact_le__natfloor__eq,axiom,
    ! [X17,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_RComplete_Onatfloor(X36))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X17),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).

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

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

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [X15,X70] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_odd__nonzero,axiom,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X14),X14) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_le__imp__0__less,axiom,
    ! [X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
     => 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),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096,axiom,
    ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X31)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096) ).

fof(fact_abs__minus__commute,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)) = c_Groups_Oabs__class_Oabs(X7,c_Groups_Ominus__class_Ominus(X7,X5,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_norm__minus__commute,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)) = c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ominus__class_Ominus(X7,X5,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X12,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X12,X12) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Oone__class_Oone(tc_Int_Oint)),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_nonzero__inverse__mult__distrib,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X5),c_Rings_Oinverse__class_Oinverse(X7,X6)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).

fof(fact_poly__div__minus__left,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Ofield(X7)
     => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X11),X10) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X11,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__div__minus__left) ).

fof(fact_poly__div__minus__right,axiom,
    ! [X10,X11,X7] :
      ( class_Fields_Ofield(X7)
     => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X11,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X10)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X7),X11,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__div__minus__right) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_diff__diff__cancel,axiom,
    ! [X30,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X30)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X24)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_le__funE,axiom,
    ! [X36,X1,X2,X7,X41] :
      ( class_Orderings_Oord(X41)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X41,hAPP(X2,X36),hAPP(X1,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_le__funD,axiom,
    ! [X36,X1,X2,X7,X41] :
      ( class_Orderings_Oord(X41)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X2,X1)
       => c_Orderings_Oord__class_Oless__eq(X41,hAPP(X2,X36),hAPP(X1,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_less__imp__diff__less,axiom,
    ! [X30,X26,X25] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X26)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X30),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X14,X10,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X10)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add1,axiom,
    ! [X12,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X10,X14,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X14)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X12,X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X14,X10,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X12,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X10,X14,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X14)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X12,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_norm__divide,axiom,
    ! [X5,X6,X7] :
      ( ( class_Fields_Ofield__inverse__zero(X7)
        & class_RealVector_Oreal__normed__field(X7) )
     => c_RealVector_Onorm__class_Onorm(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__divide) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [X6,X5,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Oabs__class_Oabs(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_nonzero__norm__divide,axiom,
    ! [X6,X5,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_RealVector_Onorm__class_Onorm(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6),c_RealVector_Onorm__class_Onorm(X7,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).

fof(fact_less__number__of,axiom,
    ! [X37,X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_le__number__of,axiom,
    ! [X37,X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_order__less__trans,axiom,
    ! [X14,X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless(X7,X10,X14)
         => c_Orderings_Oord__class_Oless(X7,X11,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X14,X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless(X7,X10,X14)
         => c_Orderings_Oord__class_Oless(X7,X11,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X14,X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X14)
         => c_Orderings_Oord__class_Oless(X7,X11,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X14,X11,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X10,X11)
       => ( c_Orderings_Oord__class_Oless(X7,X14,X10)
         => c_Orderings_Oord__class_Oless(X7,X14,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X14,X11,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => ( c_Orderings_Oord__class_Oless(X7,X14,X10)
         => c_Orderings_Oord__class_Oless(X7,X14,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X14,X11,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X10,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X14,X10)
         => c_Orderings_Oord__class_Oless(X7,X14,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__trans,axiom,
    ! [X14,X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X14)
         => c_Orderings_Oord__class_Oless__eq(X7,X11,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X14,X11,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X14,X10)
         => c_Orderings_Oord__class_Oless__eq(X7,X14,X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_Limits_Ominus__diff__minus,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).

fof(fact_sgn__mult,axiom,
    ! [X10,X11,X7] :
      ( class_RealVector_Oreal__normed__div__algebra(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Osgn__class_Osgn(X7,X11),c_Groups_Osgn__class_Osgn(X7,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).

fof(fact_sgn__times,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Osgn__class_Osgn(X7,X6),c_Groups_Osgn__class_Osgn(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_minus__add__distrib,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5)) = c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X5),c_Groups_Ouminus__class_Ouminus(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_abs__divide,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Oabs__class_Oabs(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

fof(fact_real__natfloor__add__one__gt,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X11)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X70,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_add__number__of__eq,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_number__of__mult,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X70,X15)) = c_Groups_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_number__of__diff,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X70,X15)) = c_Groups_Ominus__class_Ominus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).

fof(fact_number__of__add,axiom,
    ! [X15,X70,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X15)) = c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,X70),c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_neg__less__iff__less,axiom,
    ! [X17,X18,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X18),c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X36),c_Groups_Ouminus__class_Ouminus(X7,X37))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X17,X18,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X18),c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [X28,X27] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X28) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X28 = 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),X27)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X28) )
        | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [X5,X6] :
      ( 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,X6,X5)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [X5,X6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [X28,X29,X27] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X29)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X27) = X28
      <=> X29 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_add__minus__cancel,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_zle__trans,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X26)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_le__trans,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X25)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X26)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_real__le__trans,axiom,
    ! [X26,X25,X24] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X25)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X24,X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

fof(fact_poly__minus,axiom,
    ! [X11,X23,X7] :
      ( class_Rings_Ocomm__ring(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X23)),X11) = c_Groups_Ouminus__class_Ouminus(X7,hAPP(c_Polynomial_Opoly(X7,X23),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).

fof(fact_minus__less__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X18)
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X18),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_abs__le__D2,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X6),X5)
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

fof(fact_minus__le__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X18)
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X18),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_less__minus__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ouminus__class_Ouminus(X7,X18))
      <=> c_Orderings_Oord__class_Oless(X7,X18,c_Groups_Ouminus__class_Ouminus(X7,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(fact_le__minus__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ouminus__class_Ouminus(X7,X18))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X18,c_Groups_Ouminus__class_Ouminus(X7,X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X15,X70] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_real__of__nat__add,axiom,
    ! [X30,X12] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X12),c_RealDef_Oreal(tc_Nat_Onat,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X15,X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X6,X5,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_abs__add__one__gt__zero,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).

fof(fact_inverse__positive__imp__positive,axiom,
    ! [X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Oinverse(X7,X6))
       => ( X6 != c_Groups_Ozero__class_Ozero(X7)
         => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).

fof(fact_inverse__negative__imp__negative,axiom,
    ! [X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Groups_Ozero__class_Ozero(X7))
       => ( X6 != c_Groups_Ozero__class_Ozero(X7)
         => c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X28),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X66))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_real__of__nat__less__iff,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_RealDef_Oreal(tc_Nat_Onat,X42))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X28),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X66))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_real__of__nat__le__iff,axiom,
    ! [X42,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_RealDef_Oreal(tc_Nat_Onat,X42))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).

fof(fact_mult__left_Ominus,axiom,
    ! [X10,X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),X10) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X11,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

fof(fact_mult_Ominus__left,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

fof(fact_divide_Ominus,axiom,
    ! [X10,X11,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ouminus__class_Ouminus(X7,X11),X10) = c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Odivide(X7,X11,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).

fof(fact_mult__right_Ominus,axiom,
    ! [X11,X87,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X87,c_Groups_Ouminus__class_Ouminus(X7,X11)) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X87,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

fof(fact_mult_Ominus__right,axiom,
    ! [X5,X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

fof(fact_minus__mult__left,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oring(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Otimes__class_Otimes(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_minus__divide__left,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__mult__right,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oring(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Otimes__class_Otimes(X7,X6,X5)) = c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_minus__divide__right,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Odivide(X7,X6,X5)) = c_Rings_Oinverse__class_Odivide(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_subseq__def,axiom,
    ! [X2] :
      ( c_SEQ_Osubseq(X2)
    <=> ! [X52,X4] :
          ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X52,X4)
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X52),hAPP(X2,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_inverse__positive__iff__positive,axiom,
    ! [X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Oinverse(X7,X17))
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

fof(fact_sgn__greater,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Osgn__class_Osgn(X7,X17))
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
    ! [X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Oinverse(X7,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).

fof(fact_inverse__negative__iff__negative,axiom,
    ! [X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).

fof(fact_sgn__less,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Osgn__class_Osgn(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
    ! [X17,X7] :
      ( class_Fields_Olinordered__field__inverse__zero(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Rings_Oinverse__class_Oinverse(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_less__special_I1_J,axiom,
    ! [X37,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [X37,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Int_Onumber__class_Onumber__of(X7,X37))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Int_Onumber__class_Onumber__of(X7,X36),c_Groups_Ozero__class_Ozero(X7))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X36,c_Int_OPls) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_compl__mono,axiom,
    ! [X10,X11,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X10),c_Groups_Ouminus__class_Ouminus(X7,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X5),c_Groups_Ouminus__class_Ouminus(X7,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_zero__less__two,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oplus__class_Oplus(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Oone__class_Oone(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_real__natfloor__gt__diff__one,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).

fof(fact_square__eq__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Rings_Oidom(X7)
     => ( c_Groups_Otimes__class_Otimes(X7,X17,X17) = c_Groups_Otimes__class_Otimes(X7,X18,X18)
      <=> ( X17 = X18
          | X17 = c_Groups_Ouminus__class_Ouminus(X7,X18) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact_minus__add__cancel,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Oplus__class_Oplus(X7,X6,X5)) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_neg__less__nonneg,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X17)
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_minus__le__self__iff,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X17),X17)
      <=> c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_less__minus__self__iff,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_le__minus__self__iff,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ouminus__class_Ouminus(X7,X17))
      <=> c_Orderings_Oord__class_Oless__eq(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_nat__less__cases,axiom,
    ! [X50,X21,X42] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
       => hBOOL(hAPP(hAPP(X50,X21),X42)) )
     => ( ( X42 = X21
         => hBOOL(hAPP(hAPP(X50,X21),X42)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42)
           => hBOOL(hAPP(hAPP(X50,X21),X42)) )
         => hBOOL(hAPP(hAPP(X50,X21),X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_negative__imp__inverse__negative,axiom,
    ! [X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => c_Orderings_Oord__class_Oless(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).

fof(fact_positive__imp__inverse__positive,axiom,
    ! [X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Rings_Oinverse__class_Oinverse(X7,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).

fof(fact_abs__le__D1,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X6),X5)
       => c_Orderings_Oord__class_Oless__eq(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [X19,X16,X18,X17,X7] :
      ( class_Groups_Oab__group__add(X7)
     => ( c_Groups_Ominus__class_Ominus(X7,X17,X18) = c_Groups_Ominus__class_Ominus(X7,X16,X19)
       => ( X17 = X18
        <=> X16 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_minus__diff__eq,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5)) = c_Groups_Ominus__class_Ominus(X7,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_xt1_I5_J,axiom,
    ! [X11,X10,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
         => X11 = X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__antisym,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
         => X11 = X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_order__antisym__conv,axiom,
    ! [X36,X37,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X37,X36)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__eq__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Oorder(X7)
     => ( X36 = X37
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
          & c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X21))
    <=> 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_real__of__nat__gt__zero__cancel__iff) ).

fof(fact_less__add__one,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_add__right__cancel,axiom,
    ! [X16,X17,X18,X7] :
      ( class_Groups_Ocancel__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X18,X17) = c_Groups_Oplus__class_Oplus(X7,X16,X17)
      <=> X18 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X9,X6,X5,X7] :
      ( class_Groups_Ocancel__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X5,X6) = c_Groups_Oplus__class_Oplus(X7,X9,X6)
       => X5 = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Ocancel__ab__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X6,X5) = c_Groups_Oplus__class_Oplus(X7,X6,X9)
       => X5 = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X16,X18,X17,X7] :
      ( class_Groups_Ocancel__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X17,X18) = c_Groups_Oplus__class_Oplus(X7,X17,X16)
      <=> X18 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X9,X5,X6,X7] :
      ( class_Groups_Ocancel__semigroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X6,X5) = c_Groups_Oplus__class_Oplus(X7,X6,X9)
       => X5 = X9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_natceiling__le,axiom,
    ! [X6,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X6))
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).

fof(fact_le__natfloor,axiom,
    ! [X6,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),X6)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_RComplete_Onatfloor(X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).

fof(fact_order__root,axiom,
    ! [X17,X44,X7] :
      ( class_Rings_Oidom(X7)
     => ( hAPP(c_Polynomial_Opoly(X7,X44),X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> ( X44 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
          | c_Polynomial_Oorder(X7,X17,X44) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [X30,X12] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X12 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_real__natfloor__le,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_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X11)),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).

fof(fact_less__0__number__of,axiom,
    ! [X73] :
      ( 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,X73))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X73) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_zero__le__square,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__ring(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Otimes__class_Otimes(X7,X6,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X6,X5,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X5 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Rings_Oinverse__class_Odivide(X7,X6,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

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

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

fof(fact_zle__antisym,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14)
       => X14 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__antisym,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12)
       => X12 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_real__le__antisym,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X15)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
       => X14 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).

fof(fact_add__diff__cancel,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Oplus__class_Oplus(X7,X6,X5),X5) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_diff__add__cancel,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ominus__class_Ominus(X7,X6,X5),X5) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X21,X28,X42] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28)
    <=> X42 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X21,X42,X28] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X42) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21)
    <=> X42 = X21 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_minus__mult__minus,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oring(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Groups_Otimes__class_Otimes(X7,X6,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__divide__divide,axiom,
    ! [X5,X6,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Rings_Oinverse__class_Odivide(X7,X6,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_minus__mult__commute,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Oring(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X5) = c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_le__Suc__ex__iff,axiom,
    ! [X66,X28] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X66)
    <=> ? [X4] : X66 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(fact_le__iff__add,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
    <=> ? [X45] : X21 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X45) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_diff__add__0,axiom,
    ! [X12,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X12)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).

fof(fact_divide__eq__eq,axiom,
    ! [X17,X16,X18,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => ( c_Rings_Oinverse__class_Odivide(X7,X18,X16) = X17
      <=> ( ( X16 != c_Groups_Ozero__class_Ozero(X7)
           => X18 = c_Groups_Otimes__class_Otimes(X7,X17,X16) )
          & ( X16 = c_Groups_Ozero__class_Ozero(X7)
           => X17 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [X16,X18,X17,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => ( X17 = c_Rings_Oinverse__class_Odivide(X7,X18,X16)
      <=> ( ( X16 != c_Groups_Ozero__class_Ozero(X7)
           => c_Groups_Otimes__class_Otimes(X7,X17,X16) = X18 )
          & ( X16 = c_Groups_Ozero__class_Ozero(X7)
           => X17 = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_diff__add__inverse,axiom,
    ! [X12,X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X12),X30) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__add__inverse2,axiom,
    ! [X30,X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30),X30) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_div__le__dividend,axiom,
    ! [X30,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(fact_diff__le__self,axiom,
    ! [X30,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(fact_le__add1,axiom,
    ! [X12,X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X12,X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_divide__eq__imp,axiom,
    ! [X6,X5,X9,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X9 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 = c_Groups_Otimes__class_Otimes(X7,X6,X9)
         => c_Rings_Oinverse__class_Odivide(X7,X5,X9) = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X17,X18,X16,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X16 != c_Groups_Ozero__class_Ozero(X7)
       => ( c_Rings_Oinverse__class_Odivide(X7,X18,X16) = X17
        <=> X18 = c_Groups_Otimes__class_Otimes(X7,X17,X16) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_eq__divide__imp,axiom,
    ! [X5,X6,X9,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X9 != c_Groups_Ozero__class_Ozero(X7)
       => ( c_Groups_Otimes__class_Otimes(X7,X6,X9) = X5
         => X6 = c_Rings_Oinverse__class_Odivide(X7,X5,X9) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_le__natfloor__eq__one,axiom,
    ! [X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X36))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).

fof(fact_natceiling__le__eq__one,axiom,
    ! [X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X36),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oabs__class_Oabs(X7,X17))
      <=> X17 != c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [X5,X6] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_zdiv__zminus2,axiom,
    ! [X5,X6] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X5)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X6),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_xt1_I11_J,axiom,
    ! [X6,X5,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X6)
       => ( X6 != X5
         => c_Orderings_Oord__class_Oless(X7,X5,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X5,X6,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
       => ( X6 != X5
         => c_Orderings_Oord__class_Oless(X7,X6,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
          | X11 = X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X5,X6,X7] :
      ( class_Orderings_Oorder(X7)
     => ( X6 != X5
       => ( c_Orderings_Oord__class_Oless__eq(X7,X6,X5)
         => c_Orderings_Oord__class_Oless(X7,X6,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__less,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless(X7,X36,X37)
          | X36 = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
          & X36 != X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_xt1_I12_J,axiom,
    ! [X5,X6,X7] :
      ( class_Orderings_Oorder(X7)
     => ( X6 != X5
       => ( c_Orderings_Oord__class_Oless__eq(X7,X5,X6)
         => c_Orderings_Oord__class_Oless(X7,X5,X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_natfloor__mono,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X11),c_RComplete_Onatfloor(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).

fof(fact_natceiling__mono,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X11),c_RComplete_Onatceiling(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oabs__class_Oabs(X7,X17),c_Groups_Ozero__class_Ozero(X7))
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_order__less__imp__le,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,X11,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oabs__class_Oabs(X7,X6)),c_Groups_Ozero__class_Ozero(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X77] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X77)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_zero__less__norm__iff,axiom,
    ! [X36,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X36))
      <=> X36 != c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

fof(fact_complex__mod__minus__le__complex__mod,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X11)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) = c_Groups_Oplus__class_Oplus(X7,X6,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [X10,X11,X7] :
      ( class_Rings_Ocomm__ring__1(X7)
     => c_Groups_Ominus__class_Ominus(X7,X11,X10) = c_Groups_Oplus__class_Oplus(X7,X11,c_Groups_Ouminus__class_Ouminus(X7,X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_diff__def,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X6,X5) = c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

fof(fact_ab__diff__minus,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X6,X5) = c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_norm__le__zero__iff,axiom,
    ! [X36,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X36),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> X36 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

fof(fact_diff__is__0__eq,axiom,
    ! [X21,X42] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_zless__le,axiom,
    ! [X69,X77] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X77,X69)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X77,X69)
        & X77 != X69 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => ( X12 != X30
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
        | X42 = X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_nat__less__le,axiom,
    ! [X21,X42] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
        & X42 != X21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_less__eq__real__def,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X37)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X36,X37)
        | X36 = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

fof(fact_real__less__def,axiom,
    ! [X37,X36] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X36,X37)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X36,X37)
        & X36 != X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

fof(fact_div__less,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_uminus__apply,axiom,
    ! [X36,X68,X41,X7] :
      ( class_Groups_Ouminus(X7)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X41,X7),X68),X36) = c_Groups_Ouminus__class_Ouminus(X7,hAPP(X68,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_sgn__neg,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => c_Groups_Osgn__class_Osgn(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_sgn__1__neg,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Groups_Osgn__class_Osgn(X7,X17) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7))
      <=> c_Orderings_Oord__class_Oless(X7,X17,c_Groups_Ozero__class_Ozero(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X10,X11] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X30,X12] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
        | X12 = X30 )
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_abs__of__neg,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Ozero__class_Ozero(X7))
       => c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_real__of__nat__one,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [X15,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [X15,X14] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X15) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(fact_complex__diff__def,axiom,
    ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X11,X10) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X11,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).

fof(fact_real__diff__def,axiom,
    ! [X39,X13] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X39) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X39)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).

fof(fact_minus__real__def,axiom,
    ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X10) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [X77] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X77),c_Groups_Oone__class_Oone(tc_Int_Oint))
    <=> X77 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

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

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_real__add__minus__iff,axiom,
    ! [X17,X36] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X36 = X17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

fof(fact_sgn__pos,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => c_Groups_Osgn__class_Osgn(X7,X6) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_sgn__1__pos,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Groups_Osgn__class_Osgn(X7,X17) = c_Groups_Oone__class_Oone(X7)
      <=> c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( X36 != X37
      <=> ( c_Orderings_Oord__class_Oless(X7,X36,X37)
          | c_Orderings_Oord__class_Oless(X7,X37,X36) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
        | X11 = X10
        | c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_abs__of__pos,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => c_Groups_Oabs__class_Oabs(X7,X6) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),X6)
       => c_Groups_Oabs__class_Oabs(X7,X6) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
        | c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__linear,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
        | c_Orderings_Oord__class_Oless__eq(X7,X10,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X9,X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,X9) = c_Groups_Oplus__class_Oplus(X7,X9,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_inverse__unique,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( c_Groups_Otimes__class_Otimes(X7,X6,X5) = c_Groups_Oone__class_Oone(X7)
       => c_Rings_Oinverse__class_Oinverse(X7,X6) = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).

fof(fact_minus__unique,axiom,
    ! [X5,X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X6,X5) = c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Ouminus__class_Ouminus(X7,X6) = X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X7,X18)
      <=> c_Groups_Oplus__class_Oplus(X7,X17,X18) = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_add__eq__0__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X36,X37) = c_Groups_Ozero__class_Ozero(X7)
      <=> X37 = c_Groups_Ouminus__class_Ouminus(X7,X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),c_Groups_Oabs__class_Oabs(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_divisors__zero,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Ono__zero__divisors(X7)
     => ( c_Groups_Otimes__class_Otimes(X7,X6,X5) = c_Groups_Ozero__class_Ozero(X7)
       => ( X6 = c_Groups_Ozero__class_Ozero(X7)
          | X5 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Ono__zero__divisors(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => ( X5 != c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Otimes__class_Otimes(X7,X6,X5) != c_Groups_Ozero__class_Ozero(X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Rings_Oring__no__zero__divisors(X7)
     => ( c_Groups_Otimes__class_Otimes(X7,X17,X18) = c_Groups_Ozero__class_Ozero(X7)
      <=> ( X17 = c_Groups_Ozero__class_Ozero(X7)
          | X18 = c_Groups_Ozero__class_Ozero(X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

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

fof(fact_nat__neq__iff,axiom,
    ! [X21,X42] :
      ( X42 != X21
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_right__inverse__eq,axiom,
    ! [X17,X18,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X18 != c_Groups_Ozero__class_Ozero(X7)
       => ( c_Rings_Oinverse__class_Odivide(X7,X17,X18) = c_Groups_Oone__class_Oone(X7)
        <=> X17 = X18 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_zle__linear,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X14,X15)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_nat__le__linear,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_real__le__linear,axiom,
    ! [X15,X14] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X15)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

fof(fact_diff__poly__code_I1_J,axiom,
    ! [X22,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X22) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).

fof(fact_zadd__commute,axiom,
    ! [X15,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [X30,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Oplus__class_Oplus(X7,X17,X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Oplus__class_Oplus(X7,X17,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    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_right__minus__eq,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ominus__class_Ominus(X7,X17,X18) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Oab__group__add(X7)
     => ( X17 = X18
      <=> c_Groups_Ominus__class_Ominus(X7,X17,X18) = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_real__add__eq__0__iff,axiom,
    ! [X37,X36] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,X37) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X37 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

fof(fact_add__0__iff,axiom,
    ! [X17,X18,X7] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
     => ( X18 = c_Groups_Oplus__class_Oplus(X7,X18,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_poly__zero,axiom,
    ! [X44,X7] :
      ( ( class_Int_Oring__char__0(X7)
        & class_Rings_Oidom(X7) )
     => ( c_Polynomial_Opoly(X7,X44) = c_Polynomial_Opoly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))
      <=> X44 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).

fof(fact_field__inverse,axiom,
    ! [X6,X7] :
      ( class_Fields_Ofield(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),X6) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).

fof(fact_left__inverse,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Otimes__class_Otimes(X7,c_Rings_Oinverse__class_Oinverse(X7,X6),X6) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).

fof(fact_right__inverse,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Otimes__class_Otimes(X7,X6,c_Rings_Oinverse__class_Oinverse(X7,X6)) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).

fof(fact_less__imp__neq,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => X11 != X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => X11 != X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => X10 != X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_eq__number__of__0,axiom,
    ! [X73] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X73) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [X73] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X73)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_divide__Numeral0,axiom,
    ! [X11,X7] :
      ( ( class_Fields_Ofield__inverse__zero(X7)
        & class_Int_Onumber__ring(X7) )
     => c_Rings_Oinverse__class_Odivide(X7,X11,c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

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

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

fof(fact_neq0__conv,axiom,
    ! [X21] :
      ( X21 != 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_neq0__conv) ).

fof(fact_abs__ge__zero,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oabs__class_Oabs(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_nonzero__inverse__minus__eq,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Ouminus__class_Ouminus(X7,X6)) = c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).

fof(fact_nonzero__abs__inverse,axiom,
    ! [X6,X7] :
      ( class_Fields_Olinordered__field(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Groups_Oabs__class_Oabs(X7,c_Rings_Oinverse__class_Oinverse(X7,X6)) = c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Oabs__class_Oabs(X7,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__inverse) ).

fof(fact_le__0__eq,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_left__minus,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_ab__left__minus,axiom,
    ! [X6,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_right__minus,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ouminus__class_Ouminus(X7,X6)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_add__is__0,axiom,
    ! [X21,X42] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_nonzero__norm__inverse,axiom,
    ! [X6,X7] :
      ( class_RealVector_Oreal__normed__div__algebra(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_RealVector_Onorm__class_Onorm(X7,c_Rings_Oinverse__class_Oinverse(X7,X6)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).

fof(fact_gr__implies__not0,axiom,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_norm__number__of,axiom,
    ! [X15,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_RealVector_Oreal__normed__algebra__1(X7) )
     => c_RealVector_Onorm__class_Onorm(X7,c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__number__of) ).

fof(fact_norm__ge__zero,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X7,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X30,X12] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X30) = X12
     => X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__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_real__natceiling__ge,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).

fof(fact_poly__1,axiom,
    ! [X11,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))),X11) = c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).

fof(fact_poly__0,axiom,
    ! [X11,X7] :
      ( class_Rings_Ocomm__semiring__0(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))),X11) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).

fof(fact_abs__ge__self,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,X6,c_Groups_Oabs__class_Oabs(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

fof(fact_less__not__refl2,axiom,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X12)
     => X12 != X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__not__refl3,axiom,
    ! [X56,X39] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X56)
     => X39 != X56 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_inverse__minus__eq,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring__inverse__zero(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Ouminus__class_Ouminus(X7,X6)) = c_Groups_Ouminus__class_Ouminus(X7,c_Rings_Oinverse__class_Oinverse(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).

fof(fact_sgn__minus,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Ouminus__class_Ouminus(X7,X11)) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Osgn__class_Osgn(X7,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).

fof(fact_add__poly__code_I1_J,axiom,
    ! [X22,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X22) = X22 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

fof(fact_diff__poly__code_I2_J,axiom,
    ! [X23,X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X7),X23,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).

fof(fact_add__poly__code_I2_J,axiom,
    ! [X23,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X23,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

fof(fact_g_I1_J,axiom,
    ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X4)),v_r),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).

fof(fact_seq__suble,axiom,
    ! [X21,X2] :
      ( c_SEQ_Osubseq(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,hAPP(X2,X21)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).

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_mth1,axiom,
    ? [X3,X33] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X33),v_r)
      & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mth1) ).

fof(fact_add__numeral__0,axiom,
    ! [X6,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X6,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_number__of__minus,axiom,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)) = c_Groups_Ouminus__class_Ouminus(X7,c_Int_Onumber__class_Onumber__of(X7,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X15,X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Int_Onumber__class_Onumber__of(X7,X15)) = c_Int_Onumber__class_Onumber__of(X7,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_real__mult__inverse__left,axiom,
    ! [X11] :
      ( X11 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => 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_diff__0,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
    ! [X6,X7] :
      ( class_Fields_Ofield(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,X6) = c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oone__class_Oone(X7),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).

fof(fact_inverse__eq__divide,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,X6) = c_Rings_Oinverse__class_Odivide(X7,c_Groups_Oone__class_Oone(X7),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).

fof(fact_real__of__nat__ge__zero,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).

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,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),X14) = 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,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring__inverse__zero(X7)
     => ( ( X6 = c_Groups_Ozero__class_Ozero(X7)
         => c_Rings_Oinverse__class_Odivide(X7,X6,X6) = c_Groups_Ozero__class_Ozero(X7) )
        & ( X6 != c_Groups_Ozero__class_Ozero(X7)
         => c_Rings_Oinverse__class_Odivide(X7,X6,X6) = c_Groups_Oone__class_Oone(X7) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_zero__less__one,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oone__class_Oone(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_zero__le__one,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Ozero__class_Ozero(X7),c_Groups_Oone__class_Oone(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_mult__zero__left,axiom,
    ! [X6,X7] :
      ( class_Rings_Omult__zero(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_mult_Ozero__left,axiom,
    ! [X5,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ozero__class_Ozero(X7),X5) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).

fof(fact_mult__left_Ozero,axiom,
    ! [X10,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ozero__class_Ozero(X7),X10) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_div__0,axiom,
    ! [X6,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Divides_Odiv__class_Odiv(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

fof(fact_divide__zero__left,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ozero__class_Ozero(X7),X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_divide_Ozero,axiom,
    ! [X10,X7] :
      ( class_RealVector_Oreal__normed__field(X7)
     => c_Rings_Oinverse__class_Odivide(X7,c_Groups_Ozero__class_Ozero(X7),X10) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).

fof(fact_mult__zero__right,axiom,
    ! [X6,X7] :
      ( class_Rings_Omult__zero(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_mult_Ozero__right,axiom,
    ! [X6,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

fof(fact_mult__right_Ozero,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__algebra(X7)
     => c_Groups_Otimes__class_Otimes(X7,X11,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_div__by__0,axiom,
    ! [X6,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Divides_Odiv__class_Odiv(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(fact_divide__zero,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring__inverse__zero(X7)
     => c_Rings_Oinverse__class_Odivide(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_div__self,axiom,
    ! [X6,X7] :
      ( class_Divides_Osemiring__div(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Divides_Odiv__class_Odiv(X7,X6,X6) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).

fof(fact_divide__self,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Odivide(X7,X6,X6) = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X15] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_mult__1,axiom,
    ! [X6,X7] :
      ( class_Groups_Ocomm__monoid__mult(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oone__class_Oone(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__left,axiom,
    ! [X6,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oone__class_Oone(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,c_Groups_Oone__class_Oone(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X6,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X6,X7] :
      ( class_Groups_Omonoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X6,X7] :
      ( class_Groups_Ocomm__monoid__mult(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_mult__1__right,axiom,
    ! [X6,X7] :
      ( class_Groups_Omonoid__mult(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Otimes__class_Otimes(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_div__by__1,axiom,
    ! [X6,X7] :
      ( class_Divides_Osemiring__div(X7)
     => c_Divides_Odiv__class_Odiv(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(fact_divide__1,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Odivide(X7,X6,c_Groups_Oone__class_Oone(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_diff__0__right,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X6,X7] :
      ( class_Rings_Ocomm__semiring__1(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X6,X7] :
      ( class_Groups_Ocomm__monoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X6,X7] :
      ( class_Groups_Omonoid__add(X7)
     => c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_diff__self,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ominus__class_Ominus(X7,X6,X6) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(fact_order__eq__refl,axiom,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( X11 = X10
       => c_Orderings_Oord__class_Oless__eq(X7,X11,X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_nonzero__inverse__eq__imp__eq,axiom,
    ! [X5,X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( c_Rings_Oinverse__class_Oinverse(X7,X6) = c_Rings_Oinverse__class_Oinverse(X7,X5)
       => ( X6 != c_Groups_Ozero__class_Ozero(X7)
         => ( X5 != c_Groups_Ozero__class_Ozero(X7)
           => X6 = X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).

fof(fact_zero__le__natfloor,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).

fof(fact_zero__le__natceiling,axiom,
    ! [X11] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).

fof(fact_order__refl,axiom,
    ! [X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => c_Orderings_Oord__class_Oless__eq(X7,X11,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

fof(fact_sgn__sgn,axiom,
    ! [X6,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Osgn__class_Osgn(X7,X6)) = c_Groups_Osgn__class_Osgn(X7,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_abs__minus__cancel,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Ouminus__class_Ouminus(X7,X6)) = c_Groups_Oabs__class_Oabs(X7,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_abs__idempotent,axiom,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Oabs__class_Oabs(X7,X6)) = c_Groups_Oabs__class_Oabs(X7,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

fof(fact_norm__minus__cancel,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ouminus__class_Ouminus(X7,X11)) = c_RealVector_Onorm__class_Onorm(X7,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).

fof(fact_eq__number__of,axiom,
    ! [X37,X36,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Int_Oring__char__0(X7) )
     => ( c_Int_Onumber__class_Onumber__of(X7,X36) = c_Int_Onumber__class_Onumber__of(X7,X37)
      <=> X36 = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_poly__eq__iff,axiom,
    ! [X43,X44,X7] :
      ( ( class_Int_Oring__char__0(X7)
        & class_Rings_Oidom(X7) )
     => ( c_Polynomial_Opoly(X7,X44) = c_Polynomial_Opoly(X7,X43)
      <=> X44 = X43 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

fof(fact_gr0I,axiom,
    ! [X30] :
      ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_abs__norm__cancel,axiom,
    ! [X6,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X6)) = c_RealVector_Onorm__class_Onorm(X7,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).

fof(fact_zdiv__self,axiom,
    ! [X6] :
      ( X6 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X6) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

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

fof(fact_diff__0__eq__0,axiom,
    ! [X30] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_norm__sgn,axiom,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(X7)
         => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Osgn__class_Osgn(X7,X11)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X7)
         => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Osgn__class_Osgn(X7,X11)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).

fof(fact_real__mult__1,axiom,
    ! [X14] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

fof(fact_zadd__0,axiom,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X30] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_zadd__0__right,axiom,
    ! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_eq__imp__le,axiom,
    ! [X30,X12] :
      ( X12 = X30
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_minus__poly__code_I1_J,axiom,
    ! [X7] :
      ( class_Groups_Oab__group__add(X7)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

fof(fact_diff__self__eq__0,axiom,
    ! [X12] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X37,X36,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X36) = c_Groups_Ouminus__class_Ouminus(X7,X37)
      <=> X36 = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X17) = c_Groups_Ouminus__class_Ouminus(X7,X18)
      <=> X17 = X18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_nonzero__inverse__inverse__eq,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Oinverse(X7,c_Rings_Oinverse__class_Oinverse(X7,X6)) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).

fof(fact_zle__refl,axiom,
    ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_le__refl,axiom,
    ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_real__le__refl,axiom,
    ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

fof(fact_add__Pls,axiom,
    ! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X26) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [X26] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,c_Int_OPls) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_add__Pls__right,axiom,
    ! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Int_OPls) = X26,
    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_double__compl,axiom,
    ! [X11,X7] :
      ( class_Lattices_Oboolean__algebra(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X6,X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ouminus__class_Ouminus(X7,X6)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_abs__real__of__nat__cancel,axiom,
    ! [X11] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11)) = c_RealDef_Oreal(tc_Nat_Onat,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).

fof(fact_minus__equation__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X17) = X18
      <=> c_Groups_Ouminus__class_Ouminus(X7,X18) = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X18,X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X7,X18)
      <=> X18 = c_Groups_Ouminus__class_Ouminus(X7,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_psize__eq__0__iff,axiom,
    ! [X44,X7] :
      ( class_Groups_Ozero(X7)
     => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X7,X44) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> X44 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

fof(fact_real__of__nat__inject,axiom,
    ! [X42,X21] :
      ( c_RealDef_Oreal(tc_Nat_Onat,X21) = c_RealDef_Oreal(tc_Nat_Onat,X42)
    <=> X21 = X42 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Ouminus__class_Ouminus(X7,X17)
      <=> c_Groups_Ozero__class_Ozero(X7) = X17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_inverse__eq__1__iff,axiom,
    ! [X36,X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => ( c_Rings_Oinverse__class_Oinverse(X7,X36) = c_Groups_Oone__class_Oone(X7)
      <=> X36 = c_Groups_Oone__class_Oone(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).

fof(fact_inverse__zero__imp__zero,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( c_Rings_Oinverse__class_Oinverse(X7,X6) = c_Groups_Ozero__class_Ozero(X7)
       => X6 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).

fof(fact_nonzero__imp__inverse__nonzero,axiom,
    ! [X6,X7] :
      ( class_Rings_Odivision__ring(X7)
     => ( X6 != c_Groups_Ozero__class_Ozero(X7)
       => c_Rings_Oinverse__class_Oinverse(X7,X6) != c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).

fof(fact_inverse__nonzero__iff__nonzero,axiom,
    ! [X17,X7] :
      ( class_Rings_Odivision__ring__inverse__zero(X7)
     => ( c_Rings_Oinverse__class_Oinverse(X7,X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).

fof(fact_sgn__0__0,axiom,
    ! [X17,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( c_Groups_Osgn__class_Osgn(X7,X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(fact_sgn__zero__iff,axiom,
    ! [X36,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( c_Groups_Osgn__class_Osgn(X7,X36) = c_Groups_Ozero__class_Ozero(X7)
      <=> X36 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [X17,X7] :
      ( class_Groups_Ogroup__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_abs__eq__0,axiom,
    ! [X17,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ( c_Groups_Oabs__class_Oabs(X7,X17) = c_Groups_Ozero__class_Ozero(X7)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).

fof(fact_natfloor__number__of__eq,axiom,
    ! [X30] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X30)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__number__of__eq) ).

fof(fact_natceiling__number__of__eq,axiom,
    ! [X30] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X30)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__number__of__eq) ).

fof(fact_norm__eq__zero,axiom,
    ! [X36,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ( c_RealVector_Onorm__class_Onorm(X7,X36) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      <=> X36 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X90,X89] :
      ( class_Groups_Ouminus(X89)
     => class_Groups_Ouminus(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [X90,X89] :
      ( class_Groups_Ominus(X89)
     => class_Groups_Ominus(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X90,X89] :
      ( class_Lattices_Oboolean__algebra(X89)
     => class_Lattices_Oboolean__algebra(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X90,X89] :
      ( class_Orderings_Oord(X89)
     => class_Orderings_Oord(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X90,X89] :
      ( class_Orderings_Oorder(X89)
     => class_Orderings_Oorder(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X90,X89] :
      ( class_Orderings_Opreorder(X89)
     => class_Orderings_Opreorder(tc_fun(X90,X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(fact_zminus__zminus,axiom,
    ! [X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)) = X14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_neg__equal__zero,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( c_Groups_Ouminus__class_Ouminus(X7,X17) = X17
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_equal__neg__zero,axiom,
    ! [X17,X7] :
      ( class_Groups_Olinordered__ab__group__add(X7)
     => ( X17 = c_Groups_Ouminus__class_Ouminus(X7,X17)
      <=> X17 = c_Groups_Ozero__class_Ozero(X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_inverse__1,axiom,
    ! [X7] :
      ( class_Rings_Odivision__ring(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Oone__class_Oone(X7)) = c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).

fof(fact_inverse__zero,axiom,
    ! [X7] :
      ( class_Rings_Odivision__ring__inverse__zero(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).

fof(fact_field__inverse__zero,axiom,
    ! [X7] :
      ( class_Fields_Ofield__inverse__zero(X7)
     => c_Rings_Oinverse__class_Oinverse(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).

fof(fact_sgn__one,axiom,
    ! [X7] :
      ( class_RealVector_Oreal__normed__algebra__1(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Oone__class_Oone(X7)) = c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).

fof(fact_sgn0,axiom,
    ! [X7] :
      ( class_Groups_Osgn__if(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

fof(fact_sgn__zero,axiom,
    ! [X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_Groups_Osgn__class_Osgn(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).

fof(fact_minus__zero,axiom,
    ! [X7] :
      ( class_Groups_Ogroup__add(X7)
     => c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_abs__one,axiom,
    ! [X7] :
      ( class_Rings_Olinordered__idom(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Oone__class_Oone(X7)) = c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_abs__zero,axiom,
    ! [X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => c_Groups_Oabs__class_Oabs(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

fof(fact_norm__one,axiom,
    ! [X7] :
      ( class_RealVector_Oreal__normed__algebra__1(X7)
     => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Oone__class_Oone(X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).

fof(fact_norm__zero,axiom,
    ! [X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => c_RealVector_Onorm__class_Onorm(X7,c_Groups_Ozero__class_Ozero(X7)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).

fof(fact_natfloor__real__of__nat,axiom,
    ! [X30] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X30)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).

fof(fact_natceiling__real__of__nat,axiom,
    ! [X30] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X30)) = X30,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).

fof(fact_real__of__nat__zero__iff,axiom,
    ! [X21] :
      ( c_RealDef_Oreal(tc_Nat_Onat,X21) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).

fof(fact_real__norm__def,axiom,
    ! [X13] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X13) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).

fof(fact_number__of__Pls,axiom,
    ! [X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X7] :
      ( class_Int_Onumber__ring(X7)
     => c_Groups_Ozero__class_Ozero(X7) = c_Int_Onumber__class_Onumber__of(X7,c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_zero__neq__one,axiom,
    ! [X7] :
      ( class_Rings_Ozero__neq__one(X7)
     => c_Groups_Ozero__class_Ozero(X7) != c_Groups_Oone__class_Oone(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_one__neq__zero,axiom,
    ! [X7] :
      ( class_Rings_Ozero__neq__one(X7)
     => c_Groups_Oone__class_Oone(X7) != c_Groups_Ozero__class_Ozero(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_complex__i__not__number__of,axiom,
    ! [X15] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
    ! [X89] :
      ( class_Groups_Ocancel__comm__monoid__add(X89)
     => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__1(X89)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__1(X89)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
    ! [X89] :
      ( class_Rings_Oidom(X89)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
    ! [X89] :
      ( class_Rings_Oidom(X89)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__0(X89)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__0(X89)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__0(X89)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__ring(X89)
     => class_Rings_Oring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Osgn__if(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).

fof(arity_Polynomial__Opoly__Int_Onumber,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__ring__1(X89)
     => class_Int_Onumber(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).

fof(arity_Polynomial__Opoly__Int_Onumber__ring,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__ring__1(X89)
     => class_Int_Onumber__ring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).

fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
    ! [X89] :
      ( class_Groups_Oab__group__add(X89)
     => class_Groups_Ouminus(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).

fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
    ! [X89] :
      ( class_Groups_Oab__group__add(X89)
     => class_Groups_Ominus(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).

fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
    ! [X89] :
      ( class_Fields_Ofield(X89)
     => class_Divides_Osemiring__div(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).

fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    ! [X89] :
      ( class_Rings_Oidom(X89)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__ring__1(X89)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__1(X89)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__1(X89)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__1(X89)
     => class_Groups_Oone(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
    ! [X89] :
      ( class_Rings_Oidom(X89)
     => class_Rings_Oidom(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
    ! [X89] :
      ( class_Groups_Ocomm__monoid__add(X89)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
    ! [X89] :
      ( class_Groups_Ocomm__monoid__add(X89)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Orderings_Oord(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
    ! [X89] :
      ( class_Groups_Ozero(X89)
     => class_Groups_Ozero(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oabs__if(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__semiring__0(X89)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
    ! [X89] :
      ( class_Rings_Ocomm__ring(X89)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
    ! [X89] :
      ( class_Groups_Oab__group__add(X89)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
    ! [X89] :
      ( class_Groups_Oab__group__add(X89)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
    ! [X89] :
      ( class_Groups_Ocomm__monoid__add(X89)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
    ! [X89] :
      ( class_Groups_Ocancel__comm__monoid__add(X89)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
    ! [X89] :
      ( class_Groups_Ocancel__comm__monoid__add(X89)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
    ! [X89] :
      ( class_Rings_Olinordered__idom(X89)
     => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X89)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).

fof(fact_number__of__is__id,axiom,
    ! [X26] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X26) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

fof(fact_th31,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th31) ).

fof(fact_e,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e) ).

fof(fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
    & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).

fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).

fof(fact_wr,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wr) ).

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_th000_I2_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th000_I2_J) ).

fof(fact_th000_I1_J,axiom,
    c_Orderings_Oord__class_Oless__eq(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_th000_I1_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_rp,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).

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_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_real__of__nat__1,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).

fof(fact_real__of__nat__zero,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).

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_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__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_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_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_natfloor__one,axiom,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).

fof(fact_natfloor__zero,axiom,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).

fof(fact_natceiling__one,axiom,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).

fof(fact_natceiling__zero,axiom,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).

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(fact_complex__i__not__one,axiom,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).

fof(fact_complex__i__not__zero,axiom,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).

fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

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_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_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_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_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_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_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

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_Int__Oint__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

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_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_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_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_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_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_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_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_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_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_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_Int__Oint__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(arity_Int__Oint__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(arity_Nat__Onat__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

fof(arity_Int__Oint__Rings_Oring,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

fof(arity_RealDef__Oreal__Rings_Oring,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

fof(arity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Nat__Onat__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).

fof(arity_RealDef__Oreal__Int_Onumber,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).

fof(arity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

fof(arity_HOL__Obool__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(arity_Int__Oint__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).

fof(arity_HOL__Obool__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(arity_Int__Oint__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(arity_Nat__Onat__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).

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_HOL__Obool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

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_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_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

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__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__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

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_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

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_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_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_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_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_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_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_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_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_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_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(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

fof(arity_Int__Oint__Groups_Oone,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

fof(arity_RealDef__Oreal__Groups_Oone,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

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_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

fof(arity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_Int__Oint__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(arity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

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__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

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_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(fact_fz_I1_J,axiom,
    c_SEQ_Osubseq(v_f____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

fof(i_0_1243,plain,
    ! [X42,X18,X85,X17] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X85)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X42)),X85)
       => ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X85),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X42)),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_th0]) ).

fof(i_0_1244,plain,
    ~ ! [X74] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X74)),
    inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).

fof(i_0_1245,plain,
    ! [X70,X15] :
      ( ( 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,X15))
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X70)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X15))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) )
      & ( ~ 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,X15))
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X70)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X15))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X70),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(i_0_1246,plain,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
         => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__if]) ).

fof(i_0_1247,plain,
    ! [X12,X30] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
       => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X12,X30) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30),X30)) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__geq]) ).

fof(i_0_1248,plain,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Nat_OSuc(X30))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
       => X12 = c_Nat_OSuc(X30) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_1249,plain,
    ! [X21,X42] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X21)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X42) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_1250,plain,
    ! [X21,X42] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X21)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X42)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_1251,plain,
    ! [X42,X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X42)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X42))
      <=> X21 = X42 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_1252,plain,
    ! [X12,X30] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X12)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Nat_OSuc(X12))
       => X12 = X30 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_1253,plain,
    ! [X30,X12] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Nat_OSuc(X30))
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
       => X12 = X30 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_1254,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X30),X30),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_1255,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
    inference(fof_nnf,[status(thm)],[fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096]) ).

fof(i_0_1256,plain,
    ! [X4157] : c_Int_OBit0(X4157) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4157,X4157),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_1257,plain,
    ! [X3756] : c_Nat_OSuc(X3756) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3756,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_1258,plain,
    ! [X4016] : c_Int_OBit1(X4016) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4016),X4016),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_1259,plain,
    ! [X4185] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4185,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,X4185,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X4185,
    inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).

fof(i_0_1260,plain,
    ! [X4372,X4373,X4374,X4375] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4375,X4374)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4373,X4372)),X4374)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4374),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4373,X4372)),X4375)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1243])]) ).

fof(i_0_1261,plain,
    ! [X4362,X4363] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X4363))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4362)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X4363),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4362)),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(i_0_1262,plain,
    ! [X4364,X4365] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X4365))),X4364) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X4365),X4364),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(i_0_1263,plain,
    ! [X4366,X4367] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4367,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X4366)))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4367,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X4366)),
    inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(i_0_1264,plain,
    ! [X4217] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk45_0)
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4217,v_z____)))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4217,v_z____)),esk45_0)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X4217),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096])])])]) ).

fof(i_0_1265,plain,
    ! [X4010] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4010,v_z____)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4010,v_z____)),v_d____)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X4010),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_d_I2_J])]) ).

fof(i_0_1266,plain,
    ! [X4175,X4176] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4176,c_Groups_Ozero__class_Ozero(X4176),c_Rings_Oinverse__class_Odivide(X4176,X4175,c_Int_Onumber__class_Onumber__of(X4176,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | c_Orderings_Oord__class_Oless(X4176,c_Groups_Ozero__class_Ozero(X4176),X4175)
        | ~ class_Fields_Olinordered__field__inverse__zero(X4176)
        | ~ class_Int_Onumber__ring(X4176) )
      & ( ~ c_Orderings_Oord__class_Oless(X4176,c_Groups_Ozero__class_Ozero(X4176),X4175)
        | c_Orderings_Oord__class_Oless(X4176,c_Groups_Ozero__class_Ozero(X4176),c_Rings_Oinverse__class_Odivide(X4176,X4175,c_Int_Onumber__class_Onumber__of(X4176,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4176)
        | ~ class_Int_Onumber__ring(X4176) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_1267,plain,
    ! [X4361] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(X4361)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4361,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(variable_rename,[status(thm)],[fact_div2__Suc__Suc]) ).

fof(i_0_1268,plain,
    ! [X4014,X4015] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4015,X4014),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4015) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4014,X4015),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[fact_real__average__minus__first]) ).

fof(i_0_1269,plain,
    ! [X4012,X4013] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4013,X4012),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4012) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4013,X4012),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[fact_real__average__minus__second]) ).

fof(i_0_1270,plain,
    ! [X4011] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4011,v_z____)),v_d____)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X4011),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_th1])]) ).

fof(i_0_1271,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk47_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096])]) ).

fof(i_0_1272,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk46_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1244])])]) ).

fof(i_0_1273,plain,
    ! [X4371] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4371)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4371,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero])]) ).

fof(i_0_1274,plain,
    ! [X4181,X4182] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4182,X4181)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4182,X4181),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4181) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__gt__half__sum])]) ).

fof(i_0_1275,plain,
    ! [X4183,X4184] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4184,X4183)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4184,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4184,X4183),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_1276,plain,
    ! [X4179,X4180] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X4180)
      | ~ class_Int_Onumber__ring(X4180)
      | ~ c_Orderings_Oord__class_Oless(X4180,c_Groups_Ozero__class_Ozero(X4180),X4179)
      | c_Orderings_Oord__class_Oless(X4180,c_Groups_Ozero__class_Ozero(X4180),c_Rings_Oinverse__class_Odivide(X4180,X4179,c_Int_Onumber__class_Onumber__of(X4180,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_1277,plain,
    ! [X4370] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4370)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X4370,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_div__2__gt__zero])]) ).

fof(i_0_1278,plain,
    ! [X4186] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X4186)
      | ~ class_Int_Onumber__ring(X4186)
      | c_Orderings_Oord__class_Oless(X4186,c_Groups_Ozero__class_Ozero(X4186),c_Rings_Oinverse__class_Odivide(X4186,c_Groups_Oone__class_Oone(X4186),c_Int_Onumber__class_Onumber__of(X4186,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half])]) ).

fof(i_0_1279,plain,
    ! [X4353] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X4353))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X4353),
    inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(i_0_1280,plain,
    ! [X4350] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4350)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4350,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | X4350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X4350 = 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_1281,plain,
    ! [X4369] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4369,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | X4369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X4369 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])]) ).

fof(i_0_1282,plain,
    ! [X4356] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4356) = c_Nat_OSuc(c_Nat_OSuc(X4356)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(i_0_1283,plain,
    ! [X4357] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4357,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X4357)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(i_0_1284,plain,
    ! [X4368] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4368,X4368),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4368,
    inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).

fof(i_0_1285,plain,
    ! [X4358,X4359] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X4359)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4358),X4359) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4358,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4359,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred])]) ).

fof(i_0_1286,plain,
    ! [X3873,X3874] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk39_0,X3873)),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk39_0,X3874))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3874))))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_AALL_An_O_Acmod_A_Ig_An_J_A_060_061_Ar_059_AALL_An_O_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])])]) ).

fof(i_0_1287,plain,
    ! [X3750] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk37_0,X3750)),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk37_0,X3750))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3750))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096])]) ).

fof(i_0_1288,plain,
    ! [X3751] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk38_1(X3751)),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk38_1(X3751))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3751))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_th])]) ).

fof(i_0_1289,plain,
    ! [X3747] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk36_1(X3747)),v_r)
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk36_1(X3747))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3747))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096])]) ).

fof(i_0_1290,plain,
    ! [X3479] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X3479))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3479))))),
    inference(variable_rename,[status(thm)],[fact_g_I2_J]) ).

fof(i_0_1291,plain,
    ! [X4026,X4027] :
      ( ~ class_Int_Onumber__ring(X4027)
      | c_Groups_Ominus__class_Ominus(X4027,c_Int_Onumber__class_Onumber__of(X4027,X4026),c_Groups_Oone__class_Oone(X4027)) = c_Int_Onumber__class_Onumber__of(X4027,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4026,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J])]) ).

fof(i_0_1292,plain,
    ! [X3658,X3659,X3660,X3663,X3664,X3667] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3660)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3659,hAPP(X3658,esk28_3(X3658,X3659,X3660))),X3660)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3659,hAPP(X3658,X3663)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk29_2(X3658,X3659))))
        | ~ class_RealVector_Oreal__normed__vector(X3659) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_2(X3658,X3659))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3659,hAPP(X3658,esk30_3(X3658,X3659,X3664))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3664)))
        | ~ class_RealVector_Oreal__normed__vector(X3659) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3659,hAPP(X3658,X3667)),esk31_2(X3658,X3659))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3659,hAPP(X3658,esk30_3(X3658,X3659,X3664))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3664)))
        | ~ class_RealVector_Oreal__normed__vector(X3659) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2])])])])]) ).

fof(i_0_1293,plain,
    ! [X3668,X3669,X3670,X3673,X3674,X3677] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3670)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3669,hAPP(X3668,esk32_3(X3668,X3669,X3670))),X3670)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3669,hAPP(X3668,X3673)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk33_2(X3668,X3669))))
        | ~ class_RealVector_Oreal__normed__vector(X3669) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_2(X3668,X3669))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3669,hAPP(X3668,esk34_3(X3668,X3669,X3674))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3674)))
        | ~ class_RealVector_Oreal__normed__vector(X3669) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3669,hAPP(X3668,X3677)),esk35_2(X3668,X3669))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3669,hAPP(X3668,esk34_3(X3668,X3669,X3674))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3674)))
        | ~ class_RealVector_Oreal__normed__vector(X3669) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def])])])])]) ).

fof(i_0_1294,plain,
    ! [X4019] :
      ( ~ class_Int_Onumber__ring(X4019)
      | c_Groups_Oplus__class_Oplus(X4019,c_Groups_Oone__class_Oone(X4019),c_Groups_Oone__class_Oone(X4019)) = c_Int_Onumber__class_Onumber__of(X4019,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_1295,plain,
    ! [X4337,X4338] :
      ( ( ~ 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,X4338))
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X4337)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4338))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4337),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4338)) )
      & ( 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,X4338))
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X4337)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4338))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4337),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4338)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1245])]) ).

fof(i_0_1296,plain,
    ! [X4056,X4057] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4057),c_Int_OBit1(X4056))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4057,X4056)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4057),c_Int_OBit1(X4056)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_1297,plain,
    ! [X4052,X4053] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4053),c_Int_OBit1(X4052))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4053,X4052) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4053,X4052)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4053),c_Int_OBit1(X4052)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_1298,plain,
    ! [X4073,X4074] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4074),c_Int_OBit1(X4073))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4074,X4073) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4074,X4073)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4074),c_Int_OBit1(X4073)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_1299,plain,
    ! [X4071,X4072] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4072),c_Int_OBit1(X4071))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4072,X4071) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4072,X4071)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4072),c_Int_OBit1(X4071)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_1300,plain,
    ! [X4137,X4138] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X4138),c_Int_OBit1(X4137)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4138,X4137)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(i_0_1301,plain,
    ! [X4139,X4140] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X4140),c_Int_OBit0(X4139)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4140,X4139)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(i_0_1302,plain,
    ! [X4143,X4144] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X4144),c_Int_OBit0(X4143)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4144,X4143)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_1303,plain,
    ! [X4145,X4146] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X4146),c_Int_OBit1(X4145)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4146,X4145)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_1304,plain,
    ! [X4022,X4023] :
      ( ~ class_Int_Onumber__ring(X4023)
      | c_Groups_Ominus__class_Ominus(X4023,c_Groups_Oone__class_Oone(X4023),c_Int_Onumber__class_Onumber__of(X4023,X4022)) = c_Int_Onumber__class_Onumber__of(X4023,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4022))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).

fof(i_0_1305,plain,
    ! [X4024,X4025] :
      ( ~ class_Int_Onumber__ring(X4025)
      | c_Groups_Oplus__class_Oplus(X4025,c_Int_Onumber__class_Onumber__of(X4025,X4024),c_Groups_Oone__class_Oone(X4025)) = c_Int_Onumber__class_Onumber__of(X4025,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4024,c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_1306,plain,
    ! [X4020,X4021] :
      ( ~ class_Int_Onumber__ring(X4021)
      | c_Groups_Oplus__class_Oplus(X4021,c_Groups_Oone__class_Oone(X4021),c_Int_Onumber__class_Onumber__of(X4021,X4020)) = c_Int_Onumber__class_Onumber__of(X4021,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_1307,plain,
    ! [X4058,X4059] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4059),c_Int_OBit0(X4058))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4059,X4058) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4059,X4058)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4059),c_Int_OBit0(X4058)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_1308,plain,
    ! [X4054,X4055] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4055),c_Int_OBit0(X4054))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4055,X4054) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4055,X4054)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4055),c_Int_OBit0(X4054)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_1309,plain,
    ! [X4050,X4051] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4051),c_Int_OBit0(X4050))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4051,X4050) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4051,X4050)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4051),c_Int_OBit0(X4050)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_1310,plain,
    ! [X4048,X4049] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4049),c_Int_OBit0(X4048))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4049,X4048) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4049,X4048)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4049),c_Int_OBit0(X4048)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_1311,plain,
    ! [X4046,X4047] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4047),c_Int_OBit1(X4046))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4047,X4046) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4047,X4046)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4047),c_Int_OBit1(X4046)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_1312,plain,
    ! [X4044,X4045] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4045),c_Int_OBit1(X4044))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4045,X4044) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4045,X4044)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4045),c_Int_OBit1(X4044)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_1313,plain,
    ! [X4079,X4080] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4080),c_Int_OBit1(X4079))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4080,X4079) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4080,X4079)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4080),c_Int_OBit1(X4079)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_1314,plain,
    ! [X4075,X4076] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4076),c_Int_OBit1(X4075))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4076,X4075) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4076,X4075)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4076),c_Int_OBit1(X4075)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_1315,plain,
    ! [X4172,X4173] :
      ( ~ class_Fields_Ofield(X4173)
      | ~ class_Int_Onumber__ring(X4173)
      | c_Rings_Oinverse__class_Odivide(X4173,X4172,c_Int_Onumber__class_Onumber__of(X4173,c_Int_OBit1(c_Int_OPls))) = X4172 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_1316,plain,
    ! [X4170,X4171] :
      ( ~ class_Fields_Ofield(X4171)
      | ~ class_Int_Onumber__ring(X4171)
      | c_Rings_Oinverse__class_Odivide(X4171,X4170,c_Int_Onumber__class_Onumber__of(X4171,c_Int_OBit1(c_Int_OPls))) = X4170 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_1317,plain,
    ! [X3706,X3707,X3708] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3708,X3707)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3707,X3708)),X3706) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3707),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3708,X3706)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).

fof(i_0_1318,plain,
    ! [X3709,X3710,X3711] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3711,X3710)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3709,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3710,X3711))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3709,X3711),c_Nat_OSuc(X3710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).

fof(i_0_1319,plain,
    ! [X3848] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3848,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | X3848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X3848 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one])]) ).

fof(i_0_1320,plain,
    ! [X4028,X4029] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4029,c_Int_Onumber__class_Onumber__of(X4029,X4028),c_Groups_Oone__class_Oone(X4029))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4028,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X4029)
        | ~ class_Rings_Olinordered__idom(X4029) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4028,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless(X4029,c_Int_Onumber__class_Onumber__of(X4029,X4028),c_Groups_Oone__class_Oone(X4029))
        | ~ class_Int_Onumber__ring(X4029)
        | ~ class_Rings_Olinordered__idom(X4029) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_1321,plain,
    ! [X4034,X4035] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4035,c_Int_Onumber__class_Onumber__of(X4035,X4034),c_Groups_Oone__class_Oone(X4035))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4034,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X4035)
        | ~ class_Rings_Olinordered__idom(X4035) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4034,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless__eq(X4035,c_Int_Onumber__class_Onumber__of(X4035,X4034),c_Groups_Oone__class_Oone(X4035))
        | ~ class_Int_Onumber__ring(X4035)
        | ~ class_Rings_Olinordered__idom(X4035) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_1322,plain,
    ! [X4030,X4031] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4031,c_Groups_Oone__class_Oone(X4031),c_Int_Onumber__class_Onumber__of(X4031,X4030))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4030)
        | ~ class_Int_Onumber__ring(X4031)
        | ~ class_Rings_Olinordered__idom(X4031) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4030)
        | c_Orderings_Oord__class_Oless(X4031,c_Groups_Oone__class_Oone(X4031),c_Int_Onumber__class_Onumber__of(X4031,X4030))
        | ~ class_Int_Onumber__ring(X4031)
        | ~ class_Rings_Olinordered__idom(X4031) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_1323,plain,
    ! [X4036,X4037] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4037,c_Groups_Oone__class_Oone(X4037),c_Int_Onumber__class_Onumber__of(X4037,X4036))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4036)
        | ~ class_Int_Onumber__ring(X4037)
        | ~ class_Rings_Olinordered__idom(X4037) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4036)
        | c_Orderings_Oord__class_Oless__eq(X4037,c_Groups_Oone__class_Oone(X4037),c_Int_Onumber__class_Onumber__of(X4037,X4036))
        | ~ class_Int_Onumber__ring(X4037)
        | ~ class_Rings_Olinordered__idom(X4037) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_1324,plain,
    ! [X18,X17,X50] :
      ( hBOOL(hAPP(X50,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18)))
    <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
            & ~ hBOOL(hAPP(X50,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X51] :
              ( X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X51)
              & ~ hBOOL(hAPP(X50,X51)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(i_0_1325,plain,
    ! [X4064] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4064),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4064,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4064,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4064),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_1326,plain,
    ! [X3646,X3647,X3648] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3648),X3647),c_Nat_OSuc(X3646)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3648,X3647),X3646),
    inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).

fof(i_0_1327,plain,
    ! [X4039] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4039))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4039) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4039)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4039)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_1328,plain,
    ! [X4084] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4084))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4084) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4084)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4084)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_1329,plain,
    ! [X4065] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4065),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4065,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4065,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4065),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_1330,plain,
    ! [X4040] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4040),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4040,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4040,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4040),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_1331,plain,
    ! [X4220,X4221] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4221)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4220))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4221),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4220)),
    inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(i_0_1332,plain,
    ! [X4017,X4018] :
      ( ~ class_Int_Onumber__ring(X4018)
      | c_Int_Onumber__class_Onumber__of(X4018,c_Int_OBit1(X4017)) = c_Groups_Oplus__class_Oplus(X4018,c_Groups_Oplus__class_Oplus(X4018,c_Groups_Oone__class_Oone(X4018),c_Int_Onumber__class_Onumber__of(X4018,X4017)),c_Int_Onumber__class_Onumber__of(X4018,X4017)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_1333,plain,
    ! [X3939,X3940] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3940)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3940,X3939)
      | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3939,X3940) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3939,X3940),X3940)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).

fof(i_0_1334,plain,
    ! [X3654,X3655,X3656] :
      ( ( ~ c_SEQ_Osubseq(X3654)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3654,X3655),hAPP(X3654,c_Nat_OSuc(X3655))) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3656,esk27_1(X3656)),hAPP(X3656,c_Nat_OSuc(esk27_1(X3656))))
        | c_SEQ_Osubseq(X3656) ) ),
    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_subseq__Suc__iff])])])])]) ).

fof(i_0_1335,plain,
    ! [X3941,X3942] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3941,X3942)
        | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3941,X3942) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3942) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3941,X3942)
        | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3941,X3942) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3941,X3942),X3942))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3942) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1246])])]) ).

fof(i_0_1336,plain,
    ! [X3943,X3944] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3944)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3943,X3944)
      | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3943,X3944) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3943,X3944),X3944)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1247])]) ).

fof(i_0_1337,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
   => ? [X33] :
      ! [X47] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X47),v_r)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X33)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X47))) ) ),
    inference(fof_simplification,[status(thm)],[fact_calculation]) ).

fof(i_0_1338,plain,
    ! [X4141,X4142] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X4142),c_Int_OBit0(X4141)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4142,X4141)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(i_0_1339,plain,
    ! [X4147,X4148] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X4148),c_Int_OBit0(X4147)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4148,X4147)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_1340,plain,
    ! [X4122,X4123] :
      ( ( c_Int_OBit1(X4123) != c_Int_OBit1(X4122)
        | X4123 = X4122 )
      & ( X4123 != X4122
        | c_Int_OBit1(X4123) = c_Int_OBit1(X4122) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_1341,plain,
    ! [X3519,X3520] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3520),c_Nat_OSuc(X3519))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3520,X3519)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3520),c_Nat_OSuc(X3519)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_1342,plain,
    ! [X3491,X3492] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3492),c_Nat_OSuc(X3491))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3492,X3491) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_1343,plain,
    ! [X3623,X3624] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3624),c_Nat_OSuc(X3623))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3624,X3623) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3624,X3623)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3624),c_Nat_OSuc(X3623)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_1344,plain,
    ! [X3653] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3653)
      | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3653,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X3653 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).

fof(i_0_1345,plain,
    ! [X3651,X3652] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3652)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3652,c_Nat_OSuc(X3651)),X3652) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).

fof(i_0_1346,plain,
    ! [X4062,X4063] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4063),c_Int_OBit0(X4062))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4063,X4062) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4063,X4062)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4063),c_Int_OBit0(X4062)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_1347,plain,
    ! [X4060,X4061] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4061),c_Int_OBit0(X4060))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4061,X4060) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4061,X4060)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4061),c_Int_OBit0(X4060)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_1348,plain,
    ! [X4081,X4082] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4082),c_Int_OBit0(X4081))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4082,X4081) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4082,X4081)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4082),c_Int_OBit0(X4081)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_1349,plain,
    ! [X4077,X4078] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4078),c_Int_OBit0(X4077))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4078,X4077) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4078,X4077)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4078),c_Int_OBit0(X4077)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_1350,plain,
    ! [X3753,X3754] :
      ( ( X3754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3754,X3753) = X3753 )
      & ( X3754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3754,X3753) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3754,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3753)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).

fof(i_0_1351,plain,
    ! [X4155] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4155)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X4155)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(i_0_1352,plain,
    ! [X3700,X3701] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3701,X3700)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3700),X3701) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3700,X3701)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).

fof(i_0_1353,plain,
    ! [X4109,X4110] :
      ( ~ class_Int_Onumber__ring(X4110)
      | c_Int_Onumber__class_Onumber__of(X4110,c_Int_OBit0(X4109)) = c_Groups_Oplus__class_Oplus(X4110,c_Groups_Oplus__class_Oplus(X4110,c_Groups_Ozero__class_Ozero(X4110),c_Int_Onumber__class_Onumber__of(X4110,X4109)),c_Int_Onumber__class_Onumber__of(X4110,X4109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_1354,plain,
    ! [X3607,X3608] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3608,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3608,X3607))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_1355,plain,
    ! [X3609,X3610] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3610,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3609,X3610))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_1356,plain,
    ! [X3625,X3626] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,c_Nat_OSuc(X3625))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,X3625)
        | X3626 = c_Nat_OSuc(X3625) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,X3625)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,c_Nat_OSuc(X3625)) )
      & ( X3626 != c_Nat_OSuc(X3625)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,c_Nat_OSuc(X3625)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_1357,plain,
    ! [X3619,X3620] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3620,c_Nat_OSuc(X3619))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3620,X3619)
      | X3620 = c_Nat_OSuc(X3619) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1248])]) ).

fof(i_0_1358,plain,
    ! [X3481,X3482] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3482,X3481)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3482),c_Nat_OSuc(X3481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_1359,plain,
    ! [X69,X73,X7] :
      ( ( class_Int_Onumber(X7)
        & class_Orderings_Olinorder(X7) )
     => ( c_Orderings_Oord__class_Oless__eq(X7,c_Int_Onumber__class_Onumber__of(X7,X73),c_Int_Onumber__class_Onumber__of(X7,X69))
      <=> ~ c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X69),c_Int_Onumber__class_Onumber__of(X7,X73)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_1360,plain,
    ! [X4360] :
      ( ~ 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,X4360))
      | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4360) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4360),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).

fof(i_0_1361,plain,
    ! [X3523,X3524,X3526,X3527,X3528] :
      ( ( X3524 = c_Nat_OSuc(esk24_2(X3523,X3524))
        | X3524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3524,c_Nat_OSuc(X3523)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_2(X3523,X3524),X3523)
        | X3524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3524,c_Nat_OSuc(X3523)) )
      & ( X3527 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3527,c_Nat_OSuc(X3526)) )
      & ( X3527 != c_Nat_OSuc(X3528)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3528,X3526)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3527,c_Nat_OSuc(X3526)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])]) ).

fof(i_0_1362,plain,
    ! [X3640,X3641] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3640,c_Nat_OSuc(X3641))
        | X3640 = X3641
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3641,X3640) )
      & ( X3640 != X3641
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3640,c_Nat_OSuc(X3641))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3641,X3640) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

fof(i_0_1363,plain,
    ! [X3627,X3628] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3628,X3627)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3627),X3628) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3627),X3628)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3628,X3627) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1249])]) ).

fof(i_0_1364,plain,
    ! [X3537,X3538] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3538,X3537)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3537,c_Nat_OSuc(X3538)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3537,c_Nat_OSuc(X3538))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3538,X3537) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1250])]) ).

fof(i_0_1365,plain,
    ! [X4033] :
      ( ~ class_Int_Onumber__ring(X4033)
      | c_Int_Onumber__class_Onumber__of(X4033,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X4033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_1366,plain,
    ! [X4032] :
      ( ~ class_Int_Onumber__ring(X4032)
      | c_Groups_Oone__class_Oone(X4032) = c_Int_Onumber__class_Onumber__of(X4032,c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_1367,plain,
    ! [X4128,X4129] : c_Int_OBit0(X4129) != c_Int_OBit1(X4128),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_1368,plain,
    ! [X4126,X4127] : c_Int_OBit1(X4127) != c_Int_OBit0(X4126),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_1369,plain,
    ! [X3498,X3499,X3500] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3500,X3499)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3499,X3498)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3500),X3498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_1370,plain,
    ! [X11] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X11),
    inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).

fof(i_0_1371,plain,
    ! [X3644,X3645] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3645),c_Nat_OSuc(X3644)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3645,X3644),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(i_0_1372,plain,
    ! [X3601,X3602] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3602),X3601) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3602,c_Nat_OSuc(X3601)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_1373,plain,
    ! [X3758,X3759] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3759,c_Nat_OSuc(X3758)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3759,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3758),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(i_0_1374,plain,
    ! [X3599,X3600] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3600),X3599) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3600,X3599)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_1375,plain,
    ! [X3597,X3598] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3598,c_Nat_OSuc(X3597)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3598,X3597)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_1376,plain,
    ! [X84,X70] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X84,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X70),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X84)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X84)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_1377,plain,
    ! [X3521,X3522] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3522,c_Nat_OSuc(X3521))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3522,X3521)
        | X3522 = X3521 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3522,X3521)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3522,c_Nat_OSuc(X3521)) )
      & ( X3522 != X3521
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3522,c_Nat_OSuc(X3521)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

fof(i_0_1378,plain,
    ! [X3517,X3518] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3518,c_Nat_OSuc(X3517))
        | X3518 = X3517
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3518,X3517) )
      & ( X3518 != X3517
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3518,c_Nat_OSuc(X3517))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3518,X3517) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1251])])]) ).

fof(i_0_1379,plain,
    ! [X3515,X3516] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3516,X3515)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3516,c_Nat_OSuc(X3515))
      | X3515 = X3516 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1252])]) ).

fof(i_0_1380,plain,
    ! [X3496,X3497] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3497,c_Nat_OSuc(X3496))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3497,X3496)
      | X3497 = X3496 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1253])]) ).

fof(i_0_1381,plain,
    ! [X3493,X3494] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3494),X3493)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3494,X3493) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_1382,plain,
    ! [X3642,X3643] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3643),X3642)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3643,X3642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_1383,plain,
    ! [X3634,X3635] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3635),X3634)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3635,X3634) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3635,X3634)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3635),X3634) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_1384,plain,
    ! [X3630,X3631] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3631,X3630)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3631),X3630) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3631),X3630)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3631,X3630) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_1385,plain,
    ! [X3617,X3618] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3618),X3617)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3618,X3617) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_1386,plain,
    ! [X3632,X3633] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3633,c_Nat_OSuc(X3632))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3633,X3632) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3633,X3632)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3633,c_Nat_OSuc(X3632)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_1387,plain,
    ! [X4066] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4066),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4066,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4066,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4066),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_1388,plain,
    ! [X3611,X3612,X3614,X3615,X3616] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3612,X3611)
        | X3611 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3612,esk26_2(X3611,X3612))) )
      & ( X3614 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3615,X3616))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3615,X3614) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])]) ).

fof(i_0_1389,plain,
    ! [X3501,X3502] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3502,X3501)
      | c_Nat_OSuc(X3502) = X3501
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3502),X3501) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_1390,plain,
    ! [X30,X26,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X26),X30)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X30)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X30) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_1391,plain,
    ! [X3553] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3553))),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).

fof(i_0_1392,plain,
    ! [X3603,X3604] :
      ( ( X3604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3604 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) )
      & ( X3603 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3604 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) )
      & ( X3604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) )
      & ( X3603 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) )
      & ( X3604 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3603 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) )
      & ( X3604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3603 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3604,X3603) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_1393,plain,
    ! [X3605,X3606] :
      ( ( X3606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3606 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X3605 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3606 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X3606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X3605 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X3606 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3605 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X3606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3605 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3606,X3605) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).

fof(i_0_1394,plain,
    ! [X4068] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4068))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4068) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4068)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4068)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_1395,plain,
    ! [X4085] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4085))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4085) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4085)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4085)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_1396,plain,
    ! [X4067] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4067),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4067,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4067,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4067),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_1397,plain,
    ! [X4083] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4083),c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4083,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4083,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4083),c_Int_OPls) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_1398,plain,
    ! [X1,X2,X7,X41] :
      ( class_Orderings_Oord(X41)
     => ( c_Orderings_Oord__class_Oless(tc_fun(X7,X41),X2,X1)
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X2,X1)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X7,X41),X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_1399,plain,
    ! [X6,X7] :
      ( class_Rings_Olinordered__ring(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Otimes__class_Otimes(X7,X6,X6),c_Groups_Ozero__class_Ozero(X7)) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_1400,plain,
    ! [X3529] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3529,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X3529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3529 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3529,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).

fof(i_0_1401,plain,
    ! [X3649,X3650] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3650,X3649),c_Nat_OSuc(X3650)),
    inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).

fof(i_0_1402,plain,
    ! [X83,X73] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X73),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X83))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,X83)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,c_Int_OPls) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_1403,plain,
    ! [X3629] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3629),X3629),
    inference(variable_rename,[status(thm)],[i_0_1254]) ).

fof(i_0_1404,plain,
    ! [X4134] : c_Int_OBit1(X4134) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_1405,plain,
    ! [X4136] : c_Int_OPls != c_Int_OBit1(X4136),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_1406,plain,
    ! [X3486] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3486)
      | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3486,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X3486 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).

fof(i_0_1407,plain,
    ! [X3755] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3755)
      | X3755 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3755,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).

fof(i_0_1408,plain,
    ! [X3638,X3639] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3639),X3638) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_1409,plain,
    ! [X3503,X3504] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3504,X3503)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3504,c_Nat_OSuc(X3503)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_1410,plain,
    ! [X3636,X3637] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3637,X3636)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3637,c_Nat_OSuc(X3636)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_1411,plain,
    ! [X3621,X3622] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3622,X3621)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3622,c_Nat_OSuc(X3621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_1412,plain,
    ! [X25,X24] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X24),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_1413,plain,
    ! [X24,X25] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24),X24),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_1414,plain,
    ! [X11,X7] :
      ( ( class_Int_Onumber__ring(X7)
        & class_Rings_Olinordered__idom(X7) )
     => ( ( c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X11),c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) = c_Groups_Ouminus__class_Ouminus(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) )
        & ( ~ c_Orderings_Oord__class_Oless(X7,c_Int_Onumber__class_Onumber__of(X7,X11),c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,c_Int_Onumber__class_Onumber__of(X7,X11)) = c_Int_Onumber__class_Onumber__of(X7,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).

fof(i_0_1415,plain,
    ! [X4069] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X4069)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4069)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_1416,plain,
    ! [X30,X12] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X30)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X12,X30)) = X12 ),
    inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).

fof(i_0_1417,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
          & ~ c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_1418,plain,
    ! [X3562] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3562)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3562),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).

fof(i_0_1419,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
       => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_1420,plain,
    ! [X6,X5,X7] :
      ( class_Orderings_Oorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X5,X6)
       => ~ c_Orderings_Oord__class_Oless(X7,X6,X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_1421,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> ( c_Orderings_Oord__class_Oless(X7,X37,X36)
          | X36 = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_1422,plain,
    ! [X11,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => ~ c_Orderings_Oord__class_Oless(X7,X11,X10) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_1423,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
      <=> c_Orderings_Oord__class_Oless__eq(X7,X37,X36) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_1424,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
      <=> c_Orderings_Oord__class_Oless(X7,X37,X36) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_1425,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_1426,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_1427,plain,
    ! [X5,X6,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X6,X5)
       => ~ c_Orderings_Oord__class_Oless(X7,X5,X6) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_1428,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ( c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ~ c_Orderings_Oord__class_Oless(X7,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_1429,plain,
    ! [X3560,X3561] :
      ( c_Nat_OSuc(X3561) != c_Nat_OSuc(X3560)
      | X3561 = X3560 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_1430,plain,
    ! [X3556,X3557] :
      ( ( c_Nat_OSuc(X3557) != c_Nat_OSuc(X3556)
        | X3557 = X3556 )
      & ( X3557 != X3556
        | c_Nat_OSuc(X3557) = c_Nat_OSuc(X3556) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_1431,plain,
    ! [X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
         => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) )
        & ( X11 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
         => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X11)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7)) )
            & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)),X11)
             => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__poly__def]) ).

fof(i_0_1432,plain,
    ! [X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))
         => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X11) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X7),X11) )
        & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X7),X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)))
         => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X7),X11) = X11 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__poly__def]) ).

fof(i_0_1433,plain,
    ! [X3958] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3958,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X3958,
    inference(variable_rename,[status(thm)],[fact_div__1]) ).

fof(i_0_1434,plain,
    ! [X4124,X4125] :
      ( ( c_Int_OBit0(X4125) != c_Int_OBit0(X4124)
        | X4125 = X4124 )
      & ( X4125 != X4124
        | c_Int_OBit0(X4125) = c_Int_OBit0(X4124) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_1435,plain,
    ! [X3549] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3549),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3549,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(i_0_1436,plain,
    ! [X3484] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3484)),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_1437,plain,
    ! [X3483] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3483,c_Nat_OSuc(X3483)),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_1438,plain,
    ! [X3531,X3533,X3534] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3531)
        | X3531 = c_Nat_OSuc(esk25_1(X3531)) )
      & ( X3533 != c_Nat_OSuc(X3534)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3533) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).

fof(i_0_1439,plain,
    ! [X37,X36,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
       => ( c_Orderings_Oord__class_Oless__eq(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_1440,plain,
    ! [X6,X7] :
      ( class_Groups_Oordered__ab__group__add__abs(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Oabs__class_Oabs(X7,X6),c_Groups_Ozero__class_Ozero(X7)) ),
    inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).

fof(i_0_1441,plain,
    ! [X11,X7] :
      ( class_RealVector_Oreal__normed__vector(X7)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X7,X11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).

fof(i_0_1442,plain,
    ! [X6,X7] :
      ( class_Groups_Oabs__if(X7)
     => ( ( c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,X6) = c_Groups_Ouminus__class_Ouminus(X7,X6) )
        & ( ~ c_Orderings_Oord__class_Oless(X7,X6,c_Groups_Ozero__class_Ozero(X7))
         => c_Groups_Oabs__class_Oabs(X7,X6) = X6 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_1443,plain,
    ! [X11,X7] :
      ( class_Groups_Osgn__if(X7)
     => ( ( X11 = c_Groups_Ozero__class_Ozero(X7)
         => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Ozero__class_Ozero(X7) )
        & ( X11 != c_Groups_Ozero__class_Ozero(X7)
         => ( ( c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
             => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Oone__class_Oone(X7) )
            & ( ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Ozero__class_Ozero(X7),X11)
             => c_Groups_Osgn__class_Osgn(X7,X11) = c_Groups_Ouminus__class_Ouminus(X7,c_Groups_Oone__class_Oone(X7)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_1444,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X30),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).

fof(i_0_1445,plain,
    ! [X10,X11,X7] :
      ( class_Rings_Olinordered__idom(X7)
     => ( X11 != X10
       => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_1446,plain,
    ! [X36,X37,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X37,X36)
       => ( ~ c_Orderings_Oord__class_Oless(X7,X36,X37)
        <=> X36 = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_1447,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( X11 != X10
       => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_1448,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
       => ( X11 != X10
         => c_Orderings_Oord__class_Oless(X7,X10,X11) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_1449,plain,
    ! [X11,X10,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X10,X11)
       => c_Orderings_Oord__class_Oless(X7,X11,X10) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_1450,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_1451,plain,
    ! [X10,X11,X7] :
      ( class_Orderings_Olinorder(X7)
     => ( ~ c_Orderings_Oord__class_Oless__eq(X7,X11,X10)
       => c_Orderings_Oord__class_Oless__eq(X7,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_1452,plain,
    ! [X24] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Groups_Oabs__class_Oabs(tc_Int_Oint,X24) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X24) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Groups_Oabs__class_Oabs(tc_Int_Oint,X24) = X24 ) ),
    inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).

fof(i_0_1453,plain,
    ! [X13] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13) = X13 ) ),
    inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).

fof(i_0_1454,plain,
    ! [X6] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6) = X6 ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__real__def]) ).

fof(i_0_1455,plain,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_1456,plain,
    ! [X7] :
      ( class_Rings_Olinordered__semidom(X7)
     => ~ c_Orderings_Oord__class_Oless__eq(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(X7)) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_1457,plain,
    ! [X3757] : c_Nat_OSuc(X3757) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3757),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_1458,plain,
    ! [X10,X11] :
      ( X11 != X10
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X10)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X11) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_1459,plain,
    ! [X24] :
      ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X24) = 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_1460,plain,
    ! [X6] :
      ( ( X6 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X6 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
       => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
           => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6) = 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_1461,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_1462,plain,
    ! [X11,X7] :
      ( class_Orderings_Opreorder(X7)
     => ~ c_Orderings_Oord__class_Oless(X7,X11,X11) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_1463,plain,
    ! [X3541] : c_Nat_OSuc(X3541) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_1464,plain,
    ! [X3540] : c_Nat_OSuc(X3540) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_1465,plain,
    ! [X3495] : c_Nat_OSuc(X3495) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_1466,plain,
    ! [X3545] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3545),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_1467,plain,
    ! [X3544] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3544),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_1468,plain,
    ! [X3512] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X3512),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_1469,plain,
    ! [X3555] : c_Nat_OSuc(X3555) != X3555,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_1470,plain,
    ! [X3554] : X3554 != c_Nat_OSuc(X3554),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_1471,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_1472,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_1473,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_1474,plain,
    ! [X4135] :
      ( ( c_Int_OPls != c_Int_OBit0(X4135)
        | c_Int_OPls = X4135 )
      & ( c_Int_OPls != X4135
        | c_Int_OPls = c_Int_OBit0(X4135) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_1475,plain,
    ! [X4133] :
      ( ( c_Int_OBit0(X4133) != c_Int_OPls
        | X4133 = c_Int_OPls )
      & ( X4133 != c_Int_OPls
        | c_Int_OBit0(X4133) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_1476,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X30),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_1477,plain,
    ! [X30] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X30,X30),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

cnf(i_0_1478,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))) ),
    inference(split_conjunct,[status(thm)],[i_0_1255]) ).

cnf(i_0_1479,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_1256]) ).

cnf(i_0_1480,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[i_0_1257]) ).

cnf(i_0_1481,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_1258]) ).

fof(i_0_1482,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(i_0_1483,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact_thc1]) ).

cnf(i_0_1484,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact_th2]) ).

cnf(i_0_1485,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_1259]) ).

cnf(i_0_1486,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1260]) ).

cnf(i_0_1487,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1261]) ).

cnf(i_0_1488,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))),X2) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_1262]) ).

cnf(i_0_1489,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X2)))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X2)),
    inference(split_conjunct,[status(thm)],[i_0_1263]) ).

cnf(i_0_1490,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(split_conjunct,[status(thm)],[fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096]) ).

cnf(i_0_1491,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),esk45_0) ),
    inference(split_conjunct,[status(thm)],[i_0_1264]) ).

cnf(i_0_1492,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),v_d____) ),
    inference(split_conjunct,[status(thm)],[i_0_1265]) ).

cnf(i_0_1493,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_1266]) ).

cnf(i_0_1494,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096]) ).

cnf(i_0_1495,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(X1)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[i_0_1267]) ).

cnf(i_0_1496,plain,
    c_Groups_Ominus__class_Ominus(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)))),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,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_1268]) ).

cnf(i_0_1497,plain,
    c_Groups_Ominus__class_Ominus(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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,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_1269]) ).

cnf(i_0_1498,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),v_d____) ),
    inference(split_conjunct,[status(thm)],[i_0_1270]) ).

cnf(i_0_1499,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    inference(split_conjunct,[status(thm)],[fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096]) ).

cnf(i_0_1500,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    inference(split_conjunct,[status(thm)],[fact_th00]) ).

fof(i_0_1501,plain,
    ! [X3473,X3474,X3475,X3476,X3478] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3475,X3474,esk23_4(X3473,X3474,X3475,X3476))
        | ~ c_Orderings_Oord__class_Oless__eq(X3475,X3474,X3478)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3476,hAPP(X3473,X3478)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3476,hAPP(X3473,X3474))))
        | ~ class_RealVector_Oreal__normed__vector(X3476)
        | ~ class_Orderings_Oord(X3475) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3476,c_Groups_Ominus__class_Ominus(X3476,hAPP(X3473,X3474),hAPP(X3473,esk23_4(X3473,X3474,X3475,X3476)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(X3475,X3474,X3478)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3476,hAPP(X3473,X3478)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3476,hAPP(X3473,X3474))))
        | ~ class_RealVector_Oreal__normed__vector(X3476)
        | ~ class_Orderings_Oord(X3475) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemmaCauchy])])])])]) ).

cnf(i_0_1502,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk47_0)),
    inference(split_conjunct,[status(thm)],[i_0_1271]) ).

cnf(i_0_1503,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk46_0)),
    inference(split_conjunct,[status(thm)],[i_0_1272]) ).

cnf(i_0_1504,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
    inference(split_conjunct,[status(thm)],[fact_N2]) ).

cnf(i_0_1505,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,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[fact_e2]) ).

cnf(i_0_1506,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),
    inference(split_conjunct,[status(thm)],[fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096]) ).

cnf(i_0_1507,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,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)))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1273]) ).

cnf(i_0_1508,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_1274]) ).

cnf(i_0_1509,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_1275]) ).

cnf(i_0_1510,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_1276]) ).

cnf(i_0_1511,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_1266]) ).

cnf(i_0_1512,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,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_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1277]) ).

cnf(i_0_1513,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_1278]) ).

cnf(i_0_1514,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1),
    inference(split_conjunct,[status(thm)],[i_0_1279]) ).

cnf(i_0_1515,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    inference(split_conjunct,[status(thm)],[fact_th32]) ).

cnf(i_0_1516,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_1280]) ).

cnf(i_0_1517,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1281]) ).

cnf(i_0_1518,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(split_conjunct,[status(thm)],[fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096]) ).

fof(i_0_1519,plain,
    ! [X3095,X3096,X3097,X3098,X3099] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3097,X3098),X3096,X3095)
        | c_Orderings_Oord__class_Oless__eq(X3098,hAPP(X3096,X3099),hAPP(X3095,X3099))
        | ~ class_Orderings_Oord(X3098) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3098,hAPP(X3096,esk5_4(X3095,X3096,X3097,X3098)),hAPP(X3095,esk5_4(X3095,X3096,X3097,X3098)))
        | c_Orderings_Oord__class_Oless__eq(tc_fun(X3097,X3098),X3096,X3095)
        | ~ class_Orderings_Oord(X3098) ) ),
    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_1520,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1282]) ).

cnf(i_0_1521,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1283]) ).

cnf(i_0_1522,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,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_1284]) ).

fof(i_0_1523,plain,
    ! [X3059,X3060,X3061,X3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3062,X3061),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3060),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3059)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3062,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3060))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3061,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3059))))),
    inference(variable_rename,[status(thm)],[fact_abs__sum__triangle__ineq]) ).

cnf(i_0_1524,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3]) ).

fof(i_0_1525,plain,
    ! [X4769,X4770,X4771,X4772,X4773] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4773)
      | c_Groups_Ominus__class_Ominus(X4773,c_Groups_Otimes__class_Otimes(X4773,X4772,X4771),c_Groups_Otimes__class_Otimes(X4773,X4770,X4769)) = c_Groups_Oplus__class_Oplus(X4773,c_Groups_Oplus__class_Oplus(X4773,c_Groups_Otimes__class_Otimes(X4773,c_Groups_Ominus__class_Ominus(X4773,X4772,X4770),c_Groups_Ominus__class_Ominus(X4773,X4771,X4769)),c_Groups_Otimes__class_Otimes(X4773,c_Groups_Ominus__class_Ominus(X4773,X4772,X4770),X4769)),c_Groups_Otimes__class_Otimes(X4773,X4770,c_Groups_Ominus__class_Ominus(X4773,X4771,X4769))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).

fof(i_0_1526,plain,
    ! [X2493,X2494,X2495,X2496,X2497] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2497)
      | c_Orderings_Oord__class_Oless__eq(X2497,c_Groups_Oabs__class_Oabs(X2497,c_Groups_Ominus__class_Ominus(X2497,c_Groups_Oplus__class_Oplus(X2497,X2496,X2495),c_Groups_Oplus__class_Oplus(X2497,X2494,X2493))),c_Groups_Oplus__class_Oplus(X2497,c_Groups_Oabs__class_Oabs(X2497,c_Groups_Ominus__class_Ominus(X2497,X2496,X2494)),c_Groups_Oabs__class_Oabs(X2497,c_Groups_Ominus__class_Ominus(X2497,X2495,X2493)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).

fof(i_0_1527,plain,
    ! [X2485,X2486,X2487,X2488,X2489] :
      ( ~ class_RealVector_Oreal__normed__vector(X2489)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2489,c_Groups_Ominus__class_Ominus(X2489,c_Groups_Oplus__class_Oplus(X2489,X2488,X2487),c_Groups_Oplus__class_Oplus(X2489,X2486,X2485))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2489,c_Groups_Ominus__class_Ominus(X2489,X2488,X2486)),c_RealVector_Onorm__class_Onorm(X2489,c_Groups_Ominus__class_Ominus(X2489,X2487,X2485)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).

fof(i_0_1528,plain,
    ! [X4376,X4377,X4378,X4379] :
      ( ~ class_RealVector_Oreal__normed__field(X4379)
      | X4378 = c_Groups_Ozero__class_Ozero(X4379)
      | X4377 = c_Groups_Ozero__class_Ozero(X4379)
      | c_Rings_Oinverse__class_Odivide(X4379,c_Groups_Ominus__class_Ominus(X4379,c_Rings_Oinverse__class_Oinverse(X4379,X4378),c_Rings_Oinverse__class_Oinverse(X4379,X4377)),X4376) = c_Groups_Ouminus__class_Ouminus(X4379,c_Groups_Otimes__class_Otimes(X4379,c_Groups_Otimes__class_Otimes(X4379,c_Rings_Oinverse__class_Oinverse(X4379,X4378),c_Rings_Oinverse__class_Odivide(X4379,c_Groups_Ominus__class_Ominus(X4379,X4378,X4377),X4376)),c_Rings_Oinverse__class_Oinverse(X4379,X4377))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__inverse__lemma])]) ).

fof(i_0_1529,plain,
    ! [X4003,X4004,X4005,X4007] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk44_3(X4003,X4004,X4005))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4005) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4007,X4004)))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4007,X4004)),esk44_3(X4003,X4004,X4005))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X4003),X4007),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X4003),X4004))),X4005)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4005) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__cont])])])])]) ).

cnf(i_0_1530,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1285]) ).

cnf(i_0_1531,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk39_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_1286]) ).

cnf(i_0_1532,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk37_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_1287]) ).

cnf(i_0_1533,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk38_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_1288]) ).

cnf(i_0_1534,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk36_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_1289]) ).

cnf(i_0_1535,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))))),
    inference(split_conjunct,[status(thm)],[i_0_1290]) ).

cnf(i_0_1536,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2]) ).

cnf(i_0_1537,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).

cnf(i_0_1538,plain,
    ( c_Groups_Ominus__class_Ominus(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_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1291]) ).

cnf(i_0_1539,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk29_2(X3,X2))))
    | ~ 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_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk28_3(X3,X2,X1))),X1)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1292]) ).

cnf(i_0_1540,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(esk33_2(X3,X2))))
    | ~ 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_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk32_3(X3,X2,X1))),X1)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1293]) ).

cnf(i_0_1541,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_1294]) ).

cnf(i_0_1542,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_1543,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk35_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk34_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1293]) ).

cnf(i_0_1544,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk31_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk30_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X4)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1292]) ).

fof(i_0_1545,plain,
    ! [X3287,X3288,X3289] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3288),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3288)))),X3287)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3287) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk8_1(X3289)),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3289) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk8_1(X3289))))),X3289)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3289) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096])])])])])]) ).

cnf(i_0_1546,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_2(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk34_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1293]) ).

cnf(i_0_1547,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_2(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk30_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X3)))
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1292]) ).

fof(i_0_1548,plain,
    ! [X2510,X2511,X2512,X2513] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2513,X2512)),X2511)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2512,X2510)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2513,X2510)),X2511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ath2])]) ).

cnf(i_0_1549,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1295]) ).

fof(i_0_1550,plain,
    ! [X3877] :
      ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3877) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3877,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3877,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3877,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3877,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unimodular__reduce__norm])]) ).

cnf(i_0_1551,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1295]) ).

cnf(i_0_1552,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_1296]) ).

cnf(i_0_1553,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_1297]) ).

cnf(i_0_1554,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_1298]) ).

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_1299]) ).

fof(i_0_1556,plain,
    ! [X4380,X4381,X4382] :
      ( ~ class_Rings_Odivision__ring(X4382)
      | X4381 = c_Groups_Ozero__class_Ozero(X4382)
      | X4380 = c_Groups_Ozero__class_Ozero(X4382)
      | c_Groups_Ominus__class_Ominus(X4382,c_Rings_Oinverse__class_Oinverse(X4382,X4381),c_Rings_Oinverse__class_Oinverse(X4382,X4380)) = c_Groups_Ouminus__class_Ouminus(X4382,c_Groups_Otimes__class_Otimes(X4382,c_Groups_Otimes__class_Otimes(X4382,c_Rings_Oinverse__class_Oinverse(X4382,X4381),c_Groups_Ominus__class_Ominus(X4382,X4381,X4380)),c_Rings_Oinverse__class_Oinverse(X4382,X4380))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oinverse__diff__inverse])]) ).

fof(i_0_1557,plain,
    ! [X3937,X3938] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3938),c_RealDef_Oreal(tc_Nat_Onat,X3937)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3938,X3937))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__div3]) ).

fof(i_0_1558,plain,
    ! [X3935,X3936] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3936),c_RealDef_Oreal(tc_Nat_Onat,X3935)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3936,X3935)))),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__div2]) ).

fof(i_0_1559,plain,
    ! [X4764,X4765,X4766,X4767,X4768] :
      ( ~ class_Rings_Oring(X4768)
      | c_Groups_Ominus__class_Ominus(X4768,c_Groups_Otimes__class_Otimes(X4768,X4767,X4766),c_Groups_Otimes__class_Otimes(X4768,X4765,X4764)) = c_Groups_Oplus__class_Oplus(X4768,c_Groups_Otimes__class_Otimes(X4768,X4767,c_Groups_Ominus__class_Ominus(X4768,X4766,X4764)),c_Groups_Otimes__class_Otimes(X4768,c_Groups_Ominus__class_Ominus(X4768,X4767,X4765),X4764)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).

cnf(i_0_1560,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1300]) ).

cnf(i_0_1561,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1301]) ).

cnf(i_0_1562,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_1302]) ).

cnf(i_0_1563,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_1303]) ).

fof(i_0_1564,plain,
    ! [X4780,X4781,X4782,X4783,X4784,X4785] :
      ( ( c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,X4784,X4783),X4782) != c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,X4781,X4783),X4780)
        | c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,c_Groups_Ominus__class_Ominus(X4785,X4784,X4781),X4783),X4782) = X4780
        | ~ class_Rings_Oring(X4785) )
      & ( c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,c_Groups_Ominus__class_Ominus(X4785,X4784,X4781),X4783),X4782) != X4780
        | c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,X4784,X4783),X4782) = c_Groups_Oplus__class_Oplus(X4785,c_Groups_Otimes__class_Otimes(X4785,X4781,X4783),X4780)
        | ~ class_Rings_Oring(X4785) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).

fof(i_0_1565,plain,
    ! [X4774,X4775,X4776,X4777,X4778,X4779] :
      ( ( c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,X4778,X4777),X4776) != c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,X4775,X4777),X4774)
        | X4776 = c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,c_Groups_Ominus__class_Ominus(X4779,X4775,X4778),X4777),X4774)
        | ~ class_Rings_Oring(X4779) )
      & ( X4776 != c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,c_Groups_Ominus__class_Ominus(X4779,X4775,X4778),X4777),X4774)
        | c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,X4778,X4777),X4776) = c_Groups_Oplus__class_Oplus(X4779,c_Groups_Otimes__class_Otimes(X4779,X4775,X4777),X4774)
        | ~ class_Rings_Oring(X4779) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).

cnf(i_0_1566,plain,
    ( c_Groups_Ominus__class_Ominus(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),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1304]) ).

fof(i_0_1567,plain,
    ! [X4457,X4458,X4459,X4460,X4461] :
      ( ~ class_Rings_Osemiring(X4461)
      | c_Groups_Oplus__class_Oplus(X4461,c_Groups_Otimes__class_Otimes(X4461,X4460,X4459),c_Groups_Oplus__class_Oplus(X4461,c_Groups_Otimes__class_Otimes(X4461,X4458,X4459),X4457)) = c_Groups_Oplus__class_Oplus(X4461,c_Groups_Otimes__class_Otimes(X4461,c_Groups_Oplus__class_Oplus(X4461,X4460,X4458),X4459),X4457) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_1568,plain,
    ! [X4532,X4533,X4534,X4535,X4536] :
      ( ( X4535 = X4534
        | X4533 = X4532
        | c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4533),c_Groups_Otimes__class_Otimes(X4536,X4534,X4532)) != c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4532),c_Groups_Otimes__class_Otimes(X4536,X4534,X4533))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4536) )
      & ( X4535 != X4534
        | c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4533),c_Groups_Otimes__class_Otimes(X4536,X4534,X4532)) = c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4532),c_Groups_Otimes__class_Otimes(X4536,X4534,X4533))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4536) )
      & ( X4533 != X4532
        | c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4533),c_Groups_Otimes__class_Otimes(X4536,X4534,X4532)) = c_Groups_Oplus__class_Oplus(X4536,c_Groups_Otimes__class_Otimes(X4536,X4535,X4532),c_Groups_Otimes__class_Otimes(X4536,X4534,X4533))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4536) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_1569,plain,
    ! [X4545,X4546,X4547,X4548,X4549] :
      ( ( c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4547),c_Groups_Otimes__class_Otimes(X4549,X4546,X4545)) != c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4545),c_Groups_Otimes__class_Otimes(X4549,X4546,X4547))
        | X4548 = X4546
        | X4547 = X4545
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4549) )
      & ( X4548 != X4546
        | c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4547),c_Groups_Otimes__class_Otimes(X4549,X4546,X4545)) = c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4545),c_Groups_Otimes__class_Otimes(X4549,X4546,X4547))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4549) )
      & ( X4547 != X4545
        | c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4547),c_Groups_Otimes__class_Otimes(X4549,X4546,X4545)) = c_Groups_Oplus__class_Oplus(X4549,c_Groups_Otimes__class_Otimes(X4549,X4548,X4545),c_Groups_Otimes__class_Otimes(X4549,X4546,X4547))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4549) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

cnf(i_0_1570,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_1305]) ).

cnf(i_0_1571,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_1306]) ).

fof(i_0_1572,plain,
    ! [X3304,X3305,X3306,X3307] :
      ( ( c_Orderings_Oord__class_Oless(X3307,c_Groups_Ominus__class_Ominus(X3307,X3305,X3304),X3306)
        | ~ c_Orderings_Oord__class_Oless(X3307,c_Groups_Oabs__class_Oabs(X3307,c_Groups_Ominus__class_Ominus(X3307,X3306,X3305)),X3304)
        | ~ class_Rings_Olinordered__idom(X3307) )
      & ( c_Orderings_Oord__class_Oless(X3307,X3306,c_Groups_Oplus__class_Oplus(X3307,X3305,X3304))
        | ~ c_Orderings_Oord__class_Oless(X3307,c_Groups_Oabs__class_Oabs(X3307,c_Groups_Ominus__class_Ominus(X3307,X3306,X3305)),X3304)
        | ~ class_Rings_Olinordered__idom(X3307) )
      & ( ~ c_Orderings_Oord__class_Oless(X3307,c_Groups_Ominus__class_Ominus(X3307,X3305,X3304),X3306)
        | ~ c_Orderings_Oord__class_Oless(X3307,X3306,c_Groups_Oplus__class_Oplus(X3307,X3305,X3304))
        | c_Orderings_Oord__class_Oless(X3307,c_Groups_Oabs__class_Oabs(X3307,c_Groups_Ominus__class_Ominus(X3307,X3306,X3305)),X3304)
        | ~ class_Rings_Olinordered__idom(X3307) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).

cnf(i_0_1573,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_1307]) ).

cnf(i_0_1574,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_1308]) ).

cnf(i_0_1575,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_1309]) ).

cnf(i_0_1576,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_1310]) ).

cnf(i_0_1577,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_1311]) ).

cnf(i_0_1578,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_1312]) ).

cnf(i_0_1579,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_1313]) ).

cnf(i_0_1580,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_1314]) ).

cnf(i_0_1581,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_1296]) ).

cnf(i_0_1582,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_1297]) ).

cnf(i_0_1583,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_1298]) ).

cnf(i_0_1584,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_1299]) ).

fof(i_0_1585,plain,
    ! [X2501,X2502,X2503] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2503)
      | c_Orderings_Oord__class_Oless__eq(X2503,c_Groups_Oabs__class_Oabs(X2503,c_Groups_Ominus__class_Ominus(X2503,c_Groups_Oabs__class_Oabs(X2503,X2502),c_Groups_Oabs__class_Oabs(X2503,X2501))),c_Groups_Oabs__class_Oabs(X2503,c_Groups_Ominus__class_Ominus(X2503,X2502,X2501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).

fof(i_0_1586,plain,
    ! [X2476,X2477,X2478] :
      ( ~ class_RealVector_Oreal__normed__vector(X2478)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2478,X2477),c_RealVector_Onorm__class_Onorm(X2478,X2476))),c_RealVector_Onorm__class_Onorm(X2478,c_Groups_Ominus__class_Ominus(X2478,X2477,X2476))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).

fof(i_0_1587,plain,
    ! [X3763,X3764,X3765] :
      ( ~ class_Fields_Olinordered__field(X3765)
      | ~ c_Orderings_Oord__class_Oless(X3765,X3764,X3763)
      | c_Orderings_Oord__class_Oless(X3765,c_Rings_Oinverse__class_Odivide(X3765,c_Groups_Oplus__class_Oplus(X3765,X3764,X3763),c_Groups_Oplus__class_Oplus(X3765,c_Groups_Oone__class_Oone(X3765),c_Groups_Oone__class_Oone(X3765))),X3763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_1588,plain,
    ! [X3766,X3767,X3768] :
      ( ~ class_Fields_Olinordered__field(X3768)
      | ~ c_Orderings_Oord__class_Oless(X3768,X3767,X3766)
      | c_Orderings_Oord__class_Oless(X3768,X3767,c_Rings_Oinverse__class_Odivide(X3768,c_Groups_Oplus__class_Oplus(X3768,X3767,X3766),c_Groups_Oplus__class_Oplus(X3768,c_Groups_Oone__class_Oone(X3768),c_Groups_Oone__class_Oone(X3768)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

cnf(i_0_1589,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_1315]) ).

cnf(i_0_1590,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_1316]) ).

cnf(i_0_1591,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1317]) ).

cnf(i_0_1592,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1318]) ).

cnf(i_0_1593,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
    inference(split_conjunct,[status(thm)],[fact_th000_I3_J]) ).

fof(i_0_1594,plain,
    ! [X2614,X2615] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2615,X2614)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2615)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2614)),
    inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).

fof(i_0_1595,plain,
    ! [X2515,X2516] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2516),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2516,X2515)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2515))),
    inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).

cnf(i_0_1596,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1319]) ).

cnf(i_0_1597,plain,
    ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1320]) ).

cnf(i_0_1598,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1321]) ).

cnf(i_0_1599,plain,
    ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1322]) ).

cnf(i_0_1600,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1323]) ).

fof(i_0_1601,plain,
    ! [X3345,X3346,X3347,X3348,X3349,X3350,X3351] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3346,X3345)
        | hBOOL(hAPP(X3347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X3347,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3346,X3345))) )
      & ( X3346 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3345,X3348)
        | hBOOL(hAPP(X3347,X3348))
        | ~ hBOOL(hAPP(X3347,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3346,X3345))) )
      & ( X3350 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3349,esk15_3(X3349,X3350,X3351))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3350,X3349)
        | hBOOL(hAPP(X3351,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3350,X3349))) )
      & ( ~ hBOOL(hAPP(X3351,esk15_3(X3349,X3350,X3351)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3350,X3349)
        | hBOOL(hAPP(X3351,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3350,X3349))) )
      & ( X3350 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3349,esk15_3(X3349,X3350,X3351))
        | ~ hBOOL(hAPP(X3351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X3351,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3350,X3349))) )
      & ( ~ hBOOL(hAPP(X3351,esk15_3(X3349,X3350,X3351)))
        | ~ hBOOL(hAPP(X3351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X3351,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3350,X3349))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1324])])])])])]) ).

fof(i_0_1602,plain,
    ! [X3337,X3338,X3339,X3340,X3341,X3342,X3343] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3338,X3337)
        | hBOOL(hAPP(X3339,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X3339,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3338,X3337))) )
      & ( X3338 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3337,X3340)
        | hBOOL(hAPP(X3339,X3340))
        | ~ hBOOL(hAPP(X3339,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3338,X3337))) )
      & ( X3342 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3341,esk14_3(X3341,X3342,X3343))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3342,X3341)
        | hBOOL(hAPP(X3343,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3342,X3341))) )
      & ( ~ hBOOL(hAPP(X3343,esk14_3(X3341,X3342,X3343)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3342,X3341)
        | hBOOL(hAPP(X3343,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3342,X3341))) )
      & ( X3342 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3341,esk14_3(X3341,X3342,X3343))
        | ~ hBOOL(hAPP(X3343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X3343,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3342,X3341))) )
      & ( ~ hBOOL(hAPP(X3343,esk14_3(X3341,X3342,X3343)))
        | ~ hBOOL(hAPP(X3343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X3343,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3342,X3341))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__split])])])])])]) ).

fof(i_0_1603,plain,
    ! [X2648,X2650] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2648)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk4_1(X2648),X2650)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X2650)),v_z____)),X2648) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fz_I2_J])])])]) ).

fof(i_0_1604,plain,
    ! [X4327] :
      ( ( ~ 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),X4327),X4327),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4327,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4327,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),X4327),X4327),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).

cnf(i_0_1605,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_1325]) ).

fof(i_0_1606,plain,
    ! [X4515,X4516,X4517,X4518,X4519] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4519)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4519,X4518),X4517)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4519,X4516),X4515)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4519,c_Groups_Otimes__class_Otimes(X4519,X4518,X4516)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4517,X4515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).

fof(i_0_1607,plain,
    ! [X3156,X3157,X3158,X3159,X3160] :
      ( ~ class_RealVector_Oreal__normed__vector(X3160)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3160,X3159),X3158)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3160,X3157),X3156)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3160,c_Groups_Oplus__class_Oplus(X3160,X3159,X3157)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3158,X3156)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).

cnf(i_0_1608,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_1326]) ).

cnf(i_0_1609,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_1327]) ).

cnf(i_0_1610,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_1328]) ).

cnf(i_0_1611,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_1329]) ).

cnf(i_0_1612,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_1330]) ).

fof(i_0_1613,plain,
    ! [X3830,X3831,X3832,X3833,X3834] :
      ( ~ class_Fields_Olinordered__field(X3834)
      | ~ c_Orderings_Oord__class_Oless(X3834,c_Groups_Ozero__class_Ozero(X3834),X3833)
      | ~ c_Orderings_Oord__class_Oless__eq(X3834,X3833,X3832)
      | ~ c_Orderings_Oord__class_Oless(X3834,c_Groups_Ozero__class_Ozero(X3834),X3831)
      | ~ c_Orderings_Oord__class_Oless(X3834,X3831,X3830)
      | c_Orderings_Oord__class_Oless(X3834,c_Rings_Oinverse__class_Odivide(X3834,X3833,X3830),c_Rings_Oinverse__class_Odivide(X3834,X3832,X3831)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

fof(i_0_1614,plain,
    ! [X3835,X3836,X3837,X3838,X3839] :
      ( ~ class_Fields_Olinordered__field(X3839)
      | ~ c_Orderings_Oord__class_Oless__eq(X3839,c_Groups_Ozero__class_Ozero(X3839),X3838)
      | ~ c_Orderings_Oord__class_Oless(X3839,X3838,X3837)
      | ~ c_Orderings_Oord__class_Oless(X3839,c_Groups_Ozero__class_Ozero(X3839),X3836)
      | ~ c_Orderings_Oord__class_Oless__eq(X3839,X3836,X3835)
      | c_Orderings_Oord__class_Oless(X3839,c_Rings_Oinverse__class_Odivide(X3839,X3838,X3835),c_Rings_Oinverse__class_Odivide(X3839,X3837,X3836)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_1615,plain,
    ! [X4669,X4670,X4671,X4672,X4673] :
      ( ~ class_Rings_Oordered__semiring(X4673)
      | ~ c_Orderings_Oord__class_Oless__eq(X4673,X4672,X4671)
      | ~ c_Orderings_Oord__class_Oless__eq(X4673,X4670,X4669)
      | ~ c_Orderings_Oord__class_Oless__eq(X4673,c_Groups_Ozero__class_Ozero(X4673),X4672)
      | ~ c_Orderings_Oord__class_Oless__eq(X4673,c_Groups_Ozero__class_Ozero(X4673),X4670)
      | c_Orderings_Oord__class_Oless__eq(X4673,c_Groups_Otimes__class_Otimes(X4673,X4672,X4670),c_Groups_Otimes__class_Otimes(X4673,X4671,X4669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_1616,plain,
    ! [X4674,X4675,X4676,X4677,X4678] :
      ( ~ class_Rings_Oordered__semiring(X4678)
      | ~ c_Orderings_Oord__class_Oless__eq(X4678,X4677,X4676)
      | ~ c_Orderings_Oord__class_Oless__eq(X4678,X4675,X4674)
      | ~ c_Orderings_Oord__class_Oless__eq(X4678,c_Groups_Ozero__class_Ozero(X4678),X4676)
      | ~ c_Orderings_Oord__class_Oless__eq(X4678,c_Groups_Ozero__class_Ozero(X4678),X4675)
      | c_Orderings_Oord__class_Oless__eq(X4678,c_Groups_Otimes__class_Otimes(X4678,X4677,X4675),c_Groups_Otimes__class_Otimes(X4678,X4676,X4674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

fof(i_0_1617,plain,
    ! [X3840,X3841,X3842,X3843,X3844] :
      ( ~ class_Fields_Olinordered__field(X3844)
      | ~ c_Orderings_Oord__class_Oless__eq(X3844,c_Groups_Ozero__class_Ozero(X3844),X3843)
      | ~ c_Orderings_Oord__class_Oless__eq(X3844,X3843,X3842)
      | ~ c_Orderings_Oord__class_Oless(X3844,c_Groups_Ozero__class_Ozero(X3844),X3841)
      | ~ c_Orderings_Oord__class_Oless__eq(X3844,X3841,X3840)
      | c_Orderings_Oord__class_Oless__eq(X3844,c_Rings_Oinverse__class_Odivide(X3844,X3843,X3840),c_Rings_Oinverse__class_Odivide(X3844,X3842,X3841)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_1618,plain,
    ! [X3438,X3439,X3440] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3439,X3440),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3438,X3440))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3439,X3438)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3440,X3438)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3440,X3439) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3439,X3438)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3439,X3440),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3438,X3440))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3440,X3438)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3440,X3439) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).

fof(i_0_1619,plain,
    ! [X3196,X3197,X3198] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3197,X3198),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3196,X3198))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3197,X3196)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3198,X3196)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3198,X3197) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3197,X3196)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3197,X3198),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3196,X3198))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3198,X3196)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3198,X3197) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).

fof(i_0_1620,plain,
    ! [X4190,X4191,X4192,X4193] :
      ( ~ class_Int_Onumber__ring(X4193)
      | c_Groups_Oplus__class_Oplus(X4193,c_Int_Onumber__class_Onumber__of(X4193,X4192),c_Groups_Ominus__class_Ominus(X4193,X4191,c_Int_Onumber__class_Onumber__of(X4193,X4190))) = c_Groups_Oplus__class_Oplus(X4193,c_Int_Onumber__class_Onumber__of(X4193,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4192,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4190))),X4191) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).

fof(i_0_1621,plain,
    ! [X2611,X2612,X2613] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2613,X2612)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2612,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2613,X2611))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2612,X2613)),X2611) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ath])]) ).

cnf(i_0_1622,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) = c_Divides_Odiv__class_Odiv(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_1331]) ).

cnf(i_0_1623,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_1332]) ).

cnf(i_0_1624,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1))
    | ~ 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,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1333]) ).

fof(i_0_1625,plain,
    ! [X4730,X4731,X4732,X4733] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4733,c_Groups_Otimes__class_Otimes(X4733,X4732,X4731),c_Groups_Otimes__class_Otimes(X4733,X4732,X4730))
        | c_Orderings_Oord__class_Oless(X4733,X4731,X4730)
        | ~ c_Orderings_Oord__class_Oless(X4733,c_Groups_Ozero__class_Ozero(X4733),X4732)
        | ~ class_Rings_Olinordered__ring__strict(X4733) )
      & ( ~ c_Orderings_Oord__class_Oless(X4733,X4731,X4730)
        | c_Orderings_Oord__class_Oless(X4733,c_Groups_Otimes__class_Otimes(X4733,X4732,X4731),c_Groups_Otimes__class_Otimes(X4733,X4732,X4730))
        | ~ c_Orderings_Oord__class_Oless(X4733,c_Groups_Ozero__class_Ozero(X4733),X4732)
        | ~ class_Rings_Olinordered__ring__strict(X4733) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

fof(i_0_1626,plain,
    ! [X4711,X4712,X4713,X4714] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4714,c_Groups_Otimes__class_Otimes(X4714,X4713,X4712),c_Groups_Otimes__class_Otimes(X4714,X4713,X4711))
        | c_Orderings_Oord__class_Oless(X4714,X4711,X4712)
        | ~ c_Orderings_Oord__class_Oless(X4714,X4713,c_Groups_Ozero__class_Ozero(X4714))
        | ~ class_Rings_Olinordered__ring__strict(X4714) )
      & ( ~ c_Orderings_Oord__class_Oless(X4714,X4711,X4712)
        | c_Orderings_Oord__class_Oless(X4714,c_Groups_Otimes__class_Otimes(X4714,X4713,X4712),c_Groups_Otimes__class_Otimes(X4714,X4713,X4711))
        | ~ c_Orderings_Oord__class_Oless(X4714,X4713,c_Groups_Ozero__class_Ozero(X4714))
        | ~ class_Rings_Olinordered__ring__strict(X4714) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_1627,plain,
    ! [X4558,X4559,X4560] :
      ( ~ class_Fields_Ofield(X4560)
      | X4559 = c_Groups_Ozero__class_Ozero(X4560)
      | X4558 = c_Groups_Ozero__class_Ozero(X4560)
      | c_Groups_Oplus__class_Oplus(X4560,c_Rings_Oinverse__class_Oinverse(X4560,X4559),c_Rings_Oinverse__class_Oinverse(X4560,X4558)) = c_Groups_Otimes__class_Otimes(X4560,c_Groups_Otimes__class_Otimes(X4560,c_Groups_Oplus__class_Oplus(X4560,X4559,X4558),c_Rings_Oinverse__class_Oinverse(X4560,X4559)),c_Rings_Oinverse__class_Oinverse(X4560,X4558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).

fof(i_0_1628,plain,
    ! [X4383,X4384,X4385] :
      ( ~ class_Rings_Odivision__ring(X4385)
      | X4384 = c_Groups_Ozero__class_Ozero(X4385)
      | X4383 = c_Groups_Ozero__class_Ozero(X4385)
      | c_Groups_Ominus__class_Ominus(X4385,c_Rings_Oinverse__class_Oinverse(X4385,X4384),c_Rings_Oinverse__class_Oinverse(X4385,X4383)) = c_Groups_Otimes__class_Otimes(X4385,c_Groups_Otimes__class_Otimes(X4385,c_Rings_Oinverse__class_Oinverse(X4385,X4384),c_Groups_Ominus__class_Ominus(X4385,X4383,X4384)),c_Rings_Oinverse__class_Oinverse(X4385,X4383)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__diff])]) ).

fof(i_0_1629,plain,
    ! [X4525,X4526,X4527] :
      ( ~ class_Rings_Odivision__ring(X4527)
      | X4526 = c_Groups_Ozero__class_Ozero(X4527)
      | X4525 = c_Groups_Ozero__class_Ozero(X4527)
      | c_Groups_Oplus__class_Oplus(X4527,c_Rings_Oinverse__class_Oinverse(X4527,X4526),c_Rings_Oinverse__class_Oinverse(X4527,X4525)) = c_Groups_Otimes__class_Otimes(X4527,c_Groups_Otimes__class_Otimes(X4527,c_Rings_Oinverse__class_Oinverse(X4527,X4526),c_Groups_Oplus__class_Oplus(X4527,X4526,X4525)),c_Rings_Oinverse__class_Oinverse(X4527,X4525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).

fof(i_0_1630,plain,
    ! [X4798,X4799,X4800,X4801] :
      ( ~ class_Int_Onumber(X4801)
      | ~ class_Rings_Oring(X4801)
      | c_Groups_Otimes__class_Otimes(X4801,c_Groups_Ominus__class_Ominus(X4801,X4800,X4799),c_Int_Onumber__class_Onumber__of(X4801,X4798)) = c_Groups_Ominus__class_Ominus(X4801,c_Groups_Otimes__class_Otimes(X4801,X4800,c_Int_Onumber__class_Onumber__of(X4801,X4798)),c_Groups_Otimes__class_Otimes(X4801,X4799,c_Int_Onumber__class_Onumber__of(X4801,X4798))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).

fof(i_0_1631,plain,
    ! [X4760,X4761,X4762,X4763] :
      ( ~ class_Int_Onumber(X4763)
      | ~ class_Rings_Osemiring(X4763)
      | c_Groups_Otimes__class_Otimes(X4763,c_Groups_Oplus__class_Oplus(X4763,X4762,X4761),c_Int_Onumber__class_Onumber__of(X4763,X4760)) = c_Groups_Oplus__class_Oplus(X4763,c_Groups_Otimes__class_Otimes(X4763,X4762,c_Int_Onumber__class_Onumber__of(X4763,X4760)),c_Groups_Otimes__class_Otimes(X4763,X4761,c_Int_Onumber__class_Onumber__of(X4763,X4760))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_1632,plain,
    ! [X4794,X4795,X4796,X4797] :
      ( ~ class_Int_Onumber(X4797)
      | ~ class_Rings_Oring(X4797)
      | c_Groups_Otimes__class_Otimes(X4797,c_Int_Onumber__class_Onumber__of(X4797,X4796),c_Groups_Ominus__class_Ominus(X4797,X4795,X4794)) = c_Groups_Ominus__class_Ominus(X4797,c_Groups_Otimes__class_Otimes(X4797,c_Int_Onumber__class_Onumber__of(X4797,X4796),X4795),c_Groups_Otimes__class_Otimes(X4797,c_Int_Onumber__class_Onumber__of(X4797,X4796),X4794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).

fof(i_0_1633,plain,
    ! [X4756,X4757,X4758,X4759] :
      ( ~ class_Int_Onumber(X4759)
      | ~ class_Rings_Osemiring(X4759)
      | c_Groups_Otimes__class_Otimes(X4759,c_Int_Onumber__class_Onumber__of(X4759,X4758),c_Groups_Oplus__class_Oplus(X4759,X4757,X4756)) = c_Groups_Oplus__class_Oplus(X4759,c_Groups_Otimes__class_Otimes(X4759,c_Int_Onumber__class_Onumber__of(X4759,X4758),X4757),c_Groups_Otimes__class_Otimes(X4759,c_Int_Onumber__class_Onumber__of(X4759,X4758),X4756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

cnf(i_0_1634,plain,
    ( c_SEQ_Osubseq(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk27_1(X1)),hAPP(X1,c_Nat_OSuc(esk27_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_1334]) ).

fof(i_0_1635,plain,
    ! [X3295] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3295),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3295)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk10_0),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk10_0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096])])])])]) ).

fof(i_0_1636,plain,
    ! [X3309] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk13_0,X3309)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3309)),v_z____)),v_d____) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).

fof(i_0_1637,plain,
    ! [X3286] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_0,X3286)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X3286)),v_z____)),v_d____) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096])])]) ).

fof(i_0_1638,plain,
    ! [X2610] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X2610)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X2610)),v_z____)),v_d____) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_N1])]) ).

cnf(i_0_1639,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_1307]) ).

cnf(i_0_1640,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_1308]) ).

cnf(i_0_1641,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_1309]) ).

cnf(i_0_1642,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_1310]) ).

cnf(i_0_1643,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_1311]) ).

cnf(i_0_1644,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_1312]) ).

cnf(i_0_1645,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_1313]) ).

cnf(i_0_1646,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_1314]) ).

cnf(i_0_1647,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1335]) ).

cnf(i_0_1648,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1336]) ).

fof(i_0_1649,plain,
    ! [X4734,X4735,X4736,X4737] :
      ( ( c_Orderings_Oord__class_Oless(X4737,X4736,c_Groups_Ozero__class_Ozero(X4737))
        | c_Orderings_Oord__class_Oless(X4737,c_Groups_Ozero__class_Ozero(X4737),X4736)
        | ~ c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) )
      & ( c_Orderings_Oord__class_Oless(X4737,X4734,X4735)
        | c_Orderings_Oord__class_Oless(X4737,c_Groups_Ozero__class_Ozero(X4737),X4736)
        | ~ c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) )
      & ( c_Orderings_Oord__class_Oless(X4737,X4736,c_Groups_Ozero__class_Ozero(X4737))
        | c_Orderings_Oord__class_Oless(X4737,X4735,X4734)
        | ~ c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) )
      & ( c_Orderings_Oord__class_Oless(X4737,X4734,X4735)
        | c_Orderings_Oord__class_Oless(X4737,X4735,X4734)
        | ~ c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) )
      & ( ~ c_Orderings_Oord__class_Oless(X4737,c_Groups_Ozero__class_Ozero(X4737),X4736)
        | ~ c_Orderings_Oord__class_Oless(X4737,X4735,X4734)
        | c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) )
      & ( ~ c_Orderings_Oord__class_Oless(X4737,X4736,c_Groups_Ozero__class_Ozero(X4737))
        | ~ c_Orderings_Oord__class_Oless(X4737,X4734,X4735)
        | c_Orderings_Oord__class_Oless(X4737,c_Groups_Otimes__class_Otimes(X4737,X4736,X4735),c_Groups_Otimes__class_Otimes(X4737,X4736,X4734))
        | ~ class_Rings_Olinordered__ring__strict(X4737) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_1650,plain,
    ! [X4738,X4739,X4740,X4741] :
      ( ( c_Orderings_Oord__class_Oless(X4741,X4739,c_Groups_Ozero__class_Ozero(X4741))
        | c_Orderings_Oord__class_Oless(X4741,c_Groups_Ozero__class_Ozero(X4741),X4739)
        | ~ c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) )
      & ( c_Orderings_Oord__class_Oless(X4741,X4738,X4740)
        | c_Orderings_Oord__class_Oless(X4741,c_Groups_Ozero__class_Ozero(X4741),X4739)
        | ~ c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) )
      & ( c_Orderings_Oord__class_Oless(X4741,X4739,c_Groups_Ozero__class_Ozero(X4741))
        | c_Orderings_Oord__class_Oless(X4741,X4740,X4738)
        | ~ c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) )
      & ( c_Orderings_Oord__class_Oless(X4741,X4738,X4740)
        | c_Orderings_Oord__class_Oless(X4741,X4740,X4738)
        | ~ c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) )
      & ( ~ c_Orderings_Oord__class_Oless(X4741,c_Groups_Ozero__class_Ozero(X4741),X4739)
        | ~ c_Orderings_Oord__class_Oless(X4741,X4740,X4738)
        | c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) )
      & ( ~ c_Orderings_Oord__class_Oless(X4741,X4739,c_Groups_Ozero__class_Ozero(X4741))
        | ~ c_Orderings_Oord__class_Oless(X4741,X4738,X4740)
        | c_Orderings_Oord__class_Oless(X4741,c_Groups_Otimes__class_Otimes(X4741,X4740,X4739),c_Groups_Otimes__class_Otimes(X4741,X4738,X4739))
        | ~ class_Rings_Olinordered__ring__strict(X4741) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_1651,plain,
    ! [X3972,X3973,X3974,X3975,X3976] :
      ( ~ class_Groups_Oab__group__add(X3976)
      | c_Groups_Ominus__class_Ominus(X3976,c_Groups_Oplus__class_Oplus(X3976,X3975,X3974),c_Groups_Oplus__class_Oplus(X3976,X3973,X3972)) = c_Groups_Oplus__class_Oplus(X3976,c_Groups_Ominus__class_Ominus(X3976,X3975,X3973),c_Groups_Ominus__class_Ominus(X3976,X3974,X3972)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).

fof(i_0_1652,plain,
    ! [X3731,X3732,X3733,X3734,X3735] :
      ( ~ class_Rings_Ocomm__semiring__1(X3735)
      | c_Groups_Oplus__class_Oplus(X3735,c_Groups_Oplus__class_Oplus(X3735,X3734,X3733),c_Groups_Oplus__class_Oplus(X3735,X3732,X3731)) = c_Groups_Oplus__class_Oplus(X3735,c_Groups_Oplus__class_Oplus(X3735,X3734,X3732),c_Groups_Oplus__class_Oplus(X3735,X3733,X3731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_1653,plain,
    ! [X4386,X4387,X4388,X4389] :
      ( ~ class_Int_Onumber__ring(X4389)
      | c_Groups_Otimes__class_Otimes(X4389,c_Int_Onumber__class_Onumber__of(X4389,X4388),c_Groups_Otimes__class_Otimes(X4389,c_Int_Onumber__class_Onumber__of(X4389,X4387),X4386)) = c_Groups_Otimes__class_Otimes(X4389,c_Int_Onumber__class_Onumber__of(X4389,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4388,X4387)),X4386) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_1654,plain,
    ! [X4194,X4195,X4196,X4197] :
      ( ~ class_Int_Onumber__ring(X4197)
      | c_Groups_Oplus__class_Oplus(X4197,c_Int_Onumber__class_Onumber__of(X4197,X4196),c_Groups_Ominus__class_Ominus(X4197,c_Int_Onumber__class_Onumber__of(X4197,X4195),X4194)) = c_Groups_Ominus__class_Ominus(X4197,c_Int_Onumber__class_Onumber__of(X4197,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4196,X4195)),X4194) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).

fof(i_0_1655,plain,
    ! [X4092,X4093,X4094,X4095] :
      ( ~ class_Int_Onumber__ring(X4095)
      | c_Groups_Oplus__class_Oplus(X4095,c_Int_Onumber__class_Onumber__of(X4095,X4094),c_Groups_Oplus__class_Oplus(X4095,c_Int_Onumber__class_Onumber__of(X4095,X4093),X4092)) = c_Groups_Oplus__class_Oplus(X4095,c_Int_Onumber__class_Onumber__of(X4095,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4094,X4093)),X4092) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_1656,plain,
    ! [X3301] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3301),v_r)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk12_0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3301))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1337])])])]) ).

fof(i_0_1657,plain,
    ! [X4744,X4745,X4746,X4747,X4748,X4749] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4749)
      | X4748 = c_Groups_Ozero__class_Ozero(X4749)
      | X4747 != X4746
      | X4745 = X4744
      | c_Groups_Oplus__class_Oplus(X4749,X4747,c_Groups_Otimes__class_Otimes(X4749,X4748,X4745)) != c_Groups_Oplus__class_Oplus(X4749,X4746,c_Groups_Otimes__class_Otimes(X4749,X4748,X4744)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_1658,plain,
    ! [X4252,X4253,X4254] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4254)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4253)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4253,X4252)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4254,X4252),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4254,X4253)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).

fof(i_0_1659,plain,
    ! [X4241,X4242,X4243] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4243,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4242)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4242,X4241)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4243,X4242),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4243,X4241)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).

cnf(i_0_1660,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1338]) ).

cnf(i_0_1661,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_1339]) ).

cnf(i_0_1662,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1322]) ).

cnf(i_0_1663,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1323]) ).

cnf(i_0_1664,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1320]) ).

cnf(i_0_1665,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1321]) ).

fof(i_0_1666,plain,
    ! [X3291,X3292,X3293] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3292),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3292)),X3291)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3291) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk9_1(X3293)),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3293) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk9_1(X3293))),X3293)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X3293) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_s1])])])])])]) ).

cnf(i_0_1667,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1340]) ).

fof(i_0_1668,plain,
    ! [X2504,X2505,X2506] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2506)
      | c_Orderings_Oord__class_Oless__eq(X2506,c_Groups_Ominus__class_Ominus(X2506,c_Groups_Oabs__class_Oabs(X2506,X2505),c_Groups_Oabs__class_Oabs(X2506,X2504)),c_Groups_Oabs__class_Oabs(X2506,c_Groups_Ominus__class_Ominus(X2506,X2505,X2504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).

fof(i_0_1669,plain,
    ! [X2507,X2508,X2509] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2509)
      | c_Orderings_Oord__class_Oless__eq(X2509,c_Groups_Ominus__class_Ominus(X2509,c_Groups_Oabs__class_Oabs(X2509,X2508),c_Groups_Oabs__class_Oabs(X2509,X2507)),c_Groups_Oabs__class_Oabs(X2509,c_Groups_Ominus__class_Ominus(X2509,X2507,X2508))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).

fof(i_0_1670,plain,
    ! [X2490,X2491,X2492] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2492)
      | c_Orderings_Oord__class_Oless__eq(X2492,c_Groups_Oabs__class_Oabs(X2492,c_Groups_Ominus__class_Ominus(X2492,X2491,X2490)),c_Groups_Oplus__class_Oplus(X2492,c_Groups_Oabs__class_Oabs(X2492,X2491),c_Groups_Oabs__class_Oabs(X2492,X2490))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).

fof(i_0_1671,plain,
    ! [X2607,X2608,X2609] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2609)
      | c_Orderings_Oord__class_Oless__eq(X2609,c_Groups_Oabs__class_Oabs(X2609,c_Groups_Oplus__class_Oplus(X2609,X2608,X2607)),c_Groups_Oplus__class_Oplus(X2609,c_Groups_Oabs__class_Oabs(X2609,X2608),c_Groups_Oabs__class_Oabs(X2609,X2607))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).

fof(i_0_1672,plain,
    ! [X3849,X3850] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3850),X3849)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3849,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3850),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | c_RComplete_Onatceiling(X3849) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3850,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).

fof(i_0_1673,plain,
    ! [X2479,X2480,X2481] :
      ( ~ class_RealVector_Oreal__normed__vector(X2481)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2481,X2480),c_RealVector_Onorm__class_Onorm(X2481,X2479)),c_RealVector_Onorm__class_Onorm(X2481,c_Groups_Ominus__class_Ominus(X2481,X2480,X2479))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).

fof(i_0_1674,plain,
    ! [X2482,X2483,X2484] :
      ( ~ class_RealVector_Oreal__normed__vector(X2484)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2484,X2483),c_RealVector_Onorm__class_Onorm(X2484,X2482)),c_RealVector_Onorm__class_Onorm(X2484,c_Groups_Oplus__class_Oplus(X2484,X2483,X2482))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).

fof(i_0_1675,plain,
    ! [X4520,X4521,X4522] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4522)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4522,c_Groups_Otimes__class_Otimes(X4522,X4521,X4520)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4522,X4521),c_RealVector_Onorm__class_Onorm(X4522,X4520))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).

fof(i_0_1676,plain,
    ! [X2517,X2518,X2519] :
      ( ~ class_RealVector_Oreal__normed__vector(X2519)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2519,c_Groups_Ominus__class_Ominus(X2519,X2518,X2517)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2519,X2518),c_RealVector_Onorm__class_Onorm(X2519,X2517))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).

fof(i_0_1677,plain,
    ! [X2498,X2499,X2500] :
      ( ~ class_RealVector_Oreal__normed__vector(X2500)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2500,c_Groups_Oplus__class_Oplus(X2500,X2499,X2498)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2500,X2499),c_RealVector_Onorm__class_Onorm(X2500,X2498))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).

fof(i_0_1678,plain,
    ! [X2620,X2621,X2622,X2623] :
      ( ~ class_Rings_Ocomm__ring(X2623)
      | hAPP(c_Polynomial_Opoly(X2623,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X2623),X2622,X2621)),X2620) = c_Groups_Ominus__class_Ominus(X2623,hAPP(c_Polynomial_Opoly(X2623,X2622),X2620),hAPP(c_Polynomial_Opoly(X2623,X2621),X2620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).

fof(i_0_1679,plain,
    ! [X2624,X2625,X2626,X2627] :
      ( ~ class_Rings_Ocomm__semiring__0(X2627)
      | hAPP(c_Polynomial_Opoly(X2627,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2627),X2626,X2625)),X2624) = c_Groups_Oplus__class_Oplus(X2627,hAPP(c_Polynomial_Opoly(X2627,X2626),X2624),hAPP(c_Polynomial_Opoly(X2627,X2625),X2624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).

fof(i_0_1680,plain,
    ! [X3277,X3278,X3279] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3277,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3278,X3279))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3277,X3279),X3278)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3279,X3278) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3277,X3279),X3278)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3277,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3278,X3279))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3279,X3278) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).

fof(i_0_1681,plain,
    ! [X2978,X2979,X2980,X2981] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2981)
      | ~ c_Orderings_Oord__class_Oless(X2981,c_Groups_Oplus__class_Oplus(X2981,X2980,X2979),c_Groups_Oplus__class_Oplus(X2981,X2978,X2979))
      | c_Orderings_Oord__class_Oless(X2981,X2980,X2978) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_1682,plain,
    ! [X2957,X2958,X2959,X2960] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2960,c_Groups_Oplus__class_Oplus(X2960,X2959,X2958),c_Groups_Oplus__class_Oplus(X2960,X2957,X2958))
        | c_Orderings_Oord__class_Oless(X2960,X2959,X2957)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2960) )
      & ( ~ c_Orderings_Oord__class_Oless(X2960,X2959,X2957)
        | c_Orderings_Oord__class_Oless(X2960,c_Groups_Oplus__class_Oplus(X2960,X2959,X2958),c_Groups_Oplus__class_Oplus(X2960,X2957,X2958))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2960) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_1683,plain,
    ! [X2982,X2983,X2984,X2985] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2985)
      | ~ c_Orderings_Oord__class_Oless(X2985,c_Groups_Oplus__class_Oplus(X2985,X2984,X2983),c_Groups_Oplus__class_Oplus(X2985,X2984,X2982))
      | c_Orderings_Oord__class_Oless(X2985,X2983,X2982) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_1684,plain,
    ! [X2961,X2962,X2963,X2964] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2964,c_Groups_Oplus__class_Oplus(X2964,X2963,X2962),c_Groups_Oplus__class_Oplus(X2964,X2963,X2961))
        | c_Orderings_Oord__class_Oless(X2964,X2962,X2961)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2964) )
      & ( ~ c_Orderings_Oord__class_Oless(X2964,X2962,X2961)
        | c_Orderings_Oord__class_Oless(X2964,c_Groups_Oplus__class_Oplus(X2964,X2963,X2962),c_Groups_Oplus__class_Oplus(X2964,X2963,X2961))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2964) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_1685,plain,
    ! [X2576,X2577,X2578,X2579] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2579,c_Groups_Oplus__class_Oplus(X2579,X2578,X2577),c_Groups_Oplus__class_Oplus(X2579,X2576,X2577))
        | c_Orderings_Oord__class_Oless__eq(X2579,X2578,X2576)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2579) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2579,X2578,X2576)
        | c_Orderings_Oord__class_Oless__eq(X2579,c_Groups_Oplus__class_Oplus(X2579,X2578,X2577),c_Groups_Oplus__class_Oplus(X2579,X2576,X2577))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2579) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_1686,plain,
    ! [X2555,X2556,X2557,X2558] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2558)
      | ~ c_Orderings_Oord__class_Oless__eq(X2558,c_Groups_Oplus__class_Oplus(X2558,X2557,X2556),c_Groups_Oplus__class_Oplus(X2558,X2555,X2556))
      | c_Orderings_Oord__class_Oless__eq(X2558,X2557,X2555) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_1687,plain,
    ! [X2572,X2573,X2574,X2575] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2575,c_Groups_Oplus__class_Oplus(X2575,X2574,X2573),c_Groups_Oplus__class_Oplus(X2575,X2574,X2572))
        | c_Orderings_Oord__class_Oless__eq(X2575,X2573,X2572)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2575) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2575,X2573,X2572)
        | c_Orderings_Oord__class_Oless__eq(X2575,c_Groups_Oplus__class_Oplus(X2575,X2574,X2573),c_Groups_Oplus__class_Oplus(X2575,X2574,X2572))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2575) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_1688,plain,
    ! [X2551,X2552,X2553,X2554] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2554)
      | ~ c_Orderings_Oord__class_Oless__eq(X2554,c_Groups_Oplus__class_Oplus(X2554,X2553,X2552),c_Groups_Oplus__class_Oplus(X2554,X2553,X2551))
      | c_Orderings_Oord__class_Oless__eq(X2554,X2552,X2551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

cnf(i_0_1689,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1341]) ).

cnf(i_0_1690,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1342]) ).

cnf(i_0_1691,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1343]) ).

cnf(i_0_1692,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1344]) ).

fof(i_0_1693,plain,
    ! [X3199,X3200,X3201] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3201,X3200)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3201,X3199)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3200,X3201),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3199,X3201)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3200,X3199) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).

fof(i_0_1694,plain,
    ! [X3933,X3934] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3934,X3933)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3934),c_RealDef_Oreal(tc_Nat_Onat,X3933))),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__div4]) ).

cnf(i_0_1695,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_1325]) ).

cnf(i_0_1696,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1345]) ).

cnf(i_0_1697,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_1346]) ).

cnf(i_0_1698,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1347]) ).

fof(i_0_1699,plain,
    ! [X3373,X3374,X3375] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3375,X3374),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3375,X3373))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3374,X3373) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3374,X3373)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3375,X3374),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3375,X3373)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

cnf(i_0_1700,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_1348]) ).

cnf(i_0_1701,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1349]) ).

fof(i_0_1702,plain,
    ! [X3238,X3239,X3240] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,X3239),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,X3238))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3239,X3238) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3239,X3238)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,X3239),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,X3238)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_1703,plain,
    ! [X4701,X4702,X4703,X4704] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4704)
      | ~ c_Orderings_Oord__class_Oless(X4704,X4703,X4702)
      | ~ c_Orderings_Oord__class_Oless(X4704,c_Groups_Ozero__class_Ozero(X4704),X4701)
      | c_Orderings_Oord__class_Oless(X4704,c_Groups_Otimes__class_Otimes(X4704,X4703,X4701),c_Groups_Otimes__class_Otimes(X4704,X4702,X4701)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_1704,plain,
    ! [X4697,X4698,X4699,X4700] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4700)
      | ~ c_Orderings_Oord__class_Oless(X4700,X4699,X4698)
      | ~ c_Orderings_Oord__class_Oless(X4700,c_Groups_Ozero__class_Ozero(X4700),X4697)
      | c_Orderings_Oord__class_Oless(X4700,c_Groups_Otimes__class_Otimes(X4700,X4697,X4699),c_Groups_Otimes__class_Otimes(X4700,X4697,X4698)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_1705,plain,
    ! [X4693,X4694,X4695,X4696] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X4696)
      | ~ c_Orderings_Oord__class_Oless(X4696,X4695,X4694)
      | ~ c_Orderings_Oord__class_Oless(X4696,c_Groups_Ozero__class_Ozero(X4696),X4693)
      | c_Orderings_Oord__class_Oless(X4696,c_Groups_Otimes__class_Otimes(X4696,X4693,X4695),c_Groups_Otimes__class_Otimes(X4696,X4693,X4694)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_1706,plain,
    ! [X3799,X3800,X3801,X3802] :
      ( ~ class_Fields_Olinordered__field(X3802)
      | ~ c_Orderings_Oord__class_Oless(X3802,X3801,X3800)
      | ~ c_Orderings_Oord__class_Oless(X3802,c_Groups_Ozero__class_Ozero(X3802),X3799)
      | c_Orderings_Oord__class_Oless(X3802,c_Rings_Oinverse__class_Odivide(X3802,X3801,X3799),c_Rings_Oinverse__class_Odivide(X3802,X3800,X3799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_1707,plain,
    ! [X4649,X4650,X4651,X4652] :
      ( ~ class_Rings_Oordered__semiring(X4652)
      | ~ c_Orderings_Oord__class_Oless__eq(X4652,X4651,X4650)
      | ~ c_Orderings_Oord__class_Oless__eq(X4652,c_Groups_Ozero__class_Ozero(X4652),X4649)
      | c_Orderings_Oord__class_Oless__eq(X4652,c_Groups_Otimes__class_Otimes(X4652,X4651,X4649),c_Groups_Otimes__class_Otimes(X4652,X4650,X4649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_1708,plain,
    ! [X4657,X4658,X4659,X4660] :
      ( ~ class_Rings_Oordered__comm__semiring(X4660)
      | ~ c_Orderings_Oord__class_Oless__eq(X4660,X4659,X4658)
      | ~ c_Orderings_Oord__class_Oless__eq(X4660,c_Groups_Ozero__class_Ozero(X4660),X4657)
      | c_Orderings_Oord__class_Oless__eq(X4660,c_Groups_Otimes__class_Otimes(X4660,X4657,X4659),c_Groups_Otimes__class_Otimes(X4660,X4657,X4658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_1709,plain,
    ! [X4653,X4654,X4655,X4656] :
      ( ~ class_Rings_Oordered__semiring(X4656)
      | ~ c_Orderings_Oord__class_Oless__eq(X4656,X4655,X4654)
      | ~ c_Orderings_Oord__class_Oless__eq(X4656,c_Groups_Ozero__class_Ozero(X4656),X4653)
      | c_Orderings_Oord__class_Oless__eq(X4656,c_Groups_Otimes__class_Otimes(X4656,X4653,X4655),c_Groups_Otimes__class_Otimes(X4656,X4653,X4654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_1710,plain,
    ! [X3787,X3788,X3789,X3790] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X3790)
      | ~ c_Orderings_Oord__class_Oless__eq(X3790,X3789,X3788)
      | ~ c_Orderings_Oord__class_Oless__eq(X3790,c_Groups_Ozero__class_Ozero(X3790),X3787)
      | c_Orderings_Oord__class_Oless__eq(X3790,c_Rings_Oinverse__class_Odivide(X3790,X3789,X3787),c_Rings_Oinverse__class_Odivide(X3790,X3788,X3787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_1711,plain,
    ! [X4689,X4690,X4691,X4692] :
      ( ~ class_Rings_Olinordered__ring__strict(X4692)
      | ~ c_Orderings_Oord__class_Oless(X4692,X4691,X4690)
      | ~ c_Orderings_Oord__class_Oless(X4692,X4689,c_Groups_Ozero__class_Ozero(X4692))
      | c_Orderings_Oord__class_Oless(X4692,c_Groups_Otimes__class_Otimes(X4692,X4690,X4689),c_Groups_Otimes__class_Otimes(X4692,X4691,X4689)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_1712,plain,
    ! [X4685,X4686,X4687,X4688] :
      ( ~ class_Rings_Olinordered__ring__strict(X4688)
      | ~ c_Orderings_Oord__class_Oless(X4688,X4687,X4686)
      | ~ c_Orderings_Oord__class_Oless(X4688,X4685,c_Groups_Ozero__class_Ozero(X4688))
      | c_Orderings_Oord__class_Oless(X4688,c_Groups_Otimes__class_Otimes(X4688,X4685,X4686),c_Groups_Otimes__class_Otimes(X4688,X4685,X4687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

fof(i_0_1713,plain,
    ! [X3795,X3796,X3797,X3798] :
      ( ~ class_Fields_Olinordered__field(X3798)
      | ~ c_Orderings_Oord__class_Oless(X3798,X3797,X3796)
      | ~ c_Orderings_Oord__class_Oless(X3798,X3795,c_Groups_Ozero__class_Ozero(X3798))
      | c_Orderings_Oord__class_Oless(X3798,c_Rings_Oinverse__class_Odivide(X3798,X3796,X3795),c_Rings_Oinverse__class_Odivide(X3798,X3797,X3795)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_1714,plain,
    ! [X4661,X4662,X4663,X4664] :
      ( ~ class_Rings_Oordered__ring(X4664)
      | ~ c_Orderings_Oord__class_Oless__eq(X4664,X4663,X4662)
      | ~ c_Orderings_Oord__class_Oless__eq(X4664,X4661,c_Groups_Ozero__class_Ozero(X4664))
      | c_Orderings_Oord__class_Oless__eq(X4664,c_Groups_Otimes__class_Otimes(X4664,X4662,X4661),c_Groups_Otimes__class_Otimes(X4664,X4663,X4661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_1715,plain,
    ! [X4665,X4666,X4667,X4668] :
      ( ~ class_Rings_Oordered__ring(X4668)
      | ~ c_Orderings_Oord__class_Oless__eq(X4668,X4667,X4666)
      | ~ c_Orderings_Oord__class_Oless__eq(X4668,X4665,c_Groups_Ozero__class_Ozero(X4668))
      | c_Orderings_Oord__class_Oless__eq(X4668,c_Groups_Otimes__class_Otimes(X4668,X4665,X4666),c_Groups_Otimes__class_Otimes(X4668,X4665,X4667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

fof(i_0_1716,plain,
    ! [X3791,X3792,X3793,X3794] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X3794)
      | ~ c_Orderings_Oord__class_Oless__eq(X3794,X3793,X3792)
      | ~ c_Orderings_Oord__class_Oless__eq(X3794,X3791,c_Groups_Ozero__class_Ozero(X3794))
      | c_Orderings_Oord__class_Oless__eq(X3794,c_Rings_Oinverse__class_Odivide(X3794,X3792,X3791),c_Rings_Oinverse__class_Odivide(X3794,X3793,X3791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

cnf(i_0_1717,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_1329]) ).

cnf(i_0_1718,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_1330]) ).

cnf(i_0_1719,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_1327]) ).

cnf(i_0_1720,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_1328]) ).

fof(i_0_1721,plain,
    ! [X3900,X3901] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3901),X3900)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3900,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3901),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | c_RComplete_Onatfloor(X3900) = X3901 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).

fof(i_0_1722,plain,
    ! [X2637,X2638,X2639] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2639,X2638)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2637,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2638,X2637),X2639)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).

fof(i_0_1723,plain,
    ! [X2973,X2974,X2975,X2976,X2977] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2977)
      | ~ c_Orderings_Oord__class_Oless(X2977,X2976,X2975)
      | ~ c_Orderings_Oord__class_Oless(X2977,X2974,X2973)
      | c_Orderings_Oord__class_Oless(X2977,c_Groups_Oplus__class_Oplus(X2977,X2976,X2974),c_Groups_Oplus__class_Oplus(X2977,X2975,X2973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_1724,plain,
    ! [X3054,X3055,X3056,X3057,X3058] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3058)
      | ~ c_Orderings_Oord__class_Oless__eq(X3058,X3057,X3056)
      | ~ c_Orderings_Oord__class_Oless(X3058,X3055,X3054)
      | c_Orderings_Oord__class_Oless(X3058,c_Groups_Oplus__class_Oplus(X3058,X3057,X3055),c_Groups_Oplus__class_Oplus(X3058,X3056,X3054)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_1725,plain,
    ! [X3049,X3050,X3051,X3052,X3053] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3053)
      | ~ c_Orderings_Oord__class_Oless(X3053,X3052,X3051)
      | ~ c_Orderings_Oord__class_Oless__eq(X3053,X3050,X3049)
      | c_Orderings_Oord__class_Oless(X3053,c_Groups_Oplus__class_Oplus(X3053,X3052,X3050),c_Groups_Oplus__class_Oplus(X3053,X3051,X3049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_1726,plain,
    ! [X2559,X2560,X2561,X2562,X2563] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2563)
      | ~ c_Orderings_Oord__class_Oless__eq(X2563,X2562,X2561)
      | ~ c_Orderings_Oord__class_Oless__eq(X2563,X2560,X2559)
      | c_Orderings_Oord__class_Oless__eq(X2563,c_Groups_Oplus__class_Oplus(X2563,X2562,X2560),c_Groups_Oplus__class_Oplus(X2563,X2561,X2559)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_1727,plain,
    ! [X4750,X4751,X4752] :
      ( ( X4751 = c_Groups_Ozero__class_Ozero(X4752)
        | c_Groups_Oplus__class_Oplus(X4752,c_Groups_Otimes__class_Otimes(X4752,X4751,X4751),c_Groups_Otimes__class_Otimes(X4752,X4750,X4750)) != c_Groups_Ozero__class_Ozero(X4752)
        | ~ class_Rings_Olinordered__ring__strict(X4752) )
      & ( X4750 = c_Groups_Ozero__class_Ozero(X4752)
        | c_Groups_Oplus__class_Oplus(X4752,c_Groups_Otimes__class_Otimes(X4752,X4751,X4751),c_Groups_Otimes__class_Otimes(X4752,X4750,X4750)) != c_Groups_Ozero__class_Ozero(X4752)
        | ~ class_Rings_Olinordered__ring__strict(X4752) )
      & ( X4751 != c_Groups_Ozero__class_Ozero(X4752)
        | X4750 != c_Groups_Ozero__class_Ozero(X4752)
        | c_Groups_Oplus__class_Oplus(X4752,c_Groups_Otimes__class_Otimes(X4752,X4751,X4751),c_Groups_Otimes__class_Otimes(X4752,X4750,X4750)) = c_Groups_Ozero__class_Ozero(X4752)
        | ~ class_Rings_Olinordered__ring__strict(X4752) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_1728,plain,
    ! [X4541,X4542,X4543,X4544] :
      ( ~ class_Rings_Ocomm__semiring__1(X4544)
      | c_Groups_Oplus__class_Oplus(X4544,c_Groups_Otimes__class_Otimes(X4544,X4543,X4542),c_Groups_Otimes__class_Otimes(X4544,X4541,X4542)) = c_Groups_Otimes__class_Otimes(X4544,c_Groups_Oplus__class_Oplus(X4544,X4543,X4541),X4542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_1729,plain,
    ! [X4444,X4445,X4446,X4447] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4447)
      | c_Groups_Otimes__class_Otimes(X4447,c_Groups_Ominus__class_Ominus(X4447,X4446,X4445),X4444) = c_Groups_Ominus__class_Ominus(X4447,c_Groups_Otimes__class_Otimes(X4447,X4446,X4444),c_Groups_Otimes__class_Otimes(X4447,X4445,X4444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).

fof(i_0_1730,plain,
    ! [X4440,X4441,X4442,X4443] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4443)
      | c_Groups_Otimes__class_Otimes(X4443,c_Groups_Ominus__class_Ominus(X4443,X4442,X4441),X4440) = c_Groups_Ominus__class_Ominus(X4443,c_Groups_Otimes__class_Otimes(X4443,X4442,X4440),c_Groups_Otimes__class_Otimes(X4443,X4441,X4440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).

fof(i_0_1731,plain,
    ! [X4462,X4463,X4464,X4465] :
      ( ~ class_Rings_Ocomm__semiring(X4465)
      | c_Groups_Otimes__class_Otimes(X4465,c_Groups_Oplus__class_Oplus(X4465,X4464,X4463),X4462) = c_Groups_Oplus__class_Oplus(X4465,c_Groups_Otimes__class_Otimes(X4465,X4464,X4462),c_Groups_Otimes__class_Otimes(X4465,X4463,X4462)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_1732,plain,
    ! [X4470,X4471,X4472,X4473] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4473)
      | c_Groups_Otimes__class_Otimes(X4473,c_Groups_Oplus__class_Oplus(X4473,X4472,X4471),X4470) = c_Groups_Oplus__class_Oplus(X4473,c_Groups_Otimes__class_Otimes(X4473,X4472,X4470),c_Groups_Otimes__class_Otimes(X4473,X4471,X4470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).

fof(i_0_1733,plain,
    ! [X4466,X4467,X4468,X4469] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4469)
      | c_Groups_Otimes__class_Otimes(X4469,c_Groups_Oplus__class_Oplus(X4469,X4468,X4467),X4466) = c_Groups_Oplus__class_Oplus(X4469,c_Groups_Otimes__class_Otimes(X4469,X4468,X4466),c_Groups_Otimes__class_Otimes(X4469,X4467,X4466)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).

fof(i_0_1734,plain,
    ! [X4537,X4538,X4539,X4540] :
      ( ~ class_Rings_Ocomm__semiring__1(X4540)
      | c_Groups_Otimes__class_Otimes(X4540,c_Groups_Oplus__class_Oplus(X4540,X4539,X4538),X4537) = c_Groups_Oplus__class_Oplus(X4540,c_Groups_Otimes__class_Otimes(X4540,X4539,X4537),c_Groups_Otimes__class_Otimes(X4540,X4538,X4537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_1735,plain,
    ! [X3581,X3582,X3583,X3584] :
      ( ~ class_Rings_Odivision__ring(X3584)
      | c_Rings_Oinverse__class_Odivide(X3584,c_Groups_Ominus__class_Ominus(X3584,X3583,X3582),X3581) = c_Groups_Ominus__class_Ominus(X3584,c_Rings_Oinverse__class_Odivide(X3584,X3583,X3581),c_Rings_Oinverse__class_Odivide(X3584,X3582,X3581)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).

fof(i_0_1736,plain,
    ! [X3577,X3578,X3579,X3580] :
      ( ~ class_RealVector_Oreal__normed__field(X3580)
      | c_Rings_Oinverse__class_Odivide(X3580,c_Groups_Ominus__class_Ominus(X3580,X3579,X3578),X3577) = c_Groups_Ominus__class_Ominus(X3580,c_Rings_Oinverse__class_Odivide(X3580,X3579,X3577),c_Rings_Oinverse__class_Odivide(X3580,X3578,X3577)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Odiff])]) ).

fof(i_0_1737,plain,
    ! [X3573,X3574,X3575,X3576] :
      ( ~ class_Rings_Odivision__ring(X3576)
      | c_Rings_Oinverse__class_Odivide(X3576,c_Groups_Oplus__class_Oplus(X3576,X3575,X3574),X3573) = c_Groups_Oplus__class_Oplus(X3576,c_Rings_Oinverse__class_Odivide(X3576,X3575,X3573),c_Rings_Oinverse__class_Odivide(X3576,X3574,X3573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_1738,plain,
    ! [X3569,X3570,X3571,X3572] :
      ( ~ class_RealVector_Oreal__normed__field(X3572)
      | c_Rings_Oinverse__class_Odivide(X3572,c_Groups_Oplus__class_Oplus(X3572,X3571,X3570),X3569) = c_Groups_Oplus__class_Oplus(X3572,c_Rings_Oinverse__class_Odivide(X3572,X3571,X3569),c_Rings_Oinverse__class_Odivide(X3572,X3570,X3569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Oadd])]) ).

fof(i_0_1739,plain,
    ! [X4436,X4437,X4438,X4439] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4439)
      | c_Groups_Otimes__class_Otimes(X4439,X4438,c_Groups_Ominus__class_Ominus(X4439,X4437,X4436)) = c_Groups_Ominus__class_Ominus(X4439,c_Groups_Otimes__class_Otimes(X4439,X4438,X4437),c_Groups_Otimes__class_Otimes(X4439,X4438,X4436)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).

fof(i_0_1740,plain,
    ! [X4432,X4433,X4434,X4435] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4435)
      | c_Groups_Otimes__class_Otimes(X4435,X4434,c_Groups_Ominus__class_Ominus(X4435,X4433,X4432)) = c_Groups_Ominus__class_Ominus(X4435,c_Groups_Otimes__class_Otimes(X4435,X4434,X4433),c_Groups_Otimes__class_Otimes(X4435,X4434,X4432)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).

fof(i_0_1741,plain,
    ! [X4478,X4479,X4480,X4481] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4481)
      | c_Groups_Otimes__class_Otimes(X4481,X4480,c_Groups_Oplus__class_Oplus(X4481,X4479,X4478)) = c_Groups_Oplus__class_Oplus(X4481,c_Groups_Otimes__class_Otimes(X4481,X4480,X4479),c_Groups_Otimes__class_Otimes(X4481,X4480,X4478)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).

fof(i_0_1742,plain,
    ! [X4474,X4475,X4476,X4477] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4477)
      | c_Groups_Otimes__class_Otimes(X4477,X4476,c_Groups_Oplus__class_Oplus(X4477,X4475,X4474)) = c_Groups_Oplus__class_Oplus(X4477,c_Groups_Otimes__class_Otimes(X4477,X4476,X4475),c_Groups_Otimes__class_Otimes(X4477,X4476,X4474)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).

fof(i_0_1743,plain,
    ! [X4528,X4529,X4530,X4531] :
      ( ~ class_Rings_Ocomm__semiring__1(X4531)
      | c_Groups_Otimes__class_Otimes(X4531,X4530,c_Groups_Oplus__class_Oplus(X4531,X4529,X4528)) = c_Groups_Oplus__class_Oplus(X4531,c_Groups_Otimes__class_Otimes(X4531,X4530,X4529),c_Groups_Otimes__class_Otimes(X4531,X4530,X4528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

cnf(i_0_1744,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1350]) ).

fof(i_0_1745,plain,
    ! [X4236,X4237,X4238] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4238,X4237)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4236)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4238,X4236),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4237,X4236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).

fof(i_0_1746,plain,
    ! [X3967,X3968,X3969] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3969)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3969,X3968)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3967,X3968),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3967,X3969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).

fof(i_0_1747,plain,
    ! [X4233,X4234,X4235] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4235,X4234)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4233,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4234,X4233),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4235,X4233)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).

fof(i_0_1748,plain,
    ! [X4310,X4311,X4312,X4313] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4313,X4312)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4311,X4310)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4313,X4311),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4312,X4310)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_1749,plain,
    ! [X3435,X3436,X3437] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3437,X3436)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3435,X3437)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3437,X3435),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3436,X3435)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).

fof(i_0_1750,plain,
    ! [X3390,X3391,X3392] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3392,X3391)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3392,X3390)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3390,X3391),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3390,X3392)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).

fof(i_0_1751,plain,
    ! [X3360,X3361,X3362,X3363] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3363,X3362)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3361,X3360)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3363,X3361),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3362,X3360)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_1752,plain,
    ! [X3250,X3251,X3252,X3253] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3253,X3252)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3251,X3250)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3253,X3251),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3252,X3250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_1753,plain,
    ! [X4715,X4716,X4717] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4717)
      | ~ c_Orderings_Oord__class_Oless(X4717,c_Groups_Ozero__class_Ozero(X4717),c_Groups_Otimes__class_Otimes(X4717,X4716,X4715))
      | ~ c_Orderings_Oord__class_Oless(X4717,c_Groups_Ozero__class_Ozero(X4717),X4715)
      | c_Orderings_Oord__class_Oless(X4717,c_Groups_Ozero__class_Ozero(X4717),X4716) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_1754,plain,
    ! [X4718,X4719,X4720] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4720)
      | ~ c_Orderings_Oord__class_Oless(X4720,c_Groups_Ozero__class_Ozero(X4720),c_Groups_Otimes__class_Otimes(X4720,X4719,X4718))
      | ~ c_Orderings_Oord__class_Oless(X4720,c_Groups_Ozero__class_Ozero(X4720),X4719)
      | c_Orderings_Oord__class_Oless(X4720,c_Groups_Ozero__class_Ozero(X4720),X4718) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

fof(i_0_1755,plain,
    ! [X4257,X4258] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4257,X4258)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4258,X4257))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4258) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4257)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4258,X4257))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4258) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4257,X4258)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4257)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4258,X4257))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4258) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).

fof(i_0_1756,plain,
    ! [X3702,X3703] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3703,X3702)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3703),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X3702)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3703),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X3702))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3703,X3702) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).

fof(i_0_1757,plain,
    ! [X3736,X3737] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3737,X3736)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3737),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3736),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3737),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3736),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3737,X3736) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).

fof(i_0_1758,plain,
    ! [X4454,X4455,X4456] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4456,X4455),X4454) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4456,X4454),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4455,X4454)),
    inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).

cnf(i_0_1759,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
    inference(split_conjunct,[status(thm)],[i_0_1351]) ).

fof(i_0_1760,plain,
    ! [X3875] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk40_1(X3875),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3875)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3875) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3875,c_RealDef_Oreal(tc_Nat_Onat,esk40_1(X3875)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3875) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6])])])]) ).

cnf(i_0_1761,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1352]) ).

fof(i_0_1762,plain,
    ! [X3430,X3431,X3432] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3432,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3431,X3430))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3432,X3430),X3431) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3432,X3430),X3431)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3432,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3431,X3430)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).

fof(i_0_1763,plain,
    ! [X2634,X2635,X2636] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2636,X2635),X2634)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2636,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2634,X2635)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2636,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2634,X2635))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2636,X2635),X2634) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).

fof(i_0_1764,plain,
    ! [X3266,X3267,X3268] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3268,X3267)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3267,X3268),X3266) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3267,X3266),X3268) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).

fof(i_0_1765,plain,
    ! [X3263,X3264,X3265] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3265,X3264)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3264,X3263),X3265) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3264,X3265),X3263) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).

fof(i_0_1766,plain,
    ! [X3269,X3270,X3271] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3271,X3270)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,X3270),X3271) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3270,X3271)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).

fof(i_0_1767,plain,
    ! [X2631,X2632,X2633] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2633,X2632)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2631,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2632,X2633)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2631,X2633),X2632) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).

fof(i_0_1768,plain,
    ! [X3280,X3281,X3282] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3282,X3281)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3280,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3281,X3282)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3280,X3281),X3282) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).

fof(i_0_1769,plain,
    ! [X4261,X4262] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4261,X4262))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4261)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4262) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4261)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4261,X4262))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4262) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_1770,plain,
    ! [X4229,X4230] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4229,X4230),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4229)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4230,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4229)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4229,X4230),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4230,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])]) ).

fof(i_0_1771,plain,
    ! [X4227,X4228] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4227,X4228),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4227,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4228) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4227,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4227,X4228),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4228) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).

fof(i_0_1772,plain,
    ! [X4246,X4247] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4246,X4247))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4246,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4247,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4246,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4246,X4247))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4247,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_1773,plain,
    ! [X3466,X3467,X3468] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3468),v_r)
        | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3468)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3467)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,X3467)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,esk18_0) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk20_1(X3466)),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,esk18_0) )
      & ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk20_1(X3466))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk19_1(X3466))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,esk18_0) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,esk19_1(X3466))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3466,esk18_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096])])])])]) ).

fof(i_0_1774,plain,
    ! [X2642,X2643,X2644,X2645] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2644),v_r)
        | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2644)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2643)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2642,X2643)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2642,v_s____) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk3_1(X2645)),v_r)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2645,v_s____) )
      & ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk3_1(X2645))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk2_1(X2645))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2645,v_s____) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2645,esk2_1(X2645))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2645,v_s____) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_s])])])])])]) ).

fof(i_0_1775,plain,
    ! [X4259,X4260] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4259,X4260))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4260,X4259)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4260) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4260,X4259)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4259,X4260))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4260) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).

fof(i_0_1776,plain,
    ! [X3815,X3816,X3817] :
      ( ( c_Orderings_Oord__class_Oless(X3817,X3816,c_Groups_Ozero__class_Ozero(X3817))
        | c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3816)
        | ~ c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) )
      & ( c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3815)
        | c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3816)
        | ~ c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) )
      & ( c_Orderings_Oord__class_Oless(X3817,X3816,c_Groups_Ozero__class_Ozero(X3817))
        | c_Orderings_Oord__class_Oless(X3817,X3815,c_Groups_Ozero__class_Ozero(X3817))
        | ~ c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) )
      & ( c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3815)
        | c_Orderings_Oord__class_Oless(X3817,X3815,c_Groups_Ozero__class_Ozero(X3817))
        | ~ c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) )
      & ( ~ c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3816)
        | ~ c_Orderings_Oord__class_Oless(X3817,X3815,c_Groups_Ozero__class_Ozero(X3817))
        | c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) )
      & ( ~ c_Orderings_Oord__class_Oless(X3817,X3816,c_Groups_Ozero__class_Ozero(X3817))
        | ~ c_Orderings_Oord__class_Oless(X3817,c_Groups_Ozero__class_Ozero(X3817),X3815)
        | c_Orderings_Oord__class_Oless(X3817,c_Rings_Oinverse__class_Odivide(X3817,X3816,X3815),c_Groups_Ozero__class_Ozero(X3817))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3817) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_1777,plain,
    ! [X4631,X4632,X4633] :
      ( ( c_Orderings_Oord__class_Oless__eq(X4633,X4632,c_Groups_Ozero__class_Ozero(X4633))
        | c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4632)
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) )
      & ( c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4631)
        | c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4632)
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) )
      & ( c_Orderings_Oord__class_Oless__eq(X4633,X4632,c_Groups_Ozero__class_Ozero(X4633))
        | c_Orderings_Oord__class_Oless__eq(X4633,X4631,c_Groups_Ozero__class_Ozero(X4633))
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) )
      & ( c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4631)
        | c_Orderings_Oord__class_Oless__eq(X4633,X4631,c_Groups_Ozero__class_Ozero(X4633))
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4632)
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,X4631,c_Groups_Ozero__class_Ozero(X4633))
        | c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4633,X4632,c_Groups_Ozero__class_Ozero(X4633))
        | ~ c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Ozero__class_Ozero(X4633),X4631)
        | c_Orderings_Oord__class_Oless__eq(X4633,c_Groups_Otimes__class_Otimes(X4633,X4632,X4631),c_Groups_Ozero__class_Ozero(X4633))
        | ~ class_Rings_Olinordered__ring__strict(X4633) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_1778,plain,
    ! [X3784,X3785,X3786] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3786,X3785,c_Groups_Ozero__class_Ozero(X3786))
        | c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3785)
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) )
      & ( c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3784)
        | c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3785)
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) )
      & ( c_Orderings_Oord__class_Oless__eq(X3786,X3785,c_Groups_Ozero__class_Ozero(X3786))
        | c_Orderings_Oord__class_Oless__eq(X3786,X3784,c_Groups_Ozero__class_Ozero(X3786))
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) )
      & ( c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3784)
        | c_Orderings_Oord__class_Oless__eq(X3786,X3784,c_Groups_Ozero__class_Ozero(X3786))
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3785)
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,X3784,c_Groups_Ozero__class_Ozero(X3786))
        | c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3786,X3785,c_Groups_Ozero__class_Ozero(X3786))
        | ~ c_Orderings_Oord__class_Oless__eq(X3786,c_Groups_Ozero__class_Ozero(X3786),X3784)
        | c_Orderings_Oord__class_Oless__eq(X3786,c_Rings_Oinverse__class_Odivide(X3786,X3785,X3784),c_Groups_Ozero__class_Ozero(X3786))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3786) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_1779,plain,
    ! [X3818,X3819,X3820] :
      ( ( c_Orderings_Oord__class_Oless(X3820,X3819,c_Groups_Ozero__class_Ozero(X3820))
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3819)
        | ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) )
      & ( c_Orderings_Oord__class_Oless(X3820,X3818,c_Groups_Ozero__class_Ozero(X3820))
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3819)
        | ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) )
      & ( c_Orderings_Oord__class_Oless(X3820,X3819,c_Groups_Ozero__class_Ozero(X3820))
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3818)
        | ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) )
      & ( c_Orderings_Oord__class_Oless(X3820,X3818,c_Groups_Ozero__class_Ozero(X3820))
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3818)
        | ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) )
      & ( ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3819)
        | ~ c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),X3818)
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) )
      & ( ~ c_Orderings_Oord__class_Oless(X3820,X3819,c_Groups_Ozero__class_Ozero(X3820))
        | ~ c_Orderings_Oord__class_Oless(X3820,X3818,c_Groups_Ozero__class_Ozero(X3820))
        | c_Orderings_Oord__class_Oless(X3820,c_Groups_Ozero__class_Ozero(X3820),c_Rings_Oinverse__class_Odivide(X3820,X3819,X3818))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3820) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_1780,plain,
    ! [X4628,X4629,X4630] :
      ( ( c_Orderings_Oord__class_Oless__eq(X4630,X4629,c_Groups_Ozero__class_Ozero(X4630))
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4629)
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) )
      & ( c_Orderings_Oord__class_Oless__eq(X4630,X4628,c_Groups_Ozero__class_Ozero(X4630))
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4629)
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) )
      & ( c_Orderings_Oord__class_Oless__eq(X4630,X4629,c_Groups_Ozero__class_Ozero(X4630))
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4628)
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) )
      & ( c_Orderings_Oord__class_Oless__eq(X4630,X4628,c_Groups_Ozero__class_Ozero(X4630))
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4628)
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4629)
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),X4628)
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4630,X4629,c_Groups_Ozero__class_Ozero(X4630))
        | ~ c_Orderings_Oord__class_Oless__eq(X4630,X4628,c_Groups_Ozero__class_Ozero(X4630))
        | c_Orderings_Oord__class_Oless__eq(X4630,c_Groups_Ozero__class_Ozero(X4630),c_Groups_Otimes__class_Otimes(X4630,X4629,X4628))
        | ~ class_Rings_Olinordered__ring__strict(X4630) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_1781,plain,
    ! [X3781,X3782,X3783] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3783,X3782,c_Groups_Ozero__class_Ozero(X3783))
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3782)
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) )
      & ( c_Orderings_Oord__class_Oless__eq(X3783,X3781,c_Groups_Ozero__class_Ozero(X3783))
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3782)
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) )
      & ( c_Orderings_Oord__class_Oless__eq(X3783,X3782,c_Groups_Ozero__class_Ozero(X3783))
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3781)
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) )
      & ( c_Orderings_Oord__class_Oless__eq(X3783,X3781,c_Groups_Ozero__class_Ozero(X3783))
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3781)
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3782)
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),X3781)
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3783,X3782,c_Groups_Ozero__class_Ozero(X3783))
        | ~ c_Orderings_Oord__class_Oless__eq(X3783,X3781,c_Groups_Ozero__class_Ozero(X3783))
        | c_Orderings_Oord__class_Oless__eq(X3783,c_Groups_Ozero__class_Ozero(X3783),c_Rings_Oinverse__class_Odivide(X3783,X3782,X3781))
        | ~ class_Fields_Olinordered__field__inverse__zero(X3783) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_1782,plain,
    ! [X3925,X3926] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3926)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3925)
      | c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3926,c_RealDef_Oreal(tc_Nat_Onat,X3925))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X3926),X3925) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__div__nat])]) ).

cnf(i_0_1783,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).

cnf(i_0_1784,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_1353]) ).

fof(i_0_1785,plain,
    ! [X4587,X4588,X4589] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(X4589)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4588,c_RealVector_Onorm__class_Onorm(X4589,X4587))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4588)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4589,c_Rings_Oinverse__class_Oinverse(X4589,X4587)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__inverse__lemma])]) ).

cnf(i_0_1786,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_1354]) ).

cnf(i_0_1787,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1355]) ).

cnf(i_0_1788,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1356]) ).

cnf(i_0_1789,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1357]) ).

fof(i_0_1790,plain,
    ! [X4708,X4709,X4710] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4710)
      | ~ c_Orderings_Oord__class_Oless(X4710,X4709,c_Groups_Ozero__class_Ozero(X4710))
      | ~ c_Orderings_Oord__class_Oless(X4710,c_Groups_Ozero__class_Ozero(X4710),X4708)
      | c_Orderings_Oord__class_Oless(X4710,c_Groups_Otimes__class_Otimes(X4710,X4709,X4708),c_Groups_Ozero__class_Ozero(X4710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_1791,plain,
    ! [X4724,X4725,X4726] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4726)
      | ~ c_Orderings_Oord__class_Oless(X4726,c_Groups_Ozero__class_Ozero(X4726),X4725)
      | ~ c_Orderings_Oord__class_Oless(X4726,X4724,c_Groups_Ozero__class_Ozero(X4726))
      | c_Orderings_Oord__class_Oless(X4726,c_Groups_Otimes__class_Otimes(X4726,X4725,X4724),c_Groups_Ozero__class_Ozero(X4726)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_1792,plain,
    ! [X4721,X4722,X4723] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4723)
      | ~ c_Orderings_Oord__class_Oless(X4723,c_Groups_Ozero__class_Ozero(X4723),X4722)
      | ~ c_Orderings_Oord__class_Oless(X4723,X4721,c_Groups_Ozero__class_Ozero(X4723))
      | c_Orderings_Oord__class_Oless(X4723,c_Groups_Otimes__class_Otimes(X4723,X4721,X4722),c_Groups_Ozero__class_Ozero(X4723)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_1793,plain,
    ! [X3806,X3807,X3808] :
      ( ~ class_Fields_Olinordered__field(X3808)
      | ~ c_Orderings_Oord__class_Oless(X3808,X3807,c_Groups_Ozero__class_Ozero(X3808))
      | ~ c_Orderings_Oord__class_Oless(X3808,c_Groups_Ozero__class_Ozero(X3808),X3806)
      | c_Orderings_Oord__class_Oless(X3808,c_Rings_Oinverse__class_Odivide(X3808,X3807,X3806),c_Groups_Ozero__class_Ozero(X3808)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_1794,plain,
    ! [X3809,X3810,X3811] :
      ( ~ class_Fields_Olinordered__field(X3811)
      | ~ c_Orderings_Oord__class_Oless(X3811,c_Groups_Ozero__class_Ozero(X3811),X3810)
      | ~ c_Orderings_Oord__class_Oless(X3811,X3809,c_Groups_Ozero__class_Ozero(X3811))
      | c_Orderings_Oord__class_Oless(X3811,c_Rings_Oinverse__class_Odivide(X3811,X3810,X3809),c_Groups_Ozero__class_Ozero(X3811)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_1795,plain,
    ! [X4682,X4683,X4684] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4684,c_Groups_Ozero__class_Ozero(X4684),X4683)
        | ~ c_Orderings_Oord__class_Oless__eq(X4684,X4682,c_Groups_Ozero__class_Ozero(X4684))
        | c_Orderings_Oord__class_Oless__eq(X4684,c_Groups_Otimes__class_Otimes(X4684,X4683,X4682),c_Groups_Ozero__class_Ozero(X4684))
        | ~ class_Rings_Oordered__cancel__semiring(X4684) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4684,X4683,c_Groups_Ozero__class_Ozero(X4684))
        | ~ c_Orderings_Oord__class_Oless__eq(X4684,c_Groups_Ozero__class_Ozero(X4684),X4682)
        | c_Orderings_Oord__class_Oless__eq(X4684,c_Groups_Otimes__class_Otimes(X4684,X4683,X4682),c_Groups_Ozero__class_Ozero(X4684))
        | ~ class_Rings_Oordered__cancel__semiring(X4684) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_1796,plain,
    ! [X4643,X4644,X4645] :
      ( ~ class_Rings_Oordered__cancel__semiring(X4645)
      | ~ c_Orderings_Oord__class_Oless__eq(X4645,X4644,c_Groups_Ozero__class_Ozero(X4645))
      | ~ c_Orderings_Oord__class_Oless__eq(X4645,c_Groups_Ozero__class_Ozero(X4645),X4643)
      | c_Orderings_Oord__class_Oless__eq(X4645,c_Groups_Otimes__class_Otimes(X4645,X4644,X4643),c_Groups_Ozero__class_Ozero(X4645)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_1797,plain,
    ! [X4637,X4638,X4639] :
      ( ~ class_Rings_Oordered__cancel__semiring(X4639)
      | ~ c_Orderings_Oord__class_Oless__eq(X4639,c_Groups_Ozero__class_Ozero(X4639),X4638)
      | ~ c_Orderings_Oord__class_Oless__eq(X4639,X4637,c_Groups_Ozero__class_Ozero(X4639))
      | c_Orderings_Oord__class_Oless__eq(X4639,c_Groups_Otimes__class_Otimes(X4639,X4638,X4637),c_Groups_Ozero__class_Ozero(X4639)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_1798,plain,
    ! [X4640,X4641,X4642] :
      ( ~ class_Rings_Oordered__cancel__semiring(X4642)
      | ~ c_Orderings_Oord__class_Oless__eq(X4642,c_Groups_Ozero__class_Ozero(X4642),X4641)
      | ~ c_Orderings_Oord__class_Oless__eq(X4642,X4640,c_Groups_Ozero__class_Ozero(X4642))
      | c_Orderings_Oord__class_Oless__eq(X4642,c_Groups_Otimes__class_Otimes(X4642,X4640,X4641),c_Groups_Ozero__class_Ozero(X4642)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_1799,plain,
    ! [X3827,X3828,X3829] :
      ( ~ class_Fields_Olinordered__field(X3829)
      | ~ c_Orderings_Oord__class_Oless__eq(X3829,c_Groups_Ozero__class_Ozero(X3829),X3828)
      | ~ c_Orderings_Oord__class_Oless(X3829,X3827,c_Groups_Ozero__class_Ozero(X3829))
      | c_Orderings_Oord__class_Oless__eq(X3829,c_Rings_Oinverse__class_Odivide(X3829,X3828,X3827),c_Groups_Ozero__class_Ozero(X3829)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_1800,plain,
    ! [X3845,X3846,X3847] :
      ( ~ class_Fields_Olinordered__field(X3847)
      | ~ c_Orderings_Oord__class_Oless__eq(X3847,X3846,c_Groups_Ozero__class_Ozero(X3847))
      | ~ c_Orderings_Oord__class_Oless(X3847,c_Groups_Ozero__class_Ozero(X3847),X3845)
      | c_Orderings_Oord__class_Oless__eq(X3847,c_Rings_Oinverse__class_Odivide(X3847,X3846,X3845),c_Groups_Ozero__class_Ozero(X3847)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_1801,plain,
    ! [X2805,X2806,X2807] :
      ( ~ class_Groups_Oordered__comm__monoid__add(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_Oplus__class_Oplus(X2807,X2806,X2805),c_Groups_Ozero__class_Ozero(X2807)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_1802,plain,
    ! [X2921,X2922,X2923] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2923)
      | ~ c_Orderings_Oord__class_Oless__eq(X2923,X2922,c_Groups_Ozero__class_Ozero(X2923))
      | ~ c_Orderings_Oord__class_Oless(X2923,X2921,c_Groups_Ozero__class_Ozero(X2923))
      | c_Orderings_Oord__class_Oless(X2923,c_Groups_Oplus__class_Oplus(X2923,X2922,X2921),c_Groups_Ozero__class_Ozero(X2923)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_1803,plain,
    ! [X2918,X2919,X2920] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2920)
      | ~ c_Orderings_Oord__class_Oless(X2920,X2919,c_Groups_Ozero__class_Ozero(X2920))
      | ~ c_Orderings_Oord__class_Oless__eq(X2920,X2918,c_Groups_Ozero__class_Ozero(X2920))
      | c_Orderings_Oord__class_Oless(X2920,c_Groups_Oplus__class_Oplus(X2920,X2919,X2918),c_Groups_Ozero__class_Ozero(X2920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_1804,plain,
    ! [X3081,X3082,X3083] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3083)
      | ~ c_Orderings_Oord__class_Oless__eq(X3083,X3082,c_Groups_Ozero__class_Ozero(X3083))
      | ~ c_Orderings_Oord__class_Oless__eq(X3083,X3081,c_Groups_Ozero__class_Ozero(X3083))
      | c_Orderings_Oord__class_Oless__eq(X3083,c_Groups_Oplus__class_Oplus(X3083,X3082,X3081),c_Groups_Ozero__class_Ozero(X3083)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_1805,plain,
    ! [X4753,X4754,X4755] :
      ( ~ class_Rings_Olinordered__semidom(X4755)
      | ~ c_Orderings_Oord__class_Oless(X4755,c_Groups_Oone__class_Oone(X4755),X4754)
      | ~ c_Orderings_Oord__class_Oless(X4755,c_Groups_Oone__class_Oone(X4755),X4753)
      | c_Orderings_Oord__class_Oless(X4755,c_Groups_Oone__class_Oone(X4755),c_Groups_Otimes__class_Otimes(X4755,X4754,X4753)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_1806,plain,
    ! [X4727,X4728,X4729] :
      ( ~ class_Rings_Olinordered__semiring__strict(X4729)
      | ~ c_Orderings_Oord__class_Oless(X4729,c_Groups_Ozero__class_Ozero(X4729),X4728)
      | ~ c_Orderings_Oord__class_Oless(X4729,c_Groups_Ozero__class_Ozero(X4729),X4727)
      | c_Orderings_Oord__class_Oless(X4729,c_Groups_Ozero__class_Ozero(X4729),c_Groups_Otimes__class_Otimes(X4729,X4728,X4727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_1807,plain,
    ! [X3812,X3813,X3814] :
      ( ~ class_Fields_Olinordered__field(X3814)
      | ~ c_Orderings_Oord__class_Oless(X3814,c_Groups_Ozero__class_Ozero(X3814),X3813)
      | ~ c_Orderings_Oord__class_Oless(X3814,c_Groups_Ozero__class_Ozero(X3814),X3812)
      | c_Orderings_Oord__class_Oless(X3814,c_Groups_Ozero__class_Ozero(X3814),c_Rings_Oinverse__class_Odivide(X3814,X3813,X3812)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_1808,plain,
    ! [X2808,X2809,X2810] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2810)
      | ~ c_Orderings_Oord__class_Oless(X2810,c_Groups_Ozero__class_Ozero(X2810),X2809)
      | ~ c_Orderings_Oord__class_Oless(X2810,c_Groups_Ozero__class_Ozero(X2810),X2808)
      | c_Orderings_Oord__class_Oless(X2810,c_Groups_Ozero__class_Ozero(X2810),c_Groups_Oplus__class_Oplus(X2810,X2809,X2808)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_1809,plain,
    ! [X2907,X2908,X2909] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2909)
      | ~ c_Orderings_Oord__class_Oless__eq(X2909,c_Groups_Ozero__class_Ozero(X2909),X2908)
      | ~ c_Orderings_Oord__class_Oless(X2909,c_Groups_Ozero__class_Ozero(X2909),X2907)
      | c_Orderings_Oord__class_Oless(X2909,c_Groups_Ozero__class_Ozero(X2909),c_Groups_Oplus__class_Oplus(X2909,X2908,X2907)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_1810,plain,
    ! [X2904,X2905,X2906] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2906)
      | ~ c_Orderings_Oord__class_Oless(X2906,c_Groups_Ozero__class_Ozero(X2906),X2905)
      | ~ c_Orderings_Oord__class_Oless__eq(X2906,c_Groups_Ozero__class_Ozero(X2906),X2904)
      | c_Orderings_Oord__class_Oless(X2906,c_Groups_Ozero__class_Ozero(X2906),c_Groups_Oplus__class_Oplus(X2906,X2905,X2904)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_1811,plain,
    ! [X4679,X4680,X4681] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4681,c_Groups_Ozero__class_Ozero(X4681),X4680)
        | ~ c_Orderings_Oord__class_Oless__eq(X4681,c_Groups_Ozero__class_Ozero(X4681),X4679)
        | c_Orderings_Oord__class_Oless__eq(X4681,c_Groups_Ozero__class_Ozero(X4681),c_Groups_Otimes__class_Otimes(X4681,X4680,X4679))
        | ~ class_Rings_Oordered__ring(X4681) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4681,X4680,c_Groups_Ozero__class_Ozero(X4681))
        | ~ c_Orderings_Oord__class_Oless__eq(X4681,X4679,c_Groups_Ozero__class_Ozero(X4681))
        | c_Orderings_Oord__class_Oless__eq(X4681,c_Groups_Ozero__class_Ozero(X4681),c_Groups_Otimes__class_Otimes(X4681,X4680,X4679))
        | ~ class_Rings_Oordered__ring(X4681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_1812,plain,
    ! [X4634,X4635,X4636] :
      ( ~ class_Rings_Oordered__cancel__semiring(X4636)
      | ~ c_Orderings_Oord__class_Oless__eq(X4636,c_Groups_Ozero__class_Ozero(X4636),X4635)
      | ~ c_Orderings_Oord__class_Oless__eq(X4636,c_Groups_Ozero__class_Ozero(X4636),X4634)
      | c_Orderings_Oord__class_Oless__eq(X4636,c_Groups_Ozero__class_Ozero(X4636),c_Groups_Otimes__class_Otimes(X4636,X4635,X4634)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_1813,plain,
    ! [X3824,X3825,X3826] :
      ( ~ class_Fields_Olinordered__field(X3826)
      | ~ c_Orderings_Oord__class_Oless__eq(X3826,c_Groups_Ozero__class_Ozero(X3826),X3825)
      | ~ c_Orderings_Oord__class_Oless(X3826,c_Groups_Ozero__class_Ozero(X3826),X3824)
      | c_Orderings_Oord__class_Oless__eq(X3826,c_Groups_Ozero__class_Ozero(X3826),c_Rings_Oinverse__class_Odivide(X3826,X3825,X3824)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_1814,plain,
    ! [X3067,X3068,X3069] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3069)
      | ~ c_Orderings_Oord__class_Oless__eq(X3069,c_Groups_Ozero__class_Ozero(X3069),X3068)
      | ~ c_Orderings_Oord__class_Oless__eq(X3069,c_Groups_Ozero__class_Ozero(X3069),X3067)
      | c_Orderings_Oord__class_Oless__eq(X3069,c_Groups_Ozero__class_Ozero(X3069),c_Groups_Oplus__class_Oplus(X3069,X3068,X3067)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_1815,plain,
    ! [X4705,X4706,X4707] :
      ( ~ class_Rings_Olinordered__ring__strict(X4707)
      | ~ c_Orderings_Oord__class_Oless(X4707,X4706,c_Groups_Ozero__class_Ozero(X4707))
      | ~ c_Orderings_Oord__class_Oless(X4707,X4705,c_Groups_Ozero__class_Ozero(X4707))
      | c_Orderings_Oord__class_Oless(X4707,c_Groups_Ozero__class_Ozero(X4707),c_Groups_Otimes__class_Otimes(X4707,X4706,X4705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_1816,plain,
    ! [X3803,X3804,X3805] :
      ( ~ class_Fields_Olinordered__field(X3805)
      | ~ c_Orderings_Oord__class_Oless(X3805,X3804,c_Groups_Ozero__class_Ozero(X3805))
      | ~ c_Orderings_Oord__class_Oless(X3805,X3803,c_Groups_Ozero__class_Ozero(X3805))
      | c_Orderings_Oord__class_Oless(X3805,c_Groups_Ozero__class_Ozero(X3805),c_Rings_Oinverse__class_Odivide(X3805,X3804,X3803)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_1817,plain,
    ! [X4646,X4647,X4648] :
      ( ~ class_Rings_Oordered__ring(X4648)
      | ~ c_Orderings_Oord__class_Oless__eq(X4648,X4647,c_Groups_Ozero__class_Ozero(X4648))
      | ~ c_Orderings_Oord__class_Oless__eq(X4648,X4646,c_Groups_Ozero__class_Ozero(X4648))
      | c_Orderings_Oord__class_Oless__eq(X4648,c_Groups_Ozero__class_Ozero(X4648),c_Groups_Otimes__class_Otimes(X4648,X4647,X4646)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_1818,plain,
    ! [X3769,X3770,X3771] :
      ( ~ class_Fields_Olinordered__field(X3771)
      | ~ c_Orderings_Oord__class_Oless__eq(X3771,X3770,c_Groups_Ozero__class_Ozero(X3771))
      | ~ c_Orderings_Oord__class_Oless(X3771,X3769,c_Groups_Ozero__class_Ozero(X3771))
      | c_Orderings_Oord__class_Oless__eq(X3771,c_Groups_Ozero__class_Ozero(X3771),c_Rings_Oinverse__class_Odivide(X3771,X3770,X3769)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_1819,plain,
    ! [X3324,X3325] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3325,X3324))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3325)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3324) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3325)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3325,X3324)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3324)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3325,X3324)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_1820,plain,
    ! [X3698,X3699] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3699,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),X3698)
        | ~ 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,X3699,X3698)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3699)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3698,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,X3699,X3698)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3699)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3699,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,X3699,X3698)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3698,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3699,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,X3699,X3698)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3699)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3698)
        | 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,X3699,X3698)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3698,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),X3698)
        | 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,X3699,X3698)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff])])]) ).

fof(i_0_1821,plain,
    ! [X2965,X2966,X2967,X2968] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2968)
      | ~ c_Orderings_Oord__class_Oless(X2968,X2967,X2966)
      | c_Orderings_Oord__class_Oless(X2968,c_Groups_Oplus__class_Oplus(X2968,X2967,X2965),c_Groups_Oplus__class_Oplus(X2968,X2966,X2965)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_1822,plain,
    ! [X2969,X2970,X2971,X2972] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2972)
      | ~ c_Orderings_Oord__class_Oless(X2972,X2971,X2970)
      | c_Orderings_Oord__class_Oless(X2972,c_Groups_Oplus__class_Oplus(X2972,X2969,X2971),c_Groups_Oplus__class_Oplus(X2972,X2969,X2970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_1823,plain,
    ! [X2568,X2569,X2570,X2571] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2571)
      | ~ c_Orderings_Oord__class_Oless__eq(X2571,X2570,X2569)
      | c_Orderings_Oord__class_Oless__eq(X2571,c_Groups_Oplus__class_Oplus(X2571,X2570,X2568),c_Groups_Oplus__class_Oplus(X2571,X2569,X2568)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_1824,plain,
    ! [X2564,X2565,X2566,X2567] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X2567)
      | ~ c_Orderings_Oord__class_Oless__eq(X2567,X2566,X2565)
      | c_Orderings_Oord__class_Oless__eq(X2567,c_Groups_Oplus__class_Oplus(X2567,X2564,X2566),c_Groups_Oplus__class_Oplus(X2567,X2564,X2565)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

cnf(i_0_1825,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1341]) ).

cnf(i_0_1826,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1358]) ).

cnf(i_0_1827,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1343]) ).

fof(i_0_1828,plain,
    ! [X3927,X3928,X3929,X3930] :
      ( ( ~ c_SEQ_Odecseq(X3928,X3927)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3929,X3930)
        | c_Orderings_Oord__class_Oless__eq(X3928,hAPP(X3927,X3930),hAPP(X3927,X3929))
        | ~ class_Orderings_Oorder(X3928) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk42_2(X3927,X3928),esk43_2(X3927,X3928))
        | c_SEQ_Odecseq(X3928,X3927)
        | ~ class_Orderings_Oorder(X3928) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3928,hAPP(X3927,esk43_2(X3927,X3928)),hAPP(X3927,esk42_2(X3927,X3928)))
        | c_SEQ_Odecseq(X3928,X3927)
        | ~ class_Orderings_Oorder(X3928) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decseq__def])])])])]) ).

fof(i_0_1829,plain,
    ! [X3898,X3899] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3899),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3898)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3899,c_RealDef_Oreal(tc_Nat_Onat,X3898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).

fof(i_0_1830,plain,
    ! [X3454,X3455,X3456,X3457] :
      ( ~ class_Rings_Olinordered__semidom(X3457)
      | ~ c_Orderings_Oord__class_Oless(X3457,c_Groups_Ozero__class_Ozero(X3457),X3456)
      | ~ c_Orderings_Oord__class_Oless(X3457,X3455,X3454)
      | c_Orderings_Oord__class_Oless(X3457,X3455,c_Groups_Oplus__class_Oplus(X3457,X3456,X3454)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_1831,plain,
    ! [X2914,X2915,X2916,X2917] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2917)
      | ~ c_Orderings_Oord__class_Oless__eq(X2917,c_Groups_Ozero__class_Ozero(X2917),X2916)
      | ~ c_Orderings_Oord__class_Oless(X2917,X2915,X2914)
      | c_Orderings_Oord__class_Oless(X2917,X2915,c_Groups_Oplus__class_Oplus(X2917,X2916,X2914)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_1832,plain,
    ! [X2910,X2911,X2912,X2913] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X2913)
      | ~ c_Orderings_Oord__class_Oless(X2913,c_Groups_Ozero__class_Ozero(X2913),X2912)
      | ~ c_Orderings_Oord__class_Oless__eq(X2913,X2911,X2910)
      | c_Orderings_Oord__class_Oless(X2913,X2911,c_Groups_Oplus__class_Oplus(X2913,X2912,X2910)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_1833,plain,
    ! [X3073,X3074,X3075,X3076] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3076)
      | ~ c_Orderings_Oord__class_Oless__eq(X3076,c_Groups_Ozero__class_Ozero(X3076),X3075)
      | ~ c_Orderings_Oord__class_Oless__eq(X3076,X3074,X3073)
      | c_Orderings_Oord__class_Oless__eq(X3076,X3074,c_Groups_Oplus__class_Oplus(X3076,X3075,X3073)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_1834,plain,
    ! [X3077,X3078,X3079,X3080] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X3080)
      | ~ c_Orderings_Oord__class_Oless__eq(X3080,c_Groups_Ozero__class_Ozero(X3080),X3079)
      | ~ c_Orderings_Oord__class_Oless__eq(X3080,X3078,X3077)
      | c_Orderings_Oord__class_Oless__eq(X3080,X3078,c_Groups_Oplus__class_Oplus(X3080,X3077,X3079)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_1835,plain,
    ! [X4187,X4188,X4189] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4189,c_Int_Onumber__class_Onumber__of(X4189,X4188),c_Int_Onumber__class_Onumber__of(X4189,X4187))
        | ~ c_Orderings_Oord__class_Oless(X4189,c_Int_Onumber__class_Onumber__of(X4189,X4187),c_Int_Onumber__class_Onumber__of(X4189,X4188))
        | ~ class_Int_Onumber(X4189)
        | ~ class_Orderings_Olinorder(X4189) )
      & ( c_Orderings_Oord__class_Oless(X4189,c_Int_Onumber__class_Onumber__of(X4189,X4187),c_Int_Onumber__class_Onumber__of(X4189,X4188))
        | c_Orderings_Oord__class_Oless__eq(X4189,c_Int_Onumber__class_Onumber__of(X4189,X4188),c_Int_Onumber__class_Onumber__of(X4189,X4187))
        | ~ class_Int_Onumber(X4189)
        | ~ class_Orderings_Olinorder(X4189) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1359])])]) ).

cnf(i_0_1836,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1360]) ).

fof(i_0_1837,plain,
    ! [X2640] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2640),v_r)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X2640))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_s1m])]) ).

cnf(i_0_1838,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_1346]) ).

cnf(i_0_1839,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1347]) ).

fof(i_0_1840,plain,
    ! [X4317,X4318,X4319] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4319,X4318)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4319,X4317),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4318,X4317)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_1841,plain,
    ! [X3364,X3365,X3366] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3366,X3365)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3366,X3364),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3365,X3364)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

cnf(i_0_1842,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_1348]) ).

cnf(i_0_1843,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1349]) ).

fof(i_0_1844,plain,
    ! [X4314,X4315,X4316] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4316,X4315)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4314,X4316),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4314,X4315)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_1845,plain,
    ! [X3951,X3952,X3953] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3953,X3952)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3953,X3951),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3952,X3951)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).

fof(i_0_1846,plain,
    ! [X3212,X3213,X3214] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3214,X3213)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3214,X3212),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3213,X3212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).

fof(i_0_1847,plain,
    ! [X3215,X3216,X3217] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3217,X3216)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3215,X3216),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3215,X3217)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).

fof(i_0_1848,plain,
    ! [X3247,X3248,X3249] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3249,X3248)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3249,X3247),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3248,X3247)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_1849,plain,
    ! [X2628,X2629,X2630] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2630,X2629)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2628,X2630),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2628,X2629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).

cnf(i_0_1850,plain,
    ( X1 = c_Nat_OSuc(esk24_2(X2,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

cnf(i_0_1851,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1362]) ).

fof(i_0_1852,plain,
    ! [X4786,X4787,X4788] :
      ( ~ class_Rings_Ocomm__semiring__1(X4788)
      | c_Groups_Oplus__class_Oplus(X4788,c_Groups_Otimes__class_Otimes(X4788,X4787,X4786),X4786) = c_Groups_Otimes__class_Otimes(X4788,c_Groups_Oplus__class_Oplus(X4788,X4787,c_Groups_Oone__class_Oone(X4788)),X4786) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_1853,plain,
    ! [X4789,X4790,X4791] :
      ( ~ class_Rings_Ocomm__semiring__1(X4791)
      | c_Groups_Oplus__class_Oplus(X4791,X4790,c_Groups_Otimes__class_Otimes(X4791,X4789,X4790)) = c_Groups_Otimes__class_Otimes(X4791,c_Groups_Oplus__class_Oplus(X4791,X4789,c_Groups_Oone__class_Oone(X4791)),X4790) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

fof(i_0_1854,plain,
    ! [X3961,X3962,X3963] :
      ( ~ class_Divides_Osemiring__div(X3963)
      | X3962 = c_Groups_Ozero__class_Ozero(X3963)
      | c_Divides_Odiv__class_Odiv(X3963,c_Groups_Oplus__class_Oplus(X3963,X3962,X3961),X3962) = c_Groups_Oplus__class_Oplus(X3963,c_Divides_Odiv__class_Odiv(X3963,X3961,X3962),c_Groups_Oone__class_Oone(X3963)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).

fof(i_0_1855,plain,
    ! [X3964,X3965,X3966] :
      ( ~ class_Divides_Osemiring__div(X3966)
      | X3965 = c_Groups_Ozero__class_Ozero(X3966)
      | c_Divides_Odiv__class_Odiv(X3966,c_Groups_Oplus__class_Oplus(X3966,X3964,X3965),X3965) = c_Groups_Oplus__class_Oplus(X3966,c_Divides_Odiv__class_Odiv(X3966,X3964,X3965),c_Groups_Oone__class_Oone(X3966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).

cnf(i_0_1856,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1363]) ).

cnf(i_0_1857,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1364]) ).

cnf(i_0_1858,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_1365]) ).

cnf(i_0_1859,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_1366]) ).

cnf(i_0_1860,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_2(X1,X2),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

cnf(i_0_1861,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_1367]) ).

cnf(i_0_1862,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_1368]) ).

fof(i_0_1863,plain,
    ! [X2596,X2597,X2598] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2598)
      | c_Groups_Oabs__class_Oabs(X2598,c_Groups_Oplus__class_Oplus(X2598,c_Groups_Oabs__class_Oabs(X2598,X2597),c_Groups_Oabs__class_Oabs(X2598,X2596))) = c_Groups_Oplus__class_Oplus(X2598,c_Groups_Oabs__class_Oabs(X2598,X2597),c_Groups_Oabs__class_Oabs(X2598,X2596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).

fof(i_0_1864,plain,
    ! [X4231,X4232] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4232,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_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4232,X4231),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])]) ).

fof(i_0_1865,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(tc_Int_Oint,X4250,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4251,X4250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])]) ).

fof(i_0_1866,plain,
    ! [X4244,X4245] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4245,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ 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_Divides_Odiv__class_Odiv(tc_Int_Oint,X4245,X4244),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])]) ).

fof(i_0_1867,plain,
    ! [X4255,X4256] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4256)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4255)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4256,X4255)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).

cnf(i_0_1868,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X3))
    | X1 != c_Nat_OSuc(X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

fof(i_0_1869,plain,
    ! [X3202,X3203,X3204] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3203,X3204) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3202,X3204)
        | X3203 = X3202
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3204,X3202)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3204,X3203) )
      & ( X3203 != X3202
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3203,X3204) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3202,X3204)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3204,X3202)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3204,X3203) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).

fof(i_0_1870,plain,
    ! [X4814,X4815,X4816,X4817] :
      ( ~ class_Fields_Ofield__inverse__zero(X4817)
      | X4816 = c_Groups_Ozero__class_Ozero(X4817)
      | c_Rings_Oinverse__class_Odivide(X4817,c_Groups_Otimes__class_Otimes(X4817,X4816,X4815),c_Groups_Otimes__class_Otimes(X4817,X4816,X4814)) = c_Rings_Oinverse__class_Odivide(X4817,X4815,X4814) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_1871,plain,
    ! [X4810,X4811,X4812,X4813] :
      ( ~ class_Fields_Ofield__inverse__zero(X4813)
      | X4812 = c_Groups_Ozero__class_Ozero(X4813)
      | c_Rings_Oinverse__class_Odivide(X4813,c_Groups_Otimes__class_Otimes(X4813,X4811,X4812),c_Groups_Otimes__class_Otimes(X4813,X4810,X4812)) = c_Rings_Oinverse__class_Odivide(X4813,X4811,X4810) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_1872,plain,
    ! [X4266,X4267] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4267)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4266)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4267,X4266),X4267) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).

fof(i_0_1873,plain,
    ! [X3970,X3971] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3971)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3970)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3970,X3971),X3970) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).

fof(i_0_1874,plain,
    ! [X3326,X3327] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3327)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3326)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3326,X3327),X3326) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).

fof(i_0_1875,plain,
    ! [X3891,X3892] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3892),X3891)
      | c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3891,c_RealDef_Oreal(tc_Nat_Onat,X3892))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X3891),X3892) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).

fof(i_0_1876,plain,
    ! [X3867,X3868] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3868),X3867)
      | c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3867,c_RealDef_Oreal(tc_Nat_Onat,X3868))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X3867),X3868) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).

cnf(i_0_1877,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,c_Nat_OSuc(X2)))
    | ~ c_SEQ_Osubseq(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1334]) ).

fof(i_0_1878,plain,
    ! [X2813,X2814] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2814,c_Groups_Ozero__class_Ozero(X2814),c_Groups_Oplus__class_Oplus(X2814,X2813,X2813))
        | c_Orderings_Oord__class_Oless(X2814,c_Groups_Ozero__class_Ozero(X2814),X2813)
        | ~ class_Groups_Olinordered__ab__group__add(X2814) )
      & ( ~ c_Orderings_Oord__class_Oless(X2814,c_Groups_Ozero__class_Ozero(X2814),X2813)
        | c_Orderings_Oord__class_Oless(X2814,c_Groups_Ozero__class_Ozero(X2814),c_Groups_Oplus__class_Oplus(X2814,X2813,X2813))
        | ~ class_Groups_Olinordered__ab__group__add(X2814) ) ),
    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_1879,plain,
    ! [X3063,X3064] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3064,c_Groups_Ozero__class_Ozero(X3064),c_Groups_Oplus__class_Oplus(X3064,X3063,X3063))
        | c_Orderings_Oord__class_Oless__eq(X3064,c_Groups_Ozero__class_Ozero(X3064),X3063)
        | ~ class_Groups_Olinordered__ab__group__add(X3064) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3064,c_Groups_Ozero__class_Ozero(X3064),X3063)
        | c_Orderings_Oord__class_Oless__eq(X3064,c_Groups_Ozero__class_Ozero(X3064),c_Groups_Oplus__class_Oplus(X3064,X3063,X3063))
        | ~ class_Groups_Olinordered__ab__group__add(X3064) ) ),
    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_1880,plain,
    ! [X3463,X3464] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3464,c_Groups_Oplus__class_Oplus(X3464,X3463,X3463),c_Groups_Ozero__class_Ozero(X3464))
        | c_Orderings_Oord__class_Oless(X3464,X3463,c_Groups_Ozero__class_Ozero(X3464))
        | ~ class_Rings_Olinordered__idom(X3464) )
      & ( ~ c_Orderings_Oord__class_Oless(X3464,X3463,c_Groups_Ozero__class_Ozero(X3464))
        | c_Orderings_Oord__class_Oless(X3464,c_Groups_Oplus__class_Oplus(X3464,X3463,X3463),c_Groups_Ozero__class_Ozero(X3464))
        | ~ class_Rings_Olinordered__idom(X3464) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_1881,plain,
    ! [X2811,X2812] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2812,c_Groups_Oplus__class_Oplus(X2812,X2811,X2811),c_Groups_Ozero__class_Ozero(X2812))
        | c_Orderings_Oord__class_Oless(X2812,X2811,c_Groups_Ozero__class_Ozero(X2812))
        | ~ class_Groups_Olinordered__ab__group__add(X2812) )
      & ( ~ c_Orderings_Oord__class_Oless(X2812,X2811,c_Groups_Ozero__class_Ozero(X2812))
        | c_Orderings_Oord__class_Oless(X2812,c_Groups_Oplus__class_Oplus(X2812,X2811,X2811),c_Groups_Ozero__class_Ozero(X2812))
        | ~ class_Groups_Olinordered__ab__group__add(X2812) ) ),
    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_1882,plain,
    ! [X3065,X3066] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3066,c_Groups_Oplus__class_Oplus(X3066,X3065,X3065),c_Groups_Ozero__class_Ozero(X3066))
        | c_Orderings_Oord__class_Oless__eq(X3066,X3065,c_Groups_Ozero__class_Ozero(X3066))
        | ~ class_Groups_Olinordered__ab__group__add(X3066) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3066,X3065,c_Groups_Ozero__class_Ozero(X3066))
        | c_Orderings_Oord__class_Oless__eq(X3066,c_Groups_Oplus__class_Oplus(X3066,X3065,X3065),c_Groups_Ozero__class_Ozero(X3066))
        | ~ class_Groups_Olinordered__ab__group__add(X3066) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).

cnf(i_0_1883,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1369]) ).

fof(i_0_1884,plain,
    ! [X3727,X3728,X3729,X3730] :
      ( ~ class_Rings_Ocomm__semiring__1(X3730)
      | c_Groups_Oplus__class_Oplus(X3730,c_Groups_Oplus__class_Oplus(X3730,X3729,X3728),X3727) = c_Groups_Oplus__class_Oplus(X3730,c_Groups_Oplus__class_Oplus(X3730,X3729,X3727),X3728) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_1885,plain,
    ! [X3723,X3724,X3725,X3726] :
      ( ~ class_Rings_Ocomm__semiring__1(X3726)
      | c_Groups_Oplus__class_Oplus(X3726,c_Groups_Oplus__class_Oplus(X3726,X3725,X3724),X3723) = c_Groups_Oplus__class_Oplus(X3726,X3725,c_Groups_Oplus__class_Oplus(X3726,X3724,X3723)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_1886,plain,
    ! [X2540,X2541,X2542,X2543] :
      ( ~ class_Groups_Oab__semigroup__add(X2543)
      | c_Groups_Oplus__class_Oplus(X2543,c_Groups_Oplus__class_Oplus(X2543,X2542,X2541),X2540) = c_Groups_Oplus__class_Oplus(X2543,X2542,c_Groups_Oplus__class_Oplus(X2543,X2541,X2540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_1887,plain,
    ! [X3719,X3720,X3721,X3722] :
      ( ~ class_Rings_Ocomm__semiring__1(X3722)
      | c_Groups_Oplus__class_Oplus(X3722,X3721,c_Groups_Oplus__class_Oplus(X3722,X3720,X3719)) = c_Groups_Oplus__class_Oplus(X3722,c_Groups_Oplus__class_Oplus(X3722,X3721,X3720),X3719) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_1888,plain,
    ! [X3715,X3716,X3717,X3718] :
      ( ~ class_Rings_Ocomm__semiring__1(X3718)
      | c_Groups_Oplus__class_Oplus(X3718,X3717,c_Groups_Oplus__class_Oplus(X3718,X3716,X3715)) = c_Groups_Oplus__class_Oplus(X3718,X3716,c_Groups_Oplus__class_Oplus(X3718,X3717,X3715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

cnf(i_0_1889,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_1890,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).

cnf(i_0_1891,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[fact_Numeral1__eq1__nat]) ).

fof(i_0_1892,plain,
    ! [X3452] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3452),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3452),
    inference(variable_rename,[status(thm)],[i_0_1370]) ).

fof(i_0_1893,plain,
    ! [X2666,X2667] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2667,X2666))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2667),X2666) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2667),X2666)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2667,X2666)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).

fof(i_0_1894,plain,
    ! [X2902,X2903] :
      ( ( ~ 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,X2903,X2902))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2903),X2902) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2903),X2902)
        | 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,X2903,X2902)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).

fof(i_0_1895,plain,
    ! [X2701,X2702] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2702,X2701),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2701,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2702)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2701,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2702))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2702,X2701),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_1896,plain,
    ! [X2900,X2901] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2901,X2900),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2900,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2901)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2900,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2901))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2901,X2900),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_1897,plain,
    ! [X4612,X4613,X4614] :
      ( ~ class_Fields_Olinordered__field(X4614)
      | ~ c_Orderings_Oord__class_Oless(X4614,c_Rings_Oinverse__class_Oinverse(X4614,X4613),c_Rings_Oinverse__class_Oinverse(X4614,X4612))
      | ~ c_Orderings_Oord__class_Oless(X4614,c_Groups_Ozero__class_Ozero(X4614),X4613)
      | c_Orderings_Oord__class_Oless(X4614,X4612,X4613) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).

fof(i_0_1898,plain,
    ! [X4615,X4616,X4617] :
      ( ~ class_Fields_Olinordered__field(X4617)
      | ~ c_Orderings_Oord__class_Oless(X4617,c_Rings_Oinverse__class_Oinverse(X4617,X4616),c_Rings_Oinverse__class_Oinverse(X4617,X4615))
      | ~ c_Orderings_Oord__class_Oless(X4617,X4615,c_Groups_Ozero__class_Ozero(X4617))
      | c_Orderings_Oord__class_Oless(X4617,X4615,X4616) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).

fof(i_0_1899,plain,
    ! [X2815,X2816,X2817] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2817,X2816,X2815)
        | c_Orderings_Oord__class_Oless(X2817,c_Groups_Ominus__class_Ominus(X2817,X2816,X2815),c_Groups_Ozero__class_Ozero(X2817))
        | ~ class_Groups_Oordered__ab__group__add(X2817) )
      & ( ~ c_Orderings_Oord__class_Oless(X2817,c_Groups_Ominus__class_Ominus(X2817,X2816,X2815),c_Groups_Ozero__class_Ozero(X2817))
        | c_Orderings_Oord__class_Oless(X2817,X2816,X2815)
        | ~ class_Groups_Oordered__ab__group__add(X2817) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(i_0_1900,plain,
    ! [X3084,X3085,X3086] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3086,X3085,X3084)
        | c_Orderings_Oord__class_Oless__eq(X3086,c_Groups_Ominus__class_Ominus(X3086,X3085,X3084),c_Groups_Ozero__class_Ozero(X3086))
        | ~ class_Groups_Oordered__ab__group__add(X3086) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3086,c_Groups_Ominus__class_Ominus(X3086,X3085,X3084),c_Groups_Ozero__class_Ozero(X3086))
        | c_Orderings_Oord__class_Oless__eq(X3086,X3085,X3084)
        | ~ class_Groups_Oordered__ab__group__add(X3086) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).

cnf(i_0_1901,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_1371]) ).

cnf(i_0_1902,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(split_conjunct,[status(thm)],[i_0_1372]) ).

cnf(i_0_1903,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
    inference(split_conjunct,[status(thm)],[i_0_1373]) ).

fof(i_0_1904,plain,
    ! [X3025,X3026] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3026,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3025))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3025,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3026))),
    inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).

cnf(i_0_1905,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1374]) ).

cnf(i_0_1906,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1375]) ).

fof(i_0_1907,plain,
    ! [X2990,X2991,X2992,X2993,X2994] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2994,X2993,X2992)
        | c_Orderings_Oord__class_Oless(X2994,X2991,X2990)
        | c_Groups_Ominus__class_Ominus(X2994,X2993,X2992) != c_Groups_Ominus__class_Ominus(X2994,X2991,X2990)
        | ~ class_Groups_Oordered__ab__group__add(X2994) )
      & ( ~ c_Orderings_Oord__class_Oless(X2994,X2991,X2990)
        | c_Orderings_Oord__class_Oless(X2994,X2993,X2992)
        | c_Groups_Ominus__class_Ominus(X2994,X2993,X2992) != c_Groups_Ominus__class_Ominus(X2994,X2991,X2990)
        | ~ class_Groups_Oordered__ab__group__add(X2994) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).

fof(i_0_1908,plain,
    ! [X2580,X2581,X2582,X2583,X2584] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2584,X2583,X2582)
        | c_Orderings_Oord__class_Oless__eq(X2584,X2581,X2580)
        | c_Groups_Ominus__class_Ominus(X2584,X2583,X2582) != c_Groups_Ominus__class_Ominus(X2584,X2581,X2580)
        | ~ class_Groups_Oordered__ab__group__add(X2584) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2584,X2581,X2580)
        | c_Orderings_Oord__class_Oless__eq(X2584,X2583,X2582)
        | c_Groups_Ominus__class_Ominus(X2584,X2583,X2582) != c_Groups_Ominus__class_Ominus(X2584,X2581,X2580)
        | ~ class_Groups_Oordered__ab__group__add(X2584) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).

fof(i_0_1909,plain,
    ! [X4343,X4344] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4344,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4344),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4343)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4343) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4343,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4344),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4343)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4344)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4344,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4343,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4344),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4343)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4344,X4343))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4344,c_Int_OPls) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1376])])]) ).

fof(i_0_1910,plain,
    ! [X3302,X3303] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3303),v_r)
      | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3303)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3302)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3302,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096])]) ).

fof(i_0_1911,plain,
    ! [X3190,X3191,X3192] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3192,X3191),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3192,X3190)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3191,X3190),
    inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).

fof(i_0_1912,plain,
    ! [X3193,X3194,X3195] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3195,X3194),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3193,X3194)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3195,X3193),
    inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).

fof(i_0_1913,plain,
    ! [X2703,X2704,X2705] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2705,X2704),X2703) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2705,X2703),X2704),
    inference(variable_rename,[status(thm)],[fact_diff__commute]) ).

fof(i_0_1914,plain,
    ! [X3187,X3188,X3189] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3189,X3188),X3187) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3189,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3188,X3187)),
    inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).

fof(i_0_1915,plain,
    ! [X4297,X4298,X4299] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4299,X4298),X4297) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4299,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4298,X4297)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_1916,plain,
    ! [X3174,X3175,X3176] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3176,X3175),X3174) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3176,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3175,X3174)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_1917,plain,
    ! [X4294,X4295,X4296] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4296,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4295,X4294)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4295,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4296,X4294)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_1918,plain,
    ! [X3171,X3172,X3173] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3173,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3172,X3171)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3172,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3173,X3171)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_1919,plain,
    ! [X4331,X4332] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4331,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,X4331)
        | X4332 = X4331 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,X4331)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4331,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( X4332 != X4331
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4332,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4331,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).

cnf(i_0_1920,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1377]) ).

cnf(i_0_1921,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1378]) ).

cnf(i_0_1922,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1379]) ).

cnf(i_0_1923,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1380]) ).

fof(i_0_1924,plain,
    ! [X3298,X3299] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3299),v_r)
      | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X3299)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3298)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3298,esk11_0) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mth2])])])]) ).

fof(i_0_1925,plain,
    ! [X4328,X4329] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4329,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4328)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4329,X4328) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4329,X4328)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4329,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4328) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

cnf(i_0_1926,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1381]) ).

cnf(i_0_1927,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1382]) ).

cnf(i_0_1928,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1383]) ).

cnf(i_0_1929,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1384]) ).

cnf(i_0_1930,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1385]) ).

fof(i_0_1931,plain,
    ! [X4268,X4269] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4269,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4268,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4269,X4268) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4269,X4268)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4269,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4268,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).

fof(i_0_1932,plain,
    ! [X4333,X4334] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4334,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4333,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4334,X4333) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4334,X4333)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4334,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4333,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_1933,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1386]) ).

cnf(i_0_1934,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_1387]) ).

cnf(i_0_1935,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1388]) ).

fof(i_0_1936,plain,
    ! [X4277,X4278] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4278,X4277)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4278,X4277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4278,X4277),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4278,X4277) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).

fof(i_0_1937,plain,
    ! [X3027,X3028] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3028,X3027)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3028,X3027),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3028,X3027),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3028,X3027) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).

fof(i_0_1938,plain,
    ! [X3328,X3329] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3329,X3328))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3328,X3329) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3328,X3329)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3329,X3328)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).

fof(i_0_1939,plain,
    ! [X3760,X3761,X3762] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X3762)
      | ~ c_Orderings_Oord__class_Oless(X3762,c_Groups_Ozero__class_Ozero(X3762),X3761)
      | c_Rings_Oinverse__class_Odivide(X3762,c_Groups_Oabs__class_Oabs(X3762,X3760),X3761) = c_Groups_Oabs__class_Oabs(X3762,c_Rings_Oinverse__class_Odivide(X3762,X3760,X3761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

cnf(i_0_1940,plain,
    ( c_Nat_OSuc(X1) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1389]) ).

fof(i_0_1941,plain,
    ! [X3356,X3357,X3358,X3359] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3359,X3358)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3357,X3358) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3359,X3356)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3357,X3356) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_1942,plain,
    ! [X3896,X3897] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3897)
      | c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3897,c_RealDef_Oreal(tc_Nat_Onat,X3896))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3897),X3896) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).

fof(i_0_1943,plain,
    ! [X3869,X3870] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3870)
      | c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3870,c_RealDef_Oreal(tc_Nat_Onat,X3869))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X3870),X3869) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).

fof(i_0_1944,plain,
    ! [X3310,X3311,X3312] :
      ( ( c_Orderings_Oord__class_Oless(X3312,X3311,X3310)
        | ~ c_Orderings_Oord__class_Oless(X3312,c_Groups_Oabs__class_Oabs(X3312,X3311),X3310)
        | ~ class_Rings_Olinordered__idom(X3312) )
      & ( c_Orderings_Oord__class_Oless(X3312,c_Groups_Ouminus__class_Ouminus(X3312,X3311),X3310)
        | ~ c_Orderings_Oord__class_Oless(X3312,c_Groups_Oabs__class_Oabs(X3312,X3311),X3310)
        | ~ class_Rings_Olinordered__idom(X3312) )
      & ( ~ c_Orderings_Oord__class_Oless(X3312,X3311,X3310)
        | ~ c_Orderings_Oord__class_Oless(X3312,c_Groups_Ouminus__class_Ouminus(X3312,X3311),X3310)
        | c_Orderings_Oord__class_Oless(X3312,c_Groups_Oabs__class_Oabs(X3312,X3311),X3310)
        | ~ class_Rings_Olinordered__idom(X3312) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).

fof(i_0_1945,plain,
    ! [X3043,X3044,X3045] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3045)
      | ~ c_Orderings_Oord__class_Oless__eq(X3045,X3044,X3043)
      | ~ c_Orderings_Oord__class_Oless__eq(X3045,c_Groups_Ouminus__class_Ouminus(X3045,X3044),X3043)
      | c_Orderings_Oord__class_Oless__eq(X3045,c_Groups_Oabs__class_Oabs(X3045,X3044),X3043) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).

fof(i_0_1946,plain,
    ! [X3040,X3041,X3042] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3042,X3041,X3040)
        | ~ c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Oabs__class_Oabs(X3042,X3041),X3040)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3042) )
      & ( c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Ouminus__class_Ouminus(X3042,X3041),X3040)
        | ~ c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Oabs__class_Oabs(X3042,X3041),X3040)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3042) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3042,X3041,X3040)
        | ~ c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Ouminus__class_Ouminus(X3042,X3041),X3040)
        | c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Oabs__class_Oabs(X3042,X3041),X3040)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3042) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).

fof(i_0_1947,plain,
    ! [X3353,X3354,X3355] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3355,X3354),X3353)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3355,X3353) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_1948,plain,
    ! [X3260,X3261,X3262] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3262,X3260)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3262,X3261),X3260) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3261,X3260)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3262,X3261),X3260) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1390])])]) ).

fof(i_0_1949,plain,
    ! [X3257,X3258,X3259] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3259,X3258),X3257)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3259,X3257) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_1950,plain,
    ! [X3254,X3255,X3256] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3256,X3255),X3254)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3255,X3254) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_1951,plain,
    ! [X3704,X3705] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3705,X3704)
      | c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3704,X3705)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3704),c_RealDef_Oreal(tc_Nat_Onat,X3705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).

cnf(i_0_1952,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1))),
    inference(split_conjunct,[status(thm)],[i_0_1391]) ).

fof(i_0_1953,plain,
    ! [X4818,X4819,X4820,X4821,X4822] :
      ( ( c_Rings_Oinverse__class_Odivide(X4822,X4819,X4821) != c_Rings_Oinverse__class_Odivide(X4822,X4818,X4820)
        | c_Groups_Otimes__class_Otimes(X4822,X4819,X4820) = c_Groups_Otimes__class_Otimes(X4822,X4818,X4821)
        | X4820 = c_Groups_Ozero__class_Ozero(X4822)
        | X4821 = c_Groups_Ozero__class_Ozero(X4822)
        | ~ class_Fields_Ofield(X4822) )
      & ( c_Groups_Otimes__class_Otimes(X4822,X4819,X4820) != c_Groups_Otimes__class_Otimes(X4822,X4818,X4821)
        | c_Rings_Oinverse__class_Odivide(X4822,X4819,X4821) = c_Rings_Oinverse__class_Odivide(X4822,X4818,X4820)
        | X4820 = c_Groups_Ozero__class_Ozero(X4822)
        | X4821 = c_Groups_Ozero__class_Ozero(X4822)
        | ~ class_Fields_Ofield(X4822) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

cnf(i_0_1954,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_1955,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

cnf(i_0_1956,plain,
    ( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk26_2(X2,X1)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1388]) ).

fof(i_0_1957,plain,
    ! [X3070,X3071,X3072] :
      ( ( X3071 = c_Groups_Ozero__class_Ozero(X3072)
        | c_Groups_Oplus__class_Oplus(X3072,X3071,X3070) != c_Groups_Ozero__class_Ozero(X3072)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3070)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3071)
        | ~ class_Groups_Oordered__comm__monoid__add(X3072) )
      & ( X3070 = c_Groups_Ozero__class_Ozero(X3072)
        | c_Groups_Oplus__class_Oplus(X3072,X3071,X3070) != c_Groups_Ozero__class_Ozero(X3072)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3070)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3071)
        | ~ class_Groups_Oordered__comm__monoid__add(X3072) )
      & ( X3071 != c_Groups_Ozero__class_Ozero(X3072)
        | X3070 != c_Groups_Ozero__class_Ozero(X3072)
        | c_Groups_Oplus__class_Oplus(X3072,X3071,X3070) = c_Groups_Ozero__class_Ozero(X3072)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3070)
        | ~ c_Orderings_Oord__class_Oless__eq(X3072,c_Groups_Ozero__class_Ozero(X3072),X3071)
        | ~ class_Groups_Oordered__comm__monoid__add(X3072) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_1958,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_1394]) ).

cnf(i_0_1959,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1395]) ).

cnf(i_0_1960,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_1396]) ).

cnf(i_0_1961,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_1397]) ).

fof(i_0_1962,plain,
    ! [X4604,X4605,X4606] :
      ( ~ class_Fields_Olinordered__field(X4606)
      | ~ c_Orderings_Oord__class_Oless(X4606,X4605,X4604)
      | ~ c_Orderings_Oord__class_Oless(X4606,c_Groups_Ozero__class_Ozero(X4606),X4605)
      | c_Orderings_Oord__class_Oless(X4606,c_Rings_Oinverse__class_Oinverse(X4606,X4604),c_Rings_Oinverse__class_Oinverse(X4606,X4605)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).

fof(i_0_1963,plain,
    ! [X4607,X4608,X4609] :
      ( ~ class_Fields_Olinordered__field(X4609)
      | ~ c_Orderings_Oord__class_Oless(X4609,X4608,X4607)
      | ~ c_Orderings_Oord__class_Oless(X4609,X4607,c_Groups_Ozero__class_Ozero(X4609))
      | c_Orderings_Oord__class_Oless(X4609,c_Rings_Oinverse__class_Oinverse(X4609,X4607),c_Rings_Oinverse__class_Oinverse(X4609,X4608)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).

fof(i_0_1964,plain,
    ! [X3316,X3317,X3318,X3319] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3318,X3319),X3317,X3316)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3318,X3319),X3317,X3316)
        | ~ class_Orderings_Oord(X3319) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3318,X3319),X3316,X3317)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(X3318,X3319),X3317,X3316)
        | ~ class_Orderings_Oord(X3319) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3318,X3319),X3317,X3316)
        | c_Orderings_Oord__class_Oless__eq(tc_fun(X3318,X3319),X3316,X3317)
        | c_Orderings_Oord__class_Oless(tc_fun(X3318,X3319),X3317,X3316)
        | ~ class_Orderings_Oord(X3319) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1398])])]) ).

fof(i_0_1965,plain,
    ! [X4341,X4342] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4342,X4341)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4341)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4342),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4341)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4342,X4341)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4342),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4341)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4342,X4341)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4342,X4341)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4342),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4341)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4341)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4342,X4341)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4342),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4341)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_1966,plain,
    ! [X3989,X3990,X3991,X3992,X3993] :
      ( ~ class_Groups_Ominus(X3993)
      | hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3992,X3993),X3991,X3990),X3989) = c_Groups_Ominus__class_Ominus(X3993,hAPP(X3991,X3989),hAPP(X3990,X3989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).

fof(i_0_1967,plain,
    ! [X3019,X3020] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3019),X3020)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3020),X3019) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3020,X3019)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3020),X3019) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3019),X3020)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3020,X3019)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3020),X3019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])]) ).

fof(i_0_1968,plain,
    ! [X4041,X4042,X4043] :
      ( ~ class_Int_Onumber__ring(X4043)
      | c_Groups_Ominus__class_Ominus(X4043,c_Int_Onumber__class_Onumber__of(X4043,X4042),c_Int_Onumber__class_Onumber__of(X4043,X4041)) = c_Int_Onumber__class_Onumber__of(X4043,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4042,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4041))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).

fof(i_0_1969,plain,
    ! [X4742,X4743] :
      ( ~ class_Rings_Olinordered__ring(X4743)
      | ~ c_Orderings_Oord__class_Oless(X4743,c_Groups_Otimes__class_Otimes(X4743,X4742,X4742),c_Groups_Ozero__class_Ozero(X4743)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1399])]) ).

cnf(i_0_1970,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1400]) ).

fof(i_0_1971,plain,
    ! [X3894,X3895] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3895)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3895,c_RealDef_Oreal(tc_Nat_Onat,X3894))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X3895),X3894) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).

fof(i_0_1972,plain,
    ! [X3864,X3865] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3865),X3864)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3865,c_RealDef_Oreal(tc_Nat_Onat,X3864))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3865) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3865,c_RealDef_Oreal(tc_Nat_Onat,X3864))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3865),X3864)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3865) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).

fof(i_0_1973,plain,
    ! [X3887,X3888] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3887,c_RComplete_Onatfloor(X3888))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3887),X3888)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3888) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3887),X3888)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3887,c_RComplete_Onatfloor(X3888))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3888) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).

cnf(i_0_1974,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1401]) ).

fof(i_0_1975,plain,
    ! [X3878] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3878)
      | c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3878,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X3878),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).

fof(i_0_1976,plain,
    ! [X3871] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3871)
      | c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3871,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X3871),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add__one])]) ).

fof(i_0_1977,plain,
    ! [X4345,X4346] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4346),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4345))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4346,X4345)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4346,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4346,X4345)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4346),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4345)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4346,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4346),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4345)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1402])])]) ).

fof(i_0_1978,plain,
    ! [X4282,X4283] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4283),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4282)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4283,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4282))),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(i_0_1979,plain,
    ! [X4336] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4336),X4336) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

cnf(i_0_1980,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_1403]) ).

cnf(i_0_1981,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_1404]) ).

cnf(i_0_1982,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_1405]) ).

cnf(i_0_1983,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1406]) ).

cnf(i_0_1984,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1407]) ).

fof(i_0_1985,plain,
    ! [X4326] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4326)
      | 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),X4326)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

cnf(i_0_1986,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1356]) ).

fof(i_0_1987,plain,
    ! [X2641] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X2641)))),
    inference(variable_rename,[status(thm)],[fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096]) ).

cnf(i_0_1988,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1362]) ).

fof(i_0_1989,plain,
    ! [X2602,X2603,X2604] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2604)
      | c_Groups_Oabs__class_Oabs(X2604,c_Groups_Ominus__class_Ominus(X2604,X2603,X2602)) = c_Groups_Oabs__class_Oabs(X2604,c_Groups_Ominus__class_Ominus(X2604,X2602,X2603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

fof(i_0_1990,plain,
    ! [X2599,X2600,X2601] :
      ( ~ class_RealVector_Oreal__normed__vector(X2601)
      | c_RealVector_Onorm__class_Onorm(X2601,c_Groups_Ominus__class_Ominus(X2601,X2600,X2599)) = c_RealVector_Onorm__class_Onorm(X2601,c_Groups_Ominus__class_Ominus(X2601,X2599,X2600)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).

cnf(i_0_1991,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_1387]) ).

fof(i_0_1992,plain,
    ! [X4792,X4793] :
      ( ~ class_Rings_Ocomm__semiring__1(X4793)
      | c_Groups_Oplus__class_Oplus(X4793,X4792,X4792) = c_Groups_Otimes__class_Otimes(X4793,c_Groups_Oplus__class_Oplus(X4793,c_Groups_Oone__class_Oone(X4793),c_Groups_Oone__class_Oone(X4793)),X4792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_1993,plain,
    ! [X4324,X4325] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4325,X4324)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4325,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4324) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

cnf(i_0_1994,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1408]) ).

cnf(i_0_1995,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1383]) ).

cnf(i_0_1996,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1384]) ).

cnf(i_0_1997,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1377]) ).

cnf(i_0_1998,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1409]) ).

cnf(i_0_1999,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1410]) ).

cnf(i_0_2000,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1386]) ).

cnf(i_0_2001,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1356]) ).

cnf(i_0_2002,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1411]) ).

fof(i_0_2003,plain,
    ! [X3378,X3379] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3379,X3378),X3379),
    inference(variable_rename,[status(thm)],[i_0_1412]) ).

fof(i_0_2004,plain,
    ! [X3376,X3377] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376),X3376),
    inference(variable_rename,[status(thm)],[i_0_1413]) ).

fof(i_0_2005,plain,
    ! [X4554,X4555,X4556] :
      ( ~ class_Rings_Odivision__ring(X4556)
      | X4555 = c_Groups_Ozero__class_Ozero(X4556)
      | X4554 = c_Groups_Ozero__class_Ozero(X4556)
      | c_Rings_Oinverse__class_Oinverse(X4556,c_Groups_Otimes__class_Otimes(X4556,X4555,X4554)) = c_Groups_Otimes__class_Otimes(X4556,c_Rings_Oinverse__class_Oinverse(X4556,X4554),c_Rings_Oinverse__class_Oinverse(X4556,X4555)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).

fof(i_0_2006,plain,
    ! [X3986,X3987,X3988] :
      ( ~ class_Fields_Ofield(X3988)
      | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X3988),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3988),X3987),X3986) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3988),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X3988),X3987,X3986)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__div__minus__left])]) ).

fof(i_0_2007,plain,
    ! [X3983,X3984,X3985] :
      ( ~ class_Fields_Ofield(X3985)
      | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X3985),X3984,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3985),X3983)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3985),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X3985),X3984,X3983)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__div__minus__right])]) ).

fof(i_0_2008,plain,
    ! [X3275,X3276] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3276,X3275)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3275,X3276),X3276) = X3275 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).

fof(i_0_2009,plain,
    ! [X3210,X3211] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3211,X3210)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3210,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3210,X3211)) = X3211 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).

fof(i_0_2010,plain,
    ! [X3283,X3284] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3284,X3283)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3284,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3283,X3284)) = X3283 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).

fof(i_0_2011,plain,
    ! [X3148,X3149,X3150,X3151,X3152] :
      ( ~ class_Orderings_Oord(X3152)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3151,X3152),X3150,X3149)
      | c_Orderings_Oord__class_Oless__eq(X3152,hAPP(X3150,X3148),hAPP(X3149,X3148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_2012,plain,
    ! [X3110,X3111,X3112,X3113,X3114] :
      ( ~ class_Orderings_Oord(X3114)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3113,X3114),X3112,X3111)
      | c_Orderings_Oord__class_Oless__eq(X3114,hAPP(X3112,X3110),hAPP(X3111,X3110)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_2013,plain,
    ! [X3393,X3394,X3395] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3395,X3394)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3395,X3393),X3394) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).

fof(i_0_2014,plain,
    ! [X3917,X3918,X3919] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3919,X3918)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3919,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3918,X3917)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_2015,plain,
    ! [X3370,X3371,X3372] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3372,X3371)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3372,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3371,X3370)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_2016,plain,
    ! [X3914,X3915,X3916] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3916,X3915)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3916,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3914,X3915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_2017,plain,
    ! [X3367,X3368,X3369] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3369,X3368)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3369,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3367,X3368)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_2018,plain,
    ! [X3908,X3909,X3910] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3910,X3909)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3910,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3909,X3908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_2019,plain,
    ! [X3241,X3242,X3243] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3243,X3242)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3243,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3242,X3241)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_2020,plain,
    ! [X3911,X3912,X3913] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3913,X3912)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3913,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3911,X3912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_2021,plain,
    ! [X3244,X3245,X3246] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3246,X3245)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3246,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3244,X3245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

cnf(i_0_2022,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_2023,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_2024,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

cnf(i_0_2025,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

fof(i_0_2026,plain,
    ! [X3546,X3547,X3548] :
      ( ~ class_Fields_Ofield__inverse__zero(X3548)
      | ~ class_RealVector_Oreal__normed__field(X3548)
      | c_RealVector_Onorm__class_Onorm(X3548,c_Rings_Oinverse__class_Odivide(X3548,X3547,X3546)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3548,X3547),c_RealVector_Onorm__class_Onorm(X3548,X3546)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__divide])]) ).

fof(i_0_2027,plain,
    ! [X3821,X3822,X3823] :
      ( ~ class_Fields_Olinordered__field(X3823)
      | X3822 = c_Groups_Ozero__class_Ozero(X3823)
      | c_Groups_Oabs__class_Oabs(X3823,c_Rings_Oinverse__class_Odivide(X3823,X3821,X3822)) = c_Rings_Oinverse__class_Odivide(X3823,c_Groups_Oabs__class_Oabs(X3823,X3821),c_Groups_Oabs__class_Oabs(X3823,X3822)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).

fof(i_0_2028,plain,
    ! [X3550,X3551,X3552] :
      ( ~ class_RealVector_Oreal__normed__field(X3552)
      | X3551 = c_Groups_Ozero__class_Ozero(X3552)
      | c_RealVector_Onorm__class_Onorm(X3552,c_Rings_Oinverse__class_Odivide(X3552,X3550,X3551)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3552,X3550),c_RealVector_Onorm__class_Onorm(X3552,X3551)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__divide])]) ).

cnf(i_0_2029,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_1396]) ).

cnf(i_0_2030,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_1397]) ).

cnf(i_0_2031,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_1394]) ).

cnf(i_0_2032,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1395]) ).

fof(i_0_2033,plain,
    ! [X4089,X4090,X4091] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4091,c_Int_Onumber__class_Onumber__of(X4091,X4090),c_Int_Onumber__class_Onumber__of(X4091,X4089))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4090,X4089)
        | ~ class_Int_Onumber__ring(X4091)
        | ~ class_Rings_Olinordered__idom(X4091) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4090,X4089)
        | c_Orderings_Oord__class_Oless(X4091,c_Int_Onumber__class_Onumber__of(X4091,X4090),c_Int_Onumber__class_Onumber__of(X4091,X4089))
        | ~ class_Int_Onumber__ring(X4091)
        | ~ class_Rings_Olinordered__idom(X4091) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_2034,plain,
    ! [X4086,X4087,X4088] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4088,c_Int_Onumber__class_Onumber__of(X4088,X4087),c_Int_Onumber__class_Onumber__of(X4088,X4086))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4087,X4086)
        | ~ class_Int_Onumber__ring(X4088)
        | ~ class_Rings_Olinordered__idom(X4088) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4087,X4086)
        | c_Orderings_Oord__class_Oless__eq(X4088,c_Int_Onumber__class_Onumber__of(X4088,X4087),c_Int_Onumber__class_Onumber__of(X4088,X4086))
        | ~ class_Int_Onumber__ring(X4088)
        | ~ class_Rings_Olinordered__idom(X4088) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_2035,plain,
    ! [X2720,X2721,X2722,X2723] :
      ( ~ class_Orderings_Opreorder(X2723)
      | ~ c_Orderings_Oord__class_Oless(X2723,X2722,X2721)
      | ~ c_Orderings_Oord__class_Oless(X2723,X2721,X2720)
      | c_Orderings_Oord__class_Oless(X2723,X2722,X2720) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_2036,plain,
    ! [X2885,X2886,X2887,X2888] :
      ( ~ class_Orderings_Opreorder(X2888)
      | ~ c_Orderings_Oord__class_Oless__eq(X2888,X2887,X2886)
      | ~ c_Orderings_Oord__class_Oless(X2888,X2886,X2885)
      | c_Orderings_Oord__class_Oless(X2888,X2887,X2885) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_2037,plain,
    ! [X2877,X2878,X2879,X2880] :
      ( ~ class_Orderings_Opreorder(X2880)
      | ~ c_Orderings_Oord__class_Oless(X2880,X2879,X2878)
      | ~ c_Orderings_Oord__class_Oless__eq(X2880,X2878,X2877)
      | c_Orderings_Oord__class_Oless(X2880,X2879,X2877) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_2038,plain,
    ! [X2716,X2717,X2718,X2719] :
      ( ~ class_Orderings_Oorder(X2719)
      | ~ c_Orderings_Oord__class_Oless(X2719,X2718,X2717)
      | ~ c_Orderings_Oord__class_Oless(X2719,X2716,X2718)
      | c_Orderings_Oord__class_Oless(X2719,X2716,X2717) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_2039,plain,
    ! [X2889,X2890,X2891,X2892] :
      ( ~ class_Orderings_Oorder(X2892)
      | ~ c_Orderings_Oord__class_Oless__eq(X2892,X2891,X2890)
      | ~ c_Orderings_Oord__class_Oless(X2892,X2889,X2891)
      | c_Orderings_Oord__class_Oless(X2892,X2889,X2890) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_2040,plain,
    ! [X2881,X2882,X2883,X2884] :
      ( ~ class_Orderings_Oorder(X2884)
      | ~ c_Orderings_Oord__class_Oless(X2884,X2883,X2882)
      | ~ c_Orderings_Oord__class_Oless__eq(X2884,X2881,X2883)
      | c_Orderings_Oord__class_Oless(X2884,X2881,X2882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_2041,plain,
    ! [X3137,X3138,X3139,X3140] :
      ( ~ class_Orderings_Opreorder(X3140)
      | ~ c_Orderings_Oord__class_Oless__eq(X3140,X3139,X3138)
      | ~ c_Orderings_Oord__class_Oless__eq(X3140,X3138,X3137)
      | c_Orderings_Oord__class_Oless__eq(X3140,X3139,X3137) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_2042,plain,
    ! [X3144,X3145,X3146,X3147] :
      ( ~ class_Orderings_Oorder(X3147)
      | ~ c_Orderings_Oord__class_Oless__eq(X3147,X3146,X3145)
      | ~ c_Orderings_Oord__class_Oless__eq(X3147,X3144,X3146)
      | c_Orderings_Oord__class_Oless__eq(X3147,X3144,X3145) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_2043,plain,
    ! [X3922,X3923,X3924] :
      ( ~ class_Groups_Oab__group__add(X3924)
      | c_Groups_Ominus__class_Ominus(X3924,c_Groups_Ouminus__class_Ouminus(X3924,X3923),c_Groups_Ouminus__class_Ouminus(X3924,X3922)) = c_Groups_Ouminus__class_Ouminus(X3924,c_Groups_Ominus__class_Ominus(X3924,X3923,X3922)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).

fof(i_0_2044,plain,
    ! [X4399,X4400,X4401] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(X4401)
      | c_Groups_Osgn__class_Osgn(X4401,c_Groups_Otimes__class_Otimes(X4401,X4400,X4399)) = c_Groups_Otimes__class_Otimes(X4401,c_Groups_Osgn__class_Osgn(X4401,X4400),c_Groups_Osgn__class_Osgn(X4401,X4399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__mult])]) ).

fof(i_0_2045,plain,
    ! [X4402,X4403,X4404] :
      ( ~ class_Rings_Olinordered__idom(X4404)
      | c_Groups_Osgn__class_Osgn(X4404,c_Groups_Otimes__class_Otimes(X4404,X4403,X4402)) = c_Groups_Otimes__class_Otimes(X4404,c_Groups_Osgn__class_Osgn(X4404,X4403),c_Groups_Osgn__class_Osgn(X4404,X4402)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_2046,plain,
    ! [X2942,X2943,X2944] :
      ( ~ class_Groups_Oab__group__add(X2944)
      | c_Groups_Ouminus__class_Ouminus(X2944,c_Groups_Oplus__class_Oplus(X2944,X2943,X2942)) = c_Groups_Oplus__class_Oplus(X2944,c_Groups_Ouminus__class_Ouminus(X2944,X2943),c_Groups_Ouminus__class_Ouminus(X2944,X2942)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_2047,plain,
    ! [X2945,X2946,X2947] :
      ( ~ class_Groups_Ogroup__add(X2947)
      | c_Groups_Ouminus__class_Ouminus(X2947,c_Groups_Oplus__class_Oplus(X2947,X2946,X2945)) = c_Groups_Oplus__class_Oplus(X2947,c_Groups_Ouminus__class_Ouminus(X2947,X2945),c_Groups_Ouminus__class_Ouminus(X2947,X2946)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

fof(i_0_2048,plain,
    ! [X3778,X3779,X3780] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X3780)
      | c_Groups_Oabs__class_Oabs(X3780,c_Rings_Oinverse__class_Odivide(X3780,X3779,X3778)) = c_Rings_Oinverse__class_Odivide(X3780,c_Groups_Oabs__class_Oabs(X3780,X3779),c_Groups_Oabs__class_Oabs(X3780,X3778)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).

fof(i_0_2049,plain,
    ! [X3890] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3890,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X3890)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).

fof(i_0_2050,plain,
    ! [X4390,X4391,X4392] :
      ( ~ class_Int_Onumber__ring(X4392)
      | c_Groups_Otimes__class_Otimes(X4392,c_Int_Onumber__class_Onumber__of(X4392,X4391),c_Int_Onumber__class_Onumber__of(X4392,X4390)) = c_Int_Onumber__class_Onumber__of(X4392,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4391,X4390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_2051,plain,
    ! [X4096,X4097,X4098] :
      ( ~ class_Int_Onumber__ring(X4098)
      | c_Groups_Oplus__class_Oplus(X4098,c_Int_Onumber__class_Onumber__of(X4098,X4097),c_Int_Onumber__class_Onumber__of(X4098,X4096)) = c_Int_Onumber__class_Onumber__of(X4098,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4097,X4096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_2052,plain,
    ! [X4393,X4394,X4395] :
      ( ~ class_Int_Onumber__ring(X4395)
      | c_Int_Onumber__class_Onumber__of(X4395,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4394,X4393)) = c_Groups_Otimes__class_Otimes(X4395,c_Int_Onumber__class_Onumber__of(X4395,X4394),c_Int_Onumber__class_Onumber__of(X4395,X4393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_2053,plain,
    ! [X4102,X4103,X4104] :
      ( ~ class_Int_Onumber__ring(X4104)
      | c_Int_Onumber__class_Onumber__of(X4104,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4103,X4102)) = c_Groups_Ominus__class_Ominus(X4104,c_Int_Onumber__class_Onumber__of(X4104,X4103),c_Int_Onumber__class_Onumber__of(X4104,X4102)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).

fof(i_0_2054,plain,
    ! [X4099,X4100,X4101] :
      ( ~ class_Int_Onumber__ring(X4101)
      | c_Int_Onumber__class_Onumber__of(X4101,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4100,X4099)) = c_Groups_Oplus__class_Oplus(X4101,c_Int_Onumber__class_Onumber__of(X4101,X4100),c_Int_Onumber__class_Onumber__of(X4101,X4099)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_2055,plain,
    ! [X4206,X4207] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4207,c_Int_Onumber__class_Onumber__of(X4207,X4206),c_Groups_Ozero__class_Ozero(X4207))
        | c_Groups_Oabs__class_Oabs(X4207,c_Int_Onumber__class_Onumber__of(X4207,X4206)) = c_Groups_Ouminus__class_Ouminus(X4207,c_Int_Onumber__class_Onumber__of(X4207,X4206))
        | ~ class_Int_Onumber__ring(X4207)
        | ~ class_Rings_Olinordered__idom(X4207) )
      & ( c_Orderings_Oord__class_Oless(X4207,c_Int_Onumber__class_Onumber__of(X4207,X4206),c_Groups_Ozero__class_Ozero(X4207))
        | c_Groups_Oabs__class_Oabs(X4207,c_Int_Onumber__class_Onumber__of(X4207,X4206)) = c_Int_Onumber__class_Onumber__of(X4207,X4206)
        | ~ class_Int_Onumber__ring(X4207)
        | ~ class_Rings_Olinordered__idom(X4207) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])])]) ).

fof(i_0_2056,plain,
    ! [X2693,X2694,X2695] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2695,c_Groups_Ouminus__class_Ouminus(X2695,X2694),c_Groups_Ouminus__class_Ouminus(X2695,X2693))
        | c_Orderings_Oord__class_Oless(X2695,X2693,X2694)
        | ~ class_Groups_Oordered__ab__group__add(X2695) )
      & ( ~ c_Orderings_Oord__class_Oless(X2695,X2693,X2694)
        | c_Orderings_Oord__class_Oless(X2695,c_Groups_Ouminus__class_Ouminus(X2695,X2694),c_Groups_Ouminus__class_Ouminus(X2695,X2693))
        | ~ class_Groups_Oordered__ab__group__add(X2695) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_2057,plain,
    ! [X3980,X3981,X3982] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3982,c_Groups_Ouminus__class_Ouminus(X3982,X3981),c_Groups_Ouminus__class_Ouminus(X3982,X3980))
        | c_Orderings_Oord__class_Oless__eq(X3982,X3980,X3981)
        | ~ class_Lattices_Oboolean__algebra(X3982) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3982,X3980,X3981)
        | c_Orderings_Oord__class_Oless__eq(X3982,c_Groups_Ouminus__class_Ouminus(X3982,X3981),c_Groups_Ouminus__class_Ouminus(X3982,X3980))
        | ~ class_Lattices_Oboolean__algebra(X3982) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_2058,plain,
    ! [X2936,X2937,X2938] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2938,c_Groups_Ouminus__class_Ouminus(X2938,X2937),c_Groups_Ouminus__class_Ouminus(X2938,X2936))
        | c_Orderings_Oord__class_Oless__eq(X2938,X2936,X2937)
        | ~ class_Groups_Oordered__ab__group__add(X2938) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2938,X2936,X2937)
        | c_Orderings_Oord__class_Oless__eq(X2938,c_Groups_Ouminus__class_Ouminus(X2938,X2937),c_Groups_Ouminus__class_Ouminus(X2938,X2936))
        | ~ class_Groups_Oordered__ab__group__add(X2938) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_2059,plain,
    ! [X4263,X4264] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4264,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),X4264)
        | X4263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4263,X4264)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4264)
        | X4263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4264,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4264,X4263)
        | X4263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4263,X4264)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4264,X4263)
        | X4263 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X4263 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) = 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),X4264)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4264,X4263)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4264,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4263,X4264)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4264,X4263) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])]) ).

fof(i_0_2060,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(tc_Int_Oint,X4249,X4248)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4249,X4248) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])]) ).

fof(i_0_2061,plain,
    ! [X4239,X4240] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4240,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4239,X4240)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4240,X4239) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial])]) ).

fof(i_0_2062,plain,
    ! [X3272,X3273,X3274] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3273,X3274) != X3272
        | X3273 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3272,X3274)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3274,X3273) )
      & ( X3273 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3272,X3274)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3273,X3274) = X3272
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3274,X3273) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).

fof(i_0_2063,plain,
    ! [X2948,X2949,X2950] :
      ( ~ class_Groups_Ogroup__add(X2950)
      | c_Groups_Oplus__class_Oplus(X2950,X2949,c_Groups_Oplus__class_Oplus(X2950,c_Groups_Ouminus__class_Ouminus(X2950,X2949),X2948)) = X2948 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_2064,plain,
    ! [X4303,X4304,X4305] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4305,X4304)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4304,X4303)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4305,X4303) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_2065,plain,
    ! [X3207,X3208,X3209] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3209,X3208)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3208,X3207)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3209,X3207) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_2066,plain,
    ! [X3164,X3165,X3166] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3166,X3165)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3165,X3164)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3166,X3164) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).

cnf(i_0_2067,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1378]) ).

cnf(i_0_2068,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1363]) ).

cnf(i_0_2069,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1364]) ).

fof(i_0_2070,plain,
    ! [X2767,X2768,X2769] :
      ( ~ class_Rings_Ocomm__ring(X2769)
      | hAPP(c_Polynomial_Opoly(X2769,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X2769),X2768)),X2767) = c_Groups_Ouminus__class_Ouminus(X2769,hAPP(c_Polynomial_Opoly(X2769,X2768),X2767)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).

fof(i_0_2071,plain,
    ! [X2687,X2688,X2689] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2689,c_Groups_Ouminus__class_Ouminus(X2689,X2688),X2687)
        | c_Orderings_Oord__class_Oless(X2689,c_Groups_Ouminus__class_Ouminus(X2689,X2687),X2688)
        | ~ class_Groups_Oordered__ab__group__add(X2689) )
      & ( ~ c_Orderings_Oord__class_Oless(X2689,c_Groups_Ouminus__class_Ouminus(X2689,X2687),X2688)
        | c_Orderings_Oord__class_Oless(X2689,c_Groups_Ouminus__class_Ouminus(X2689,X2688),X2687)
        | ~ class_Groups_Oordered__ab__group__add(X2689) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_2072,plain,
    ! [X3046,X3047,X3048] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3048)
      | ~ c_Orderings_Oord__class_Oless__eq(X3048,c_Groups_Oabs__class_Oabs(X3048,X3047),X3046)
      | c_Orderings_Oord__class_Oless__eq(X3048,c_Groups_Ouminus__class_Ouminus(X3048,X3047),X3046) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).

fof(i_0_2073,plain,
    ! [X2933,X2934,X2935] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2935,c_Groups_Ouminus__class_Ouminus(X2935,X2934),X2933)
        | c_Orderings_Oord__class_Oless__eq(X2935,c_Groups_Ouminus__class_Ouminus(X2935,X2933),X2934)
        | ~ class_Groups_Oordered__ab__group__add(X2935) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2935,c_Groups_Ouminus__class_Ouminus(X2935,X2933),X2934)
        | c_Orderings_Oord__class_Oless__eq(X2935,c_Groups_Ouminus__class_Ouminus(X2935,X2934),X2933)
        | ~ class_Groups_Oordered__ab__group__add(X2935) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_2074,plain,
    ! [X2673,X2674,X2675] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2675,X2674,c_Groups_Ouminus__class_Ouminus(X2675,X2673))
        | c_Orderings_Oord__class_Oless(X2675,X2673,c_Groups_Ouminus__class_Ouminus(X2675,X2674))
        | ~ class_Groups_Oordered__ab__group__add(X2675) )
      & ( ~ c_Orderings_Oord__class_Oless(X2675,X2673,c_Groups_Ouminus__class_Ouminus(X2675,X2674))
        | c_Orderings_Oord__class_Oless(X2675,X2674,c_Groups_Ouminus__class_Ouminus(X2675,X2673))
        | ~ class_Groups_Oordered__ab__group__add(X2675) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_2075,plain,
    ! [X2930,X2931,X2932] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2932,X2931,c_Groups_Ouminus__class_Ouminus(X2932,X2930))
        | c_Orderings_Oord__class_Oless__eq(X2932,X2930,c_Groups_Ouminus__class_Ouminus(X2932,X2931))
        | ~ class_Groups_Oordered__ab__group__add(X2932) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2932,X2930,c_Groups_Ouminus__class_Ouminus(X2932,X2931))
        | c_Orderings_Oord__class_Oless__eq(X2932,X2931,c_Groups_Ouminus__class_Ouminus(X2932,X2930))
        | ~ class_Groups_Oordered__ab__group__add(X2932) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_2076,plain,
    ! [X4290,X4291] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4291),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4290)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4291,X4290)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(i_0_2077,plain,
    ! [X3696,X3697] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3697,X3696)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3697),c_RealDef_Oreal(tc_Nat_Onat,X3696)),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).

cnf(i_0_2078,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_1415]) ).

fof(i_0_2079,plain,
    ! [X4273,X4274] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4274,X4273)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4274),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4273)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_2080,plain,
    ! [X3688,X3689,X3690] :
      ( ~ class_Rings_Odivision__ring(X3690)
      | X3689 = c_Groups_Ozero__class_Ozero(X3690)
      | c_Groups_Ouminus__class_Ouminus(X3690,c_Rings_Oinverse__class_Odivide(X3690,X3688,X3689)) = c_Rings_Oinverse__class_Odivide(X3690,X3688,c_Groups_Ouminus__class_Ouminus(X3690,X3689)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

cnf(i_0_2081,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_2082,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_2083,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

cnf(i_0_2084,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

fof(i_0_2085,plain,
    ! [X3453] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3453))),
    inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).

fof(i_0_2086,plain,
    ! [X3433,X3434] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3434,X3433)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3433,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3434,X3433)) = X3434 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1416])]) ).

fof(i_0_2087,plain,
    ! [X4600,X4601] :
      ( ~ class_Fields_Olinordered__field(X4601)
      | ~ c_Orderings_Oord__class_Oless(X4601,c_Groups_Ozero__class_Ozero(X4601),c_Rings_Oinverse__class_Oinverse(X4601,X4600))
      | X4600 = c_Groups_Ozero__class_Ozero(X4601)
      | c_Orderings_Oord__class_Oless(X4601,c_Groups_Ozero__class_Ozero(X4601),X4600) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).

fof(i_0_2088,plain,
    ! [X4610,X4611] :
      ( ~ class_Fields_Olinordered__field(X4611)
      | ~ c_Orderings_Oord__class_Oless(X4611,c_Rings_Oinverse__class_Oinverse(X4611,X4610),c_Groups_Ozero__class_Ozero(X4611))
      | X4610 = c_Groups_Ozero__class_Ozero(X4611)
      | c_Orderings_Oord__class_Oless(X4611,X4610,c_Groups_Ozero__class_Ozero(X4611)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).

fof(i_0_2089,plain,
    ! [X4284,X4285] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4285),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4284))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4285,X4284) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4285,X4284)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4285),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4284)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_2090,plain,
    ! [X3587,X3588] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3588),c_RealDef_Oreal(tc_Nat_Onat,X3587))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3588,X3587) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3588,X3587)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3588),c_RealDef_Oreal(tc_Nat_Onat,X3587)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).

fof(i_0_2091,plain,
    ! [X4288,X4289] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4289),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4288))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4289,X4288) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4289,X4288)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4289),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4288)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_2092,plain,
    ! [X3694,X3695] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3695),c_RealDef_Oreal(tc_Nat_Onat,X3694))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3695,X3694) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3695,X3694)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3695),c_RealDef_Oreal(tc_Nat_Onat,X3694)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).

fof(i_0_2093,plain,
    ! [X4414,X4415,X4416] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4416)
      | c_Groups_Otimes__class_Otimes(X4416,c_Groups_Ouminus__class_Ouminus(X4416,X4415),X4414) = c_Groups_Ouminus__class_Ouminus(X4416,c_Groups_Otimes__class_Otimes(X4416,X4415,X4414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).

fof(i_0_2094,plain,
    ! [X4411,X4412,X4413] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4413)
      | c_Groups_Otimes__class_Otimes(X4413,c_Groups_Ouminus__class_Ouminus(X4413,X4412),X4411) = c_Groups_Ouminus__class_Ouminus(X4413,c_Groups_Otimes__class_Otimes(X4413,X4412,X4411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).

fof(i_0_2095,plain,
    ! [X3590,X3591,X3592] :
      ( ~ class_RealVector_Oreal__normed__field(X3592)
      | c_Rings_Oinverse__class_Odivide(X3592,c_Groups_Ouminus__class_Ouminus(X3592,X3591),X3590) = c_Groups_Ouminus__class_Ouminus(X3592,c_Rings_Oinverse__class_Odivide(X3592,X3591,X3590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ominus])]) ).

fof(i_0_2096,plain,
    ! [X4408,X4409,X4410] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4410)
      | c_Groups_Otimes__class_Otimes(X4410,X4409,c_Groups_Ouminus__class_Ouminus(X4410,X4408)) = c_Groups_Ouminus__class_Ouminus(X4410,c_Groups_Otimes__class_Otimes(X4410,X4409,X4408)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).

fof(i_0_2097,plain,
    ! [X4405,X4406,X4407] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4407)
      | c_Groups_Otimes__class_Otimes(X4407,X4406,c_Groups_Ouminus__class_Ouminus(X4407,X4405)) = c_Groups_Ouminus__class_Ouminus(X4407,c_Groups_Otimes__class_Otimes(X4407,X4406,X4405)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).

fof(i_0_2098,plain,
    ! [X4426,X4427,X4428] :
      ( ~ class_Rings_Oring(X4428)
      | c_Groups_Ouminus__class_Ouminus(X4428,c_Groups_Otimes__class_Otimes(X4428,X4427,X4426)) = c_Groups_Otimes__class_Otimes(X4428,c_Groups_Ouminus__class_Ouminus(X4428,X4427),X4426) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_2099,plain,
    ! [X3593,X3594,X3595] :
      ( ~ class_Rings_Odivision__ring(X3595)
      | c_Groups_Ouminus__class_Ouminus(X3595,c_Rings_Oinverse__class_Odivide(X3595,X3594,X3593)) = c_Rings_Oinverse__class_Odivide(X3595,c_Groups_Ouminus__class_Ouminus(X3595,X3594),X3593) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_2100,plain,
    ! [X4429,X4430,X4431] :
      ( ~ class_Rings_Oring(X4431)
      | c_Groups_Ouminus__class_Ouminus(X4431,c_Groups_Otimes__class_Otimes(X4431,X4430,X4429)) = c_Groups_Otimes__class_Otimes(X4431,X4430,c_Groups_Ouminus__class_Ouminus(X4431,X4429)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_2101,plain,
    ! [X3772,X3773,X3774] :
      ( ~ class_Fields_Ofield__inverse__zero(X3774)
      | c_Groups_Ouminus__class_Ouminus(X3774,c_Rings_Oinverse__class_Odivide(X3774,X3773,X3772)) = c_Rings_Oinverse__class_Odivide(X3774,X3773,c_Groups_Ouminus__class_Ouminus(X3774,X3772)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

fof(i_0_2102,plain,
    ! [X3423,X3424,X3425,X3426] :
      ( ( ~ c_SEQ_Osubseq(X3423)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3424,X3425)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3423,X3424),hAPP(X3423,X3425)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_1(X3426),esk17_1(X3426))
        | c_SEQ_Osubseq(X3426) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3426,esk16_1(X3426)),hAPP(X3426,esk17_1(X3426)))
        | c_SEQ_Osubseq(X3426) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subseq__def])])])])])]) ).

fof(i_0_2103,plain,
    ! [X2676,X2677] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2677,c_Groups_Ouminus__class_Ouminus(X2677,X2676),c_Groups_Ozero__class_Ozero(X2677))
        | c_Orderings_Oord__class_Oless(X2677,c_Groups_Ozero__class_Ozero(X2677),X2676)
        | ~ class_Groups_Oordered__ab__group__add(X2677) )
      & ( ~ c_Orderings_Oord__class_Oless(X2677,c_Groups_Ozero__class_Ozero(X2677),X2676)
        | c_Orderings_Oord__class_Oless(X2677,c_Groups_Ouminus__class_Ouminus(X2677,X2676),c_Groups_Ozero__class_Ozero(X2677))
        | ~ class_Groups_Oordered__ab__group__add(X2677) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_2104,plain,
    ! [X2785,X2786] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ouminus__class_Ouminus(X2786,X2785),c_Groups_Ozero__class_Ozero(X2786))
        | c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ozero__class_Ozero(X2786),X2785)
        | ~ class_Groups_Oordered__ab__group__add(X2786) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ozero__class_Ozero(X2786),X2785)
        | c_Orderings_Oord__class_Oless__eq(X2786,c_Groups_Ouminus__class_Ouminus(X2786,X2785),c_Groups_Ozero__class_Ozero(X2786))
        | ~ class_Groups_Oordered__ab__group__add(X2786) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_2105,plain,
    ! [X4594,X4595] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4595,c_Groups_Ozero__class_Ozero(X4595),c_Rings_Oinverse__class_Oinverse(X4595,X4594))
        | c_Orderings_Oord__class_Oless(X4595,c_Groups_Ozero__class_Ozero(X4595),X4594)
        | ~ class_Fields_Olinordered__field__inverse__zero(X4595) )
      & ( ~ c_Orderings_Oord__class_Oless(X4595,c_Groups_Ozero__class_Ozero(X4595),X4594)
        | c_Orderings_Oord__class_Oless(X4595,c_Groups_Ozero__class_Ozero(X4595),c_Rings_Oinverse__class_Oinverse(X4595,X4594))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4595) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).

fof(i_0_2106,plain,
    ! [X4198,X4199] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),c_Groups_Osgn__class_Osgn(X4199,X4198))
        | c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),X4198)
        | ~ class_Rings_Olinordered__idom(X4199) )
      & ( ~ c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),X4198)
        | c_Orderings_Oord__class_Oless(X4199,c_Groups_Ozero__class_Ozero(X4199),c_Groups_Osgn__class_Osgn(X4199,X4198))
        | ~ class_Rings_Olinordered__idom(X4199) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

fof(i_0_2107,plain,
    ! [X4592,X4593] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4593,c_Groups_Ozero__class_Ozero(X4593),c_Rings_Oinverse__class_Oinverse(X4593,X4592))
        | c_Orderings_Oord__class_Oless__eq(X4593,c_Groups_Ozero__class_Ozero(X4593),X4592)
        | ~ class_Fields_Olinordered__field__inverse__zero(X4593) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4593,c_Groups_Ozero__class_Ozero(X4593),X4592)
        | c_Orderings_Oord__class_Oless__eq(X4593,c_Groups_Ozero__class_Ozero(X4593),c_Rings_Oinverse__class_Oinverse(X4593,X4592))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4593) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative])])]) ).

fof(i_0_2108,plain,
    ! [X4596,X4597] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4597,c_Rings_Oinverse__class_Oinverse(X4597,X4596),c_Groups_Ozero__class_Ozero(X4597))
        | c_Orderings_Oord__class_Oless(X4597,X4596,c_Groups_Ozero__class_Ozero(X4597))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4597) )
      & ( ~ c_Orderings_Oord__class_Oless(X4597,X4596,c_Groups_Ozero__class_Ozero(X4597))
        | c_Orderings_Oord__class_Oless(X4597,c_Rings_Oinverse__class_Oinverse(X4597,X4596),c_Groups_Ozero__class_Ozero(X4597))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4597) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).

fof(i_0_2109,plain,
    ! [X4200,X4201] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4201,c_Groups_Osgn__class_Osgn(X4201,X4200),c_Groups_Ozero__class_Ozero(X4201))
        | c_Orderings_Oord__class_Oless(X4201,X4200,c_Groups_Ozero__class_Ozero(X4201))
        | ~ class_Rings_Olinordered__idom(X4201) )
      & ( ~ c_Orderings_Oord__class_Oless(X4201,X4200,c_Groups_Ozero__class_Ozero(X4201))
        | c_Orderings_Oord__class_Oless(X4201,c_Groups_Osgn__class_Osgn(X4201,X4200),c_Groups_Ozero__class_Ozero(X4201))
        | ~ class_Rings_Olinordered__idom(X4201) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_2110,plain,
    ! [X4590,X4591] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4591,c_Rings_Oinverse__class_Oinverse(X4591,X4590),c_Groups_Ozero__class_Ozero(X4591))
        | c_Orderings_Oord__class_Oless__eq(X4591,X4590,c_Groups_Ozero__class_Ozero(X4591))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4591) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X4591,X4590,c_Groups_Ozero__class_Ozero(X4591))
        | c_Orderings_Oord__class_Oless__eq(X4591,c_Rings_Oinverse__class_Oinverse(X4591,X4590),c_Groups_Ozero__class_Ozero(X4591))
        | ~ class_Fields_Olinordered__field__inverse__zero(X4591) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive])])]) ).

fof(i_0_2111,plain,
    ! [X2664,X2665] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2665,c_Groups_Ozero__class_Ozero(X2665),c_Groups_Ouminus__class_Ouminus(X2665,X2664))
        | c_Orderings_Oord__class_Oless(X2665,X2664,c_Groups_Ozero__class_Ozero(X2665))
        | ~ class_Groups_Oordered__ab__group__add(X2665) )
      & ( ~ c_Orderings_Oord__class_Oless(X2665,X2664,c_Groups_Ozero__class_Ozero(X2665))
        | c_Orderings_Oord__class_Oless(X2665,c_Groups_Ozero__class_Ozero(X2665),c_Groups_Ouminus__class_Ouminus(X2665,X2664))
        | ~ class_Groups_Oordered__ab__group__add(X2665) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_2112,plain,
    ! [X2789,X2790] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2790,c_Groups_Ozero__class_Ozero(X2790),c_Groups_Ouminus__class_Ouminus(X2790,X2789))
        | c_Orderings_Oord__class_Oless__eq(X2790,X2789,c_Groups_Ozero__class_Ozero(X2790))
        | ~ class_Groups_Oordered__ab__group__add(X2790) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2790,X2789,c_Groups_Ozero__class_Ozero(X2790))
        | c_Orderings_Oord__class_Oless__eq(X2790,c_Groups_Ozero__class_Ozero(X2790),c_Groups_Ouminus__class_Ouminus(X2790,X2789))
        | ~ class_Groups_Oordered__ab__group__add(X2790) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_2113,plain,
    ! [X2838,X2839,X2840] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2840,X2839,X2838)
        | ~ c_Orderings_Oord__class_Oless(X2840,X2839,X2838)
        | ~ class_Orderings_Opreorder(X2840) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2840,X2838,X2839)
        | ~ c_Orderings_Oord__class_Oless(X2840,X2839,X2838)
        | ~ class_Orderings_Opreorder(X2840) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2840,X2839,X2838)
        | c_Orderings_Oord__class_Oless__eq(X2840,X2838,X2839)
        | c_Orderings_Oord__class_Oless(X2840,X2839,X2838)
        | ~ class_Orderings_Opreorder(X2840) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1417])])]) ).

fof(i_0_2114,plain,
    ! [X4115,X4116] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4116,c_Groups_Ozero__class_Ozero(X4116),c_Int_Onumber__class_Onumber__of(X4116,X4115))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4115)
        | ~ class_Int_Onumber__ring(X4116)
        | ~ class_Rings_Olinordered__idom(X4116) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4115)
        | c_Orderings_Oord__class_Oless(X4116,c_Groups_Ozero__class_Ozero(X4116),c_Int_Onumber__class_Onumber__of(X4116,X4115))
        | ~ class_Int_Onumber__ring(X4116)
        | ~ class_Rings_Olinordered__idom(X4116) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_2115,plain,
    ! [X4113,X4114] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4114,c_Groups_Ozero__class_Ozero(X4114),c_Int_Onumber__class_Onumber__of(X4114,X4113))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4113)
        | ~ class_Int_Onumber__ring(X4114)
        | ~ class_Rings_Olinordered__idom(X4114) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4113)
        | c_Orderings_Oord__class_Oless__eq(X4114,c_Groups_Ozero__class_Ozero(X4114),c_Int_Onumber__class_Onumber__of(X4114,X4113))
        | ~ class_Int_Onumber__ring(X4114)
        | ~ class_Rings_Olinordered__idom(X4114) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_2116,plain,
    ! [X4117,X4118] :
      ( ( ~ c_Orderings_Oord__class_Oless(X4118,c_Int_Onumber__class_Onumber__of(X4118,X4117),c_Groups_Ozero__class_Ozero(X4118))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4117,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X4118)
        | ~ class_Rings_Olinordered__idom(X4118) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4117,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(X4118,c_Int_Onumber__class_Onumber__of(X4118,X4117),c_Groups_Ozero__class_Ozero(X4118))
        | ~ class_Int_Onumber__ring(X4118)
        | ~ class_Rings_Olinordered__idom(X4118) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_2117,plain,
    ! [X4111,X4112] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X4112,c_Int_Onumber__class_Onumber__of(X4112,X4111),c_Groups_Ozero__class_Ozero(X4112))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4111,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X4112)
        | ~ class_Rings_Olinordered__idom(X4112) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4111,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(X4112,c_Int_Onumber__class_Onumber__of(X4112,X4111),c_Groups_Ozero__class_Ozero(X4112))
        | ~ class_Int_Onumber__ring(X4112)
        | ~ class_Rings_Olinordered__idom(X4112) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

cnf(i_0_2118,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_1418]) ).

fof(i_0_2119,plain,
    ! [X3977,X3978,X3979] :
      ( ~ class_Lattices_Oboolean__algebra(X3979)
      | ~ c_Orderings_Oord__class_Oless__eq(X3979,X3978,X3977)
      | c_Orderings_Oord__class_Oless__eq(X3979,c_Groups_Ouminus__class_Ouminus(X3979,X3977),c_Groups_Ouminus__class_Ouminus(X3979,X3978)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_2120,plain,
    ! [X2939,X2940,X2941] :
      ( ~ class_Groups_Oordered__ab__group__add(X2941)
      | ~ c_Orderings_Oord__class_Oless__eq(X2941,X2940,X2939)
      | c_Orderings_Oord__class_Oless__eq(X2941,c_Groups_Ouminus__class_Ouminus(X2941,X2939),c_Groups_Ouminus__class_Ouminus(X2941,X2940)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

fof(i_0_2121,plain,
    ! [X3429] :
      ( ~ class_Rings_Olinordered__semidom(X3429)
      | c_Orderings_Oord__class_Oless(X3429,c_Groups_Ozero__class_Ozero(X3429),c_Groups_Oplus__class_Oplus(X3429,c_Groups_Oone__class_Oone(X3429),c_Groups_Oone__class_Oone(X3429))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_2122,plain,
    ! [X3893] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3893,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X3893))),
    inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).

fof(i_0_2123,plain,
    ! [X4417,X4418,X4419] :
      ( ( c_Groups_Otimes__class_Otimes(X4419,X4418,X4418) != c_Groups_Otimes__class_Otimes(X4419,X4417,X4417)
        | X4418 = X4417
        | X4418 = c_Groups_Ouminus__class_Ouminus(X4419,X4417)
        | ~ class_Rings_Oidom(X4419) )
      & ( X4418 != X4417
        | c_Groups_Otimes__class_Otimes(X4419,X4418,X4418) = c_Groups_Otimes__class_Otimes(X4419,X4417,X4417)
        | ~ class_Rings_Oidom(X4419) )
      & ( X4418 != c_Groups_Ouminus__class_Ouminus(X4419,X4417)
        | c_Groups_Otimes__class_Otimes(X4419,X4418,X4418) = c_Groups_Otimes__class_Otimes(X4419,X4417,X4417)
        | ~ class_Rings_Oidom(X4419) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_2124,plain,
    ! [X2951,X2952,X2953] :
      ( ~ class_Groups_Ogroup__add(X2953)
      | c_Groups_Oplus__class_Oplus(X2953,c_Groups_Ouminus__class_Ouminus(X2953,X2952),c_Groups_Oplus__class_Oplus(X2953,X2952,X2951)) = X2951 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_2125,plain,
    ! [X2680,X2681] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2681,c_Groups_Ouminus__class_Ouminus(X2681,X2680),X2680)
        | c_Orderings_Oord__class_Oless(X2681,c_Groups_Ozero__class_Ozero(X2681),X2680)
        | ~ class_Groups_Olinordered__ab__group__add(X2681) )
      & ( ~ c_Orderings_Oord__class_Oless(X2681,c_Groups_Ozero__class_Ozero(X2681),X2680)
        | c_Orderings_Oord__class_Oless(X2681,c_Groups_Ouminus__class_Ouminus(X2681,X2680),X2680)
        | ~ class_Groups_Olinordered__ab__group__add(X2681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).

fof(i_0_2126,plain,
    ! [X2783,X2784] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2784,c_Groups_Ouminus__class_Ouminus(X2784,X2783),X2783)
        | c_Orderings_Oord__class_Oless__eq(X2784,c_Groups_Ozero__class_Ozero(X2784),X2783)
        | ~ class_Groups_Olinordered__ab__group__add(X2784) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2784,c_Groups_Ozero__class_Ozero(X2784),X2783)
        | c_Orderings_Oord__class_Oless__eq(X2784,c_Groups_Ouminus__class_Ouminus(X2784,X2783),X2783)
        | ~ class_Groups_Olinordered__ab__group__add(X2784) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_2127,plain,
    ! [X3458,X3459] :
      ( ( ~ c_Orderings_Oord__class_Oless(X3459,X3458,c_Groups_Ouminus__class_Ouminus(X3459,X3458))
        | c_Orderings_Oord__class_Oless(X3459,X3458,c_Groups_Ozero__class_Ozero(X3459))
        | ~ class_Rings_Olinordered__idom(X3459) )
      & ( ~ c_Orderings_Oord__class_Oless(X3459,X3458,c_Groups_Ozero__class_Ozero(X3459))
        | c_Orderings_Oord__class_Oless(X3459,X3458,c_Groups_Ouminus__class_Ouminus(X3459,X3458))
        | ~ class_Rings_Olinordered__idom(X3459) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_2128,plain,
    ! [X2787,X2788] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2788,X2787,c_Groups_Ouminus__class_Ouminus(X2788,X2787))
        | c_Orderings_Oord__class_Oless__eq(X2788,X2787,c_Groups_Ozero__class_Ozero(X2788))
        | ~ class_Groups_Olinordered__ab__group__add(X2788) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2788,X2787,c_Groups_Ozero__class_Ozero(X2788))
        | c_Orderings_Oord__class_Oless__eq(X2788,X2787,c_Groups_Ouminus__class_Ouminus(X2788,X2787))
        | ~ class_Groups_Olinordered__ab__group__add(X2788) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_2129,plain,
    ! [X3487,X3488,X3489] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3489)
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | X3489 = X3488
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3489,X3488) )
      & ( ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | X3489 = X3488
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3489,X3488) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3489)
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3489,X3488) )
      & ( ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3489,X3488) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3489)
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | X3489 = X3488
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489)) )
      & ( ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | X3489 = X3488
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3489)
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489)) )
      & ( ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489))
        | ~ hBOOL(hAPP(hAPP(X3487,X3488),X3489)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_2130,plain,
    ! [X4602,X4603] :
      ( ~ class_Fields_Olinordered__field(X4603)
      | ~ c_Orderings_Oord__class_Oless(X4603,X4602,c_Groups_Ozero__class_Ozero(X4603))
      | c_Orderings_Oord__class_Oless(X4603,c_Rings_Oinverse__class_Oinverse(X4603,X4602),c_Groups_Ozero__class_Ozero(X4603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).

fof(i_0_2131,plain,
    ! [X4598,X4599] :
      ( ~ class_Fields_Olinordered__field(X4599)
      | ~ c_Orderings_Oord__class_Oless(X4599,c_Groups_Ozero__class_Ozero(X4599),X4598)
      | c_Orderings_Oord__class_Oless(X4599,c_Groups_Ozero__class_Ozero(X4599),c_Rings_Oinverse__class_Oinverse(X4599,X4598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).

fof(i_0_2132,plain,
    ! [X2591,X2592,X2593] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2593)
      | ~ c_Orderings_Oord__class_Oless__eq(X2593,c_Groups_Oabs__class_Oabs(X2593,X2592),X2591)
      | c_Orderings_Oord__class_Oless__eq(X2593,X2592,X2591) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).

fof(i_0_2133,plain,
    ! [X2544,X2545,X2546,X2547,X2548] :
      ( ( X2547 != X2546
        | X2545 = X2544
        | c_Groups_Ominus__class_Ominus(X2548,X2547,X2546) != c_Groups_Ominus__class_Ominus(X2548,X2545,X2544)
        | ~ class_Groups_Oab__group__add(X2548) )
      & ( X2545 != X2544
        | X2547 = X2546
        | c_Groups_Ominus__class_Ominus(X2548,X2547,X2546) != c_Groups_Ominus__class_Ominus(X2548,X2545,X2544)
        | ~ class_Groups_Oab__group__add(X2548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).

cnf(i_0_2134,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1392]) ).

cnf(i_0_2135,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_1393]) ).

fof(i_0_2136,plain,
    ! [X2865,X2866,X2867] :
      ( ( c_Orderings_Oord__class_Oless(X2867,X2866,X2865)
        | X2866 = X2865
        | ~ c_Orderings_Oord__class_Oless__eq(X2867,X2866,X2865)
        | ~ class_Orderings_Olinorder(X2867) )
      & ( X2866 != X2865
        | ~ c_Orderings_Oord__class_Oless(X2867,X2866,X2865)
        | ~ c_Orderings_Oord__class_Oless__eq(X2867,X2866,X2865)
        | ~ class_Orderings_Olinorder(X2867) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1419])])]) ).

fof(i_0_2137,plain,
    ! [X2954,X2955,X2956] :
      ( ~ class_Groups_Oab__group__add(X2956)
      | c_Groups_Ouminus__class_Ouminus(X2956,c_Groups_Ominus__class_Ominus(X2956,X2955,X2954)) = c_Groups_Ominus__class_Ominus(X2956,X2954,X2955) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).

fof(i_0_2138,plain,
    ! [X3141,X3142,X3143] :
      ( ~ class_Orderings_Oorder(X3143)
      | ~ c_Orderings_Oord__class_Oless__eq(X3143,X3142,X3141)
      | ~ c_Orderings_Oord__class_Oless__eq(X3143,X3141,X3142)
      | X3141 = X3142 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_2139,plain,
    ! [X3134,X3135,X3136] :
      ( ~ class_Orderings_Oorder(X3136)
      | ~ c_Orderings_Oord__class_Oless__eq(X3136,X3135,X3134)
      | ~ c_Orderings_Oord__class_Oless__eq(X3136,X3134,X3135)
      | X3135 = X3134 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_2140,plain,
    ! [X3115,X3116,X3117] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3117,X3115,X3116)
        | X3115 = X3116
        | ~ c_Orderings_Oord__class_Oless__eq(X3117,X3116,X3115)
        | ~ class_Orderings_Oorder(X3117) )
      & ( X3115 != X3116
        | c_Orderings_Oord__class_Oless__eq(X3117,X3115,X3116)
        | ~ c_Orderings_Oord__class_Oless__eq(X3117,X3116,X3115)
        | ~ class_Orderings_Oorder(X3117) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_2141,plain,
    ! [X3104,X3105,X3106] :
      ( ( c_Orderings_Oord__class_Oless__eq(X3106,X3105,X3104)
        | X3105 != X3104
        | ~ class_Orderings_Oorder(X3106) )
      & ( c_Orderings_Oord__class_Oless__eq(X3106,X3104,X3105)
        | X3105 != X3104
        | ~ class_Orderings_Oorder(X3106) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X3106,X3105,X3104)
        | ~ c_Orderings_Oord__class_Oless__eq(X3106,X3104,X3105)
        | X3105 = X3104
        | ~ class_Orderings_Oorder(X3106) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_2142,plain,
    ! [X3693] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3693))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3693) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3693)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3693)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).

fof(i_0_2143,plain,
    ! [X3408,X3409] :
      ( ~ class_Rings_Olinordered__semidom(X3409)
      | c_Orderings_Oord__class_Oless(X3409,X3408,c_Groups_Oplus__class_Oplus(X3409,X3408,c_Groups_Oone__class_Oone(X3409))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_2144,plain,
    ! [X2532,X2533,X2534,X2535] :
      ( ( c_Groups_Oplus__class_Oplus(X2535,X2534,X2533) != c_Groups_Oplus__class_Oplus(X2535,X2532,X2533)
        | X2534 = X2532
        | ~ class_Groups_Ocancel__semigroup__add(X2535) )
      & ( X2534 != X2532
        | c_Groups_Oplus__class_Oplus(X2535,X2534,X2533) = c_Groups_Oplus__class_Oplus(X2535,X2532,X2533)
        | ~ class_Groups_Ocancel__semigroup__add(X2535) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_2145,plain,
    ! [X2520,X2521,X2522,X2523] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2523)
      | c_Groups_Oplus__class_Oplus(X2523,X2522,X2521) != c_Groups_Oplus__class_Oplus(X2523,X2520,X2521)
      | X2522 = X2520 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_2146,plain,
    ! [X2524,X2525,X2526,X2527] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X2527)
      | c_Groups_Oplus__class_Oplus(X2527,X2526,X2525) != c_Groups_Oplus__class_Oplus(X2527,X2526,X2524)
      | X2525 = X2524 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_2147,plain,
    ! [X2536,X2537,X2538,X2539] :
      ( ( c_Groups_Oplus__class_Oplus(X2539,X2538,X2537) != c_Groups_Oplus__class_Oplus(X2539,X2538,X2536)
        | X2537 = X2536
        | ~ class_Groups_Ocancel__semigroup__add(X2539) )
      & ( X2537 != X2536
        | c_Groups_Oplus__class_Oplus(X2539,X2538,X2537) = c_Groups_Oplus__class_Oplus(X2539,X2538,X2536)
        | ~ class_Groups_Ocancel__semigroup__add(X2539) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_2148,plain,
    ! [X2528,X2529,X2530,X2531] :
      ( ~ class_Groups_Ocancel__semigroup__add(X2531)
      | c_Groups_Oplus__class_Oplus(X2531,X2530,X2529) != c_Groups_Oplus__class_Oplus(X2531,X2530,X2528)
      | X2529 = X2528 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_2149,plain,
    ! [X2740,X2741,X2742] :
      ( ~ class_Orderings_Oorder(X2742)
      | ~ c_Orderings_Oord__class_Oless(X2742,X2741,X2740)
      | ~ c_Orderings_Oord__class_Oless(X2742,X2740,X2741) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1420])]) ).

fof(i_0_2150,plain,
    ! [X2775,X2776,X2777] :
      ( ( c_Orderings_Oord__class_Oless(X2777,X2776,X2775)
        | c_Orderings_Oord__class_Oless(X2777,X2775,X2776)
        | X2776 = X2775
        | ~ class_Orderings_Olinorder(X2777) )
      & ( ~ c_Orderings_Oord__class_Oless(X2777,X2775,X2776)
        | ~ c_Orderings_Oord__class_Oless(X2777,X2776,X2775)
        | ~ class_Orderings_Olinorder(X2777) )
      & ( X2776 != X2775
        | ~ c_Orderings_Oord__class_Oless(X2777,X2776,X2775)
        | ~ class_Orderings_Olinorder(X2777) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1421])])]) ).

fof(i_0_2151,plain,
    ! [X2859,X2860,X2861] :
      ( ~ class_Orderings_Olinorder(X2861)
      | ~ c_Orderings_Oord__class_Oless__eq(X2861,X2860,X2859)
      | ~ c_Orderings_Oord__class_Oless(X2861,X2859,X2860) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1422])]) ).

fof(i_0_2152,plain,
    ! [X2826,X2827,X2828] :
      ( ( c_Orderings_Oord__class_Oless(X2828,X2827,X2826)
        | c_Orderings_Oord__class_Oless__eq(X2828,X2826,X2827)
        | ~ class_Orderings_Olinorder(X2828) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2828,X2826,X2827)
        | ~ c_Orderings_Oord__class_Oless(X2828,X2827,X2826)
        | ~ class_Orderings_Olinorder(X2828) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1423])])]) ).

fof(i_0_2153,plain,
    ! [X2829,X2830,X2831] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2831,X2830,X2829)
        | c_Orderings_Oord__class_Oless(X2831,X2829,X2830)
        | ~ class_Orderings_Olinorder(X2831) )
      & ( ~ c_Orderings_Oord__class_Oless(X2831,X2829,X2830)
        | ~ c_Orderings_Oord__class_Oless__eq(X2831,X2830,X2829)
        | ~ class_Orderings_Olinorder(X2831) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1424])])]) ).

fof(i_0_2154,plain,
    ! [X2755,X2756,X2757] :
      ( ~ class_Orderings_Opreorder(X2757)
      | ~ 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_1425])]) ).

fof(i_0_2155,plain,
    ! [X2752,X2753,X2754] :
      ( ~ class_Orderings_Opreorder(X2754)
      | ~ c_Orderings_Oord__class_Oless(X2754,X2753,X2752)
      | ~ c_Orderings_Oord__class_Oless(X2754,X2752,X2753) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1426])]) ).

fof(i_0_2156,plain,
    ! [X2743,X2744,X2745] :
      ( ~ class_Orderings_Opreorder(X2745)
      | ~ c_Orderings_Oord__class_Oless(X2745,X2744,X2743)
      | ~ c_Orderings_Oord__class_Oless(X2745,X2743,X2744) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1427])]) ).

fof(i_0_2157,plain,
    ! [X2713,X2714,X2715] :
      ( ~ class_Orderings_Opreorder(X2715)
      | ~ c_Orderings_Oord__class_Oless(X2715,X2714,X2713)
      | ~ c_Orderings_Oord__class_Oless(X2715,X2713,X2714) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1428])]) ).

fof(i_0_2158,plain,
    ! [X3862,X3863] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3863,c_RealDef_Oreal(tc_Nat_Onat,X3862))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3863),X3862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).

fof(i_0_2159,plain,
    ! [X3885,X3886] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3886),X3885)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3886,c_RComplete_Onatfloor(X3885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).

cnf(i_0_2160,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1429]) ).

cnf(i_0_2161,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1430]) ).

fof(i_0_2162,plain,
    ! [X3853,X3854,X3855] :
      ( ( hAPP(c_Polynomial_Opoly(X3855,X3854),X3853) != c_Groups_Ozero__class_Ozero(X3855)
        | X3854 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3855))
        | c_Polynomial_Oorder(X3855,X3853,X3854) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ class_Rings_Oidom(X3855) )
      & ( X3854 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3855))
        | hAPP(c_Polynomial_Opoly(X3855,X3854),X3853) = c_Groups_Ozero__class_Ozero(X3855)
        | ~ class_Rings_Oidom(X3855) )
      & ( c_Polynomial_Oorder(X3855,X3853,X3854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Polynomial_Opoly(X3855,X3854),X3853) = c_Groups_Ozero__class_Ozero(X3855)
        | ~ class_Rings_Oidom(X3855) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).

fof(i_0_2163,plain,
    ! [X3410,X3411] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3411,X3410) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3410,X3411) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X3411 = X3410 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).

fof(i_0_2164,plain,
    ! [X3884] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3884)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X3884)),X3884) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).

fof(i_0_2165,plain,
    ! [X4351] :
      ( ( ~ 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,X4351))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4351) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X4351)
        | 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,X4351)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

cnf(i_0_2166,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1400]) ).

fof(i_0_2167,plain,
    ! [X4626,X4627] :
      ( ~ class_Rings_Olinordered__ring(X4627)
      | c_Orderings_Oord__class_Oless__eq(X4627,c_Groups_Ozero__class_Ozero(X4627),c_Groups_Otimes__class_Otimes(X4627,X4626,X4626)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_2168,plain,
    ! [X4008,X4009] :
      ( ( X4008 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009))
        | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X4009),X4008) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009))
        | ~ class_Rings_Olinordered__idom(X4009) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4009),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009)),X4008)
        | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X4009),X4008) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4009))
        | X4008 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009))
        | ~ class_Rings_Olinordered__idom(X4009) )
      & ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4009),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009)),X4008)
        | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X4009),X4008) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4009),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4009)))
        | X4008 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4009))
        | ~ class_Rings_Olinordered__idom(X4009) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1431])])]) ).

fof(i_0_2169,plain,
    ! [X3685,X3686,X3687] :
      ( ~ class_Rings_Odivision__ring(X3687)
      | X3686 = c_Groups_Ozero__class_Ozero(X3687)
      | c_Rings_Oinverse__class_Odivide(X3687,c_Groups_Ouminus__class_Ouminus(X3687,X3685),c_Groups_Ouminus__class_Ouminus(X3687,X3686)) = c_Rings_Oinverse__class_Odivide(X3687,X3685,X3686) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_2170,plain,
    ! [X4448,X4449,X4450] :
      ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4449,X4450) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4448,X4450)
        | X4449 = X4448
        | X4450 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4449 != X4448
        | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4449,X4450) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4448,X4450)
        | X4450 = 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_2171,plain,
    ! [X4451,X4452,X4453] :
      ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4453,X4452) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4453,X4451)
        | X4452 = X4451
        | X4453 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X4452 != X4451
        | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4453,X4452) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4453,X4451)
        | X4453 = 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_2172,plain,
    ! [X3314,X3315] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X3315),X3314,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3315)))
        | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X3315),X3314) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3315),X3314)
        | ~ class_Rings_Olinordered__idom(X3315) )
      & ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X3315),X3314,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3315)))
        | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X3315),X3314) = X3314
        | ~ class_Rings_Olinordered__idom(X3315) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1432])])]) ).

fof(i_0_2173,plain,
    ! [X4306,X4307] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4307,X4306)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4306,X4307)
      | X4307 = X4306 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_2174,plain,
    ! [X3205,X3206] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3206,X3205)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3205,X3206)
      | X3206 = X3205 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

fof(i_0_2175,plain,
    ! [X3167,X3168] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3168,X3167)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3167,X3168)
      | X3168 = X3167 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).

cnf(i_0_2176,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1433]) ).

fof(i_0_2177,plain,
    ! [X2585,X2586,X2587] :
      ( ~ class_Groups_Ogroup__add(X2587)
      | c_Groups_Ominus__class_Ominus(X2587,c_Groups_Oplus__class_Oplus(X2587,X2586,X2585),X2585) = X2586 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(i_0_2178,plain,
    ! [X2588,X2589,X2590] :
      ( ~ class_Groups_Ogroup__add(X2590)
      | c_Groups_Oplus__class_Oplus(X2590,c_Groups_Ominus__class_Ominus(X2590,X2589,X2588),X2588) = X2589 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

cnf(i_0_2179,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1361]) ).

cnf(i_0_2180,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1434]) ).

fof(i_0_2181,plain,
    ! [X3180,X3181,X3182] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3182,X3181) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3180,X3181)
        | X3182 = X3180 )
      & ( X3182 != X3180
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3182,X3181) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3180,X3181) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_2182,plain,
    ! [X3177,X3178,X3179] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3179,X3178) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3179,X3177)
        | X3178 = X3177 )
      & ( X3178 != X3177
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3179,X3178) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3179,X3177) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_2183,plain,
    ! [X4420,X4421,X4422] :
      ( ~ class_Rings_Oring(X4422)
      | c_Groups_Otimes__class_Otimes(X4422,c_Groups_Ouminus__class_Ouminus(X4422,X4421),c_Groups_Ouminus__class_Ouminus(X4422,X4420)) = c_Groups_Otimes__class_Otimes(X4422,X4421,X4420) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_2184,plain,
    ! [X3775,X3776,X3777] :
      ( ~ class_Fields_Ofield__inverse__zero(X3777)
      | c_Rings_Oinverse__class_Odivide(X3777,c_Groups_Ouminus__class_Ouminus(X3777,X3776),c_Groups_Ouminus__class_Ouminus(X3777,X3775)) = c_Rings_Oinverse__class_Odivide(X3777,X3776,X3775) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_2185,plain,
    ! [X4423,X4424,X4425] :
      ( ~ class_Rings_Oring(X4425)
      | c_Groups_Otimes__class_Otimes(X4425,c_Groups_Ouminus__class_Ouminus(X4425,X4424),X4423) = c_Groups_Otimes__class_Otimes(X4425,X4424,c_Groups_Ouminus__class_Ouminus(X4425,X4423)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

cnf(i_0_2186,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_1435]) ).

cnf(i_0_2187,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_1377]) ).

cnf(i_0_2188,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1436]) ).

fof(i_0_2189,plain,
    ! [X3902,X3903,X3905,X3906,X3907] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3903,X3902)
        | X3902 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3903,esk41_2(X3902,X3903)) )
      & ( X3905 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3906,X3907)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3906,X3905) ) ),
    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_2190,plain,
    ! [X3232,X3233,X3235,X3236,X3237] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3233,X3232)
        | X3232 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3233,esk6_2(X3232,X3233)) )
      & ( X3235 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3236,X3237)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3236,X3235) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).

cnf(i_0_2191,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_1437]) ).

fof(i_0_2192,plain,
    ! [X3441,X3442] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3442,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3442,X3441)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).

fof(i_0_2193,plain,
    ! [X4806,X4807,X4808,X4809] :
      ( ( X4807 = c_Groups_Ozero__class_Ozero(X4809)
        | X4808 = c_Groups_Otimes__class_Otimes(X4809,X4806,X4807)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) != X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) )
      & ( X4807 != c_Groups_Ozero__class_Ozero(X4809)
        | X4806 = c_Groups_Ozero__class_Ozero(X4809)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) != X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) )
      & ( X4807 = c_Groups_Ozero__class_Ozero(X4809)
        | X4807 != c_Groups_Ozero__class_Ozero(X4809)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) = X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) )
      & ( X4806 != c_Groups_Ozero__class_Ozero(X4809)
        | X4807 != c_Groups_Ozero__class_Ozero(X4809)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) = X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) )
      & ( X4807 = c_Groups_Ozero__class_Ozero(X4809)
        | X4808 != c_Groups_Otimes__class_Otimes(X4809,X4806,X4807)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) = X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) )
      & ( X4806 != c_Groups_Ozero__class_Ozero(X4809)
        | X4808 != c_Groups_Otimes__class_Otimes(X4809,X4806,X4807)
        | c_Rings_Oinverse__class_Odivide(X4809,X4808,X4807) = X4806
        | ~ class_Fields_Ofield__inverse__zero(X4809) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_2194,plain,
    ! [X4802,X4803,X4804,X4805] :
      ( ( X4802 = c_Groups_Ozero__class_Ozero(X4805)
        | c_Groups_Otimes__class_Otimes(X4805,X4804,X4802) = X4803
        | X4804 != c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) )
      & ( X4802 != c_Groups_Ozero__class_Ozero(X4805)
        | X4804 = c_Groups_Ozero__class_Ozero(X4805)
        | X4804 != c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) )
      & ( X4802 = c_Groups_Ozero__class_Ozero(X4805)
        | X4802 != c_Groups_Ozero__class_Ozero(X4805)
        | X4804 = c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) )
      & ( X4804 != c_Groups_Ozero__class_Ozero(X4805)
        | X4802 != c_Groups_Ozero__class_Ozero(X4805)
        | X4804 = c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) )
      & ( X4802 = c_Groups_Ozero__class_Ozero(X4805)
        | c_Groups_Otimes__class_Otimes(X4805,X4804,X4802) != X4803
        | X4804 = c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) )
      & ( X4804 != c_Groups_Ozero__class_Ozero(X4805)
        | c_Groups_Otimes__class_Otimes(X4805,X4804,X4802) != X4803
        | X4804 = c_Rings_Oinverse__class_Odivide(X4805,X4803,X4802)
        | ~ class_Fields_Ofield__inverse__zero(X4805) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_2195,plain,
    ! [X3185,X3186] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3186,X3185),X3186) = X3185,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).

fof(i_0_2196,plain,
    ! [X3183,X3184] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3184,X3183),X3183) = X3184,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).

fof(i_0_2197,plain,
    ! [X3954,X3955] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3955,X3954),X3955),
    inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).

fof(i_0_2198,plain,
    ! [X3222,X3223] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3223,X3222),X3223),
    inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).

fof(i_0_2199,plain,
    ! [X3230,X3231] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3231,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3231,X3230)),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_2200,plain,
    ! [X3228,X3229] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3229,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3228,X3229)),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_2201,plain,
    ! [X4827,X4828,X4829,X4830] :
      ( ~ class_Rings_Odivision__ring(X4830)
      | X4829 = c_Groups_Ozero__class_Ozero(X4830)
      | X4828 != c_Groups_Otimes__class_Otimes(X4830,X4827,X4829)
      | c_Rings_Oinverse__class_Odivide(X4830,X4828,X4829) = X4827 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_2202,plain,
    ! [X4831,X4832,X4833,X4834] :
      ( ( c_Rings_Oinverse__class_Odivide(X4834,X4832,X4833) != X4831
        | X4832 = c_Groups_Otimes__class_Otimes(X4834,X4831,X4833)
        | X4833 = c_Groups_Ozero__class_Ozero(X4834)
        | ~ class_Rings_Odivision__ring(X4834) )
      & ( X4832 != c_Groups_Otimes__class_Otimes(X4834,X4831,X4833)
        | c_Rings_Oinverse__class_Odivide(X4834,X4832,X4833) = X4831
        | X4833 = c_Groups_Ozero__class_Ozero(X4834)
        | ~ class_Rings_Odivision__ring(X4834) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_2203,plain,
    ! [X4823,X4824,X4825,X4826] :
      ( ~ class_Rings_Odivision__ring(X4826)
      | X4825 = c_Groups_Ozero__class_Ozero(X4826)
      | c_Groups_Otimes__class_Otimes(X4826,X4824,X4825) != X4823
      | X4824 = c_Rings_Oinverse__class_Odivide(X4826,X4823,X4825) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_2204,plain,
    ! [X3889] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X3889))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3889) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X3889)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X3889)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).

fof(i_0_2205,plain,
    ! [X3866] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3866),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3866,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3866,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3866),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one])]) ).

fof(i_0_2206,plain,
    ! [X2820,X2821] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2821,c_Groups_Ozero__class_Ozero(X2821),c_Groups_Oabs__class_Oabs(X2821,X2820))
        | X2820 != c_Groups_Ozero__class_Ozero(X2821)
        | ~ class_Groups_Oordered__ab__group__add__abs(X2821) )
      & ( X2820 = c_Groups_Ozero__class_Ozero(X2821)
        | c_Orderings_Oord__class_Oless(X2821,c_Groups_Ozero__class_Ozero(X2821),c_Groups_Oabs__class_Oabs(X2821,X2820))
        | ~ class_Groups_Oordered__ab__group__add__abs(X2821) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).

cnf(i_0_2207,plain,
    ( X1 = c_Nat_OSuc(esk25_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1438]) ).

fof(i_0_2208,plain,
    ! [X4225,X4226] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4226),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4225)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4226,X4225),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(i_0_2209,plain,
    ! [X4223,X4224] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4224,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4223)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4224),X4223),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).

fof(i_0_2210,plain,
    ! [X2874,X2875,X2876] :
      ( ~ class_Orderings_Oorder(X2876)
      | ~ c_Orderings_Oord__class_Oless__eq(X2876,X2875,X2874)
      | X2874 = X2875
      | c_Orderings_Oord__class_Oless(X2876,X2875,X2874) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_2211,plain,
    ! [X2871,X2872,X2873] :
      ( ~ class_Orderings_Oorder(X2873)
      | ~ c_Orderings_Oord__class_Oless__eq(X2873,X2872,X2871)
      | X2872 = X2871
      | c_Orderings_Oord__class_Oless(X2873,X2872,X2871) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_2212,plain,
    ! [X2868,X2869,X2870] :
      ( ~ class_Orderings_Oorder(X2870)
      | ~ c_Orderings_Oord__class_Oless__eq(X2870,X2869,X2868)
      | c_Orderings_Oord__class_Oless(X2870,X2869,X2868)
      | X2869 = X2868 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_2213,plain,
    ! [X2853,X2854,X2855] :
      ( ~ class_Orderings_Oorder(X2855)
      | X2854 = X2853
      | ~ c_Orderings_Oord__class_Oless__eq(X2855,X2854,X2853)
      | c_Orderings_Oord__class_Oless(X2855,X2854,X2853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_2214,plain,
    ! [X2841,X2842,X2843] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2843,X2842,X2841)
        | c_Orderings_Oord__class_Oless(X2843,X2842,X2841)
        | X2842 = X2841
        | ~ class_Orderings_Oorder(X2843) )
      & ( ~ c_Orderings_Oord__class_Oless(X2843,X2842,X2841)
        | c_Orderings_Oord__class_Oless__eq(X2843,X2842,X2841)
        | ~ class_Orderings_Oorder(X2843) )
      & ( X2842 != X2841
        | c_Orderings_Oord__class_Oless__eq(X2843,X2842,X2841)
        | ~ class_Orderings_Oorder(X2843) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_2215,plain,
    ! [X2835,X2836,X2837] :
      ( ( c_Orderings_Oord__class_Oless__eq(X2837,X2836,X2835)
        | ~ c_Orderings_Oord__class_Oless(X2837,X2836,X2835)
        | ~ class_Orderings_Oorder(X2837) )
      & ( X2836 != X2835
        | ~ c_Orderings_Oord__class_Oless(X2837,X2836,X2835)
        | ~ class_Orderings_Oorder(X2837) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X2837,X2836,X2835)
        | X2836 = X2835
        | c_Orderings_Oord__class_Oless(X2837,X2836,X2835)
        | ~ class_Orderings_Oorder(X2837) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_2216,plain,
    ! [X2850,X2851,X2852] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X2852,X2851,X2850)
        | X2851 = X2850
        | c_Orderings_Oord__class_Oless(X2852,X2851,X2850)
        | ~ class_Orderings_Olinorder(X2852) )
      & ( X2851 != X2850
        | c_Orderings_Oord__class_Oless__eq(X2852,X2851,X2850)
        | c_Orderings_Oord__class_Oless(X2852,X2851,X2850)
        | ~ class_Orderings_Olinorder(X2852) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1439])])]) ).

fof(i_0_2217,plain,
    ! [X2856,X2857,X2858] :
      ( ~ class_Orderings_Oorder(X2858)
      | X2857 = X2856
      | ~ c_Orderings_Oord__class_Oless__eq(X2858,X2856,X2857)
      | c_Orderings_Oord__class_Oless(X2858,X2856,X2857) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_2218,plain,
    ! [X3881,X3882] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3882,X3881)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X3882),c_RComplete_Onatfloor(X3881)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).

fof(i_0_2219,plain,
    ! [X3858,X3859] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3859,X3858)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3859),c_RComplete_Onatceiling(X3858)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).

fof(i_0_2220,plain,
    ! [X3089,X3090] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X3090,c_Groups_Oabs__class_Oabs(X3090,X3089),c_Groups_Ozero__class_Ozero(X3090))
        | X3089 = c_Groups_Ozero__class_Ozero(X3090)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3090) )
      & ( X3089 != c_Groups_Ozero__class_Ozero(X3090)
        | c_Orderings_Oord__class_Oless__eq(X3090,c_Groups_Oabs__class_Oabs(X3090,X3089),c_Groups_Ozero__class_Ozero(X3090))
        | ~ class_Groups_Oordered__ab__group__add__abs(X3090) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).

fof(i_0_2221,plain,
    ! [X2862,X2863,X2864] :
      ( ~ class_Orderings_Opreorder(X2864)
      | ~ c_Orderings_Oord__class_Oless(X2864,X2863,X2862)
      | c_Orderings_Oord__class_Oless__eq(X2864,X2863,X2862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

cnf(i_0_2222,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1438]) ).

fof(i_0_2223,plain,
    ! [X2924,X2925] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2925)
      | c_Orderings_Oord__class_Oless__eq(X2925,c_Groups_Ouminus__class_Ouminus(X2925,c_Groups_Oabs__class_Oabs(X2925,X2924)),c_Groups_Ozero__class_Ozero(X2925)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_2224,plain,
    ! [X4335] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4335)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4335) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4335)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4335) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_2225,plain,
    ! [X2660,X2661] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2661,X2660))
        | X2660 != c_Groups_Ozero__class_Ozero(X2661)
        | ~ class_RealVector_Oreal__normed__vector(X2661) )
      & ( X2660 = c_Groups_Ozero__class_Ozero(X2661)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2661,X2660))
        | ~ class_RealVector_Oreal__normed__vector(X2661) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).

fof(i_0_2226,plain,
    ! [X3018] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3018)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3018)),
    inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).

fof(i_0_2227,plain,
    ! [X2822,X2823] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2823)
      | ~ c_Orderings_Oord__class_Oless(X2823,c_Groups_Oabs__class_Oabs(X2823,X2822),c_Groups_Ozero__class_Ozero(X2823)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1440])]) ).

fof(i_0_2228,plain,
    ! [X3035,X3036,X3037] :
      ( ~ class_Groups_Ogroup__add(X3037)
      | c_Groups_Ominus__class_Ominus(X3037,X3036,c_Groups_Ouminus__class_Ouminus(X3037,X3035)) = c_Groups_Oplus__class_Oplus(X3037,X3036,X3035) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).

fof(i_0_2229,plain,
    ! [X3460,X3461,X3462] :
      ( ~ class_Rings_Ocomm__ring__1(X3462)
      | c_Groups_Ominus__class_Ominus(X3462,X3461,X3460) = c_Groups_Oplus__class_Oplus(X3462,X3461,c_Groups_Ouminus__class_Ouminus(X3462,X3460)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).

fof(i_0_2230,plain,
    ! [X3029,X3030,X3031] :
      ( ~ class_Groups_Ogroup__add(X3031)
      | c_Groups_Ominus__class_Ominus(X3031,X3030,X3029) = c_Groups_Oplus__class_Oplus(X3031,X3030,c_Groups_Ouminus__class_Ouminus(X3031,X3029)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).

fof(i_0_2231,plain,
    ! [X3032,X3033,X3034] :
      ( ~ class_Groups_Oab__group__add(X3034)
      | c_Groups_Ominus__class_Ominus(X3034,X3033,X3032) = c_Groups_Oplus__class_Oplus(X3034,X3033,c_Groups_Ouminus__class_Ouminus(X3034,X3032)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).

fof(i_0_2232,plain,
    ! [X2928,X2929] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2929,X2928),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | X2928 = c_Groups_Ozero__class_Ozero(X2929)
        | ~ class_RealVector_Oreal__normed__vector(X2929) )
      & ( X2928 != c_Groups_Ozero__class_Ozero(X2929)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2929,X2928),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ class_RealVector_Oreal__normed__vector(X2929) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).

fof(i_0_2233,plain,
    ! [X3443,X3444] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3444,X3443) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3444,X3443) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3444,X3443)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3444,X3443) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).

fof(i_0_2234,plain,
    ! [X4320,X4321] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4321,X4320)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4321,X4320) )
      & ( X4321 != X4320
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4321,X4320) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4321,X4320)
        | X4321 = X4320
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4321,X4320) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_2235,plain,
    ! [X3386,X3387] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3387,X3386)
      | X3387 = X3386
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3387,X3386) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_2236,plain,
    ! [X3382,X3383] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3383,X3382)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3383,X3382)
        | X3383 = X3382 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3383,X3382)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3383,X3382) )
      & ( X3383 != X3382
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3383,X3382) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_2237,plain,
    ! [X3380,X3381] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3381,X3380)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3381,X3380) )
      & ( X3381 != X3380
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3381,X3380) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3381,X3380)
        | X3381 = X3380
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3381,X3380) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

fof(i_0_2238,plain,
    ! [X2898,X2899] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2899,X2898)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2899,X2898)
        | X2899 = X2898 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2899,X2898)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2899,X2898) )
      & ( X2899 != X2898
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2899,X2898) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).

fof(i_0_2239,plain,
    ! [X2896,X2897] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2897,X2896)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2897,X2896) )
      & ( X2897 != X2896
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2897,X2896) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2897,X2896)
        | X2897 = X2896
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2897,X2896) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).

fof(i_0_2240,plain,
    ! [X3959,X3960] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3960,X3959)
      | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3960,X3959) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).

fof(i_0_2241,plain,
    ! [X3445,X3446] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3446,X3445)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3446,X3445) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H])]) ).

fof(i_0_2242,plain,
    ! [X3997,X3998,X3999,X4000] :
      ( ~ class_Groups_Ouminus(X4000)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3999,X4000),X3998),X3997) = c_Groups_Ouminus__class_Ouminus(X4000,hAPP(X3998,X3997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_2243,plain,
    ! [X4210,X4211] :
      ( ~ class_Rings_Olinordered__idom(X4211)
      | ~ c_Orderings_Oord__class_Oless(X4211,X4210,c_Groups_Ozero__class_Ozero(X4211))
      | c_Groups_Osgn__class_Osgn(X4211,X4210) = c_Groups_Ouminus__class_Ouminus(X4211,c_Groups_Oone__class_Oone(X4211)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_2244,plain,
    ! [X4208,X4209] :
      ( ( c_Groups_Osgn__class_Osgn(X4209,X4208) != c_Groups_Ouminus__class_Ouminus(X4209,c_Groups_Oone__class_Oone(X4209))
        | c_Orderings_Oord__class_Oless(X4209,X4208,c_Groups_Ozero__class_Ozero(X4209))
        | ~ class_Rings_Olinordered__idom(X4209) )
      & ( ~ c_Orderings_Oord__class_Oless(X4209,X4208,c_Groups_Ozero__class_Ozero(X4209))
        | c_Groups_Osgn__class_Osgn(X4209,X4208) = c_Groups_Ouminus__class_Ouminus(X4209,c_Groups_Oone__class_Oone(X4209))
        | ~ class_Rings_Olinordered__idom(X4209) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_2245,plain,
    ! [X3920,X3921] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3921,X3920)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3921,X3920) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_2246,plain,
    ! [X3388,X3389] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,X3388)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3389,X3388) )
      & ( X3389 != X3388
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3389,X3388) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_2247,plain,
    ! [X3384,X3385] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3384)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3385,X3384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_2248,plain,
    ! [X2824,X2825] :
      ( ~ class_RealVector_Oreal__normed__vector(X2825)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2825,X2824),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1441])]) ).

fof(i_0_2249,plain,
    ! [X2652,X2653] :
      ( ( ~ c_Orderings_Oord__class_Oless(X2653,X2652,c_Groups_Ozero__class_Ozero(X2653))
        | c_Groups_Oabs__class_Oabs(X2653,X2652) = c_Groups_Ouminus__class_Ouminus(X2653,X2652)
        | ~ class_Groups_Oabs__if(X2653) )
      & ( c_Orderings_Oord__class_Oless(X2653,X2652,c_Groups_Ozero__class_Ozero(X2653))
        | c_Groups_Oabs__class_Oabs(X2653,X2652) = X2652
        | ~ class_Groups_Oabs__if(X2653) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1442])])]) ).

fof(i_0_2250,plain,
    ! [X2708,X2709] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2709)
      | ~ c_Orderings_Oord__class_Oless(X2709,X2708,c_Groups_Ozero__class_Ozero(X2709))
      | c_Groups_Oabs__class_Oabs(X2709,X2708) = c_Groups_Ouminus__class_Ouminus(X2709,X2708) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_2251,plain,
    ! [X2926,X2927] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2927)
      | ~ c_Orderings_Oord__class_Oless__eq(X2927,X2926,c_Groups_Ozero__class_Ozero(X2927))
      | c_Groups_Oabs__class_Oabs(X2927,X2926) = c_Groups_Ouminus__class_Ouminus(X2927,X2926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

cnf(i_0_2252,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__of__nat__one]) ).

fof(i_0_2253,plain,
    ! [X4279,X4280] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4280,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4279)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4280,X4279),
    inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(i_0_2254,plain,
    ! [X4275,X4276] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4276,X4275) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4276,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4275)),
    inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).

fof(i_0_2255,plain,
    ! [X3447,X3448] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3448,X3447) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3448,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3447)),
    inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).

fof(i_0_2256,plain,
    ! [X3023,X3024] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3024,X3023) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3024,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3023)),
    inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).

fof(i_0_2257,plain,
    ! [X3021,X3022] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3022,X3021) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3022,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3021)),
    inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).

fof(i_0_2258,plain,
    ! [X4330] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4330),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X4330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X4330 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4330),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])]) ).

fof(i_0_2259,plain,
    ! [X3691] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3691),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | X3691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3691 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3691),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff])]) ).

fof(i_0_2260,plain,
    ! [X2472,X2473] :
      ( hAPP(X2473,esk1_2(X2472,X2473)) != hAPP(X2472,esk1_2(X2472,X2473))
      | X2473 = X2472 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_2261,plain,
    ! [X4212,X4213] :
      ( ( X4212 != c_Groups_Ozero__class_Ozero(X4213)
        | c_Groups_Osgn__class_Osgn(X4213,X4212) = c_Groups_Ozero__class_Ozero(X4213)
        | ~ class_Groups_Osgn__if(X4213) )
      & ( ~ c_Orderings_Oord__class_Oless(X4213,c_Groups_Ozero__class_Ozero(X4213),X4212)
        | c_Groups_Osgn__class_Osgn(X4213,X4212) = c_Groups_Oone__class_Oone(X4213)
        | X4212 = c_Groups_Ozero__class_Ozero(X4213)
        | ~ class_Groups_Osgn__if(X4213) )
      & ( c_Orderings_Oord__class_Oless(X4213,c_Groups_Ozero__class_Ozero(X4213),X4212)
        | c_Groups_Osgn__class_Osgn(X4213,X4212) = c_Groups_Ouminus__class_Ouminus(X4213,c_Groups_Oone__class_Oone(X4213))
        | X4212 = c_Groups_Ozero__class_Ozero(X4213)
        | ~ class_Groups_Osgn__if(X4213) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1443])])]) ).

fof(i_0_2262,plain,
    ! [X2706,X2707] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2707,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2706)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X2707 = X2706 )
      & ( X2707 != X2706
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2707,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2706)) = 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_2263,plain,
    ! [X3692] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3692),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[i_0_1444]) ).

fof(i_0_2264,plain,
    ! [X4204,X4205] :
      ( ~ class_Rings_Olinordered__idom(X4205)
      | ~ c_Orderings_Oord__class_Oless(X4205,c_Groups_Ozero__class_Ozero(X4205),X4204)
      | c_Groups_Osgn__class_Osgn(X4205,X4204) = c_Groups_Oone__class_Oone(X4205) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_2265,plain,
    ! [X4202,X4203] :
      ( ( c_Groups_Osgn__class_Osgn(X4203,X4202) != c_Groups_Oone__class_Oone(X4203)
        | c_Orderings_Oord__class_Oless(X4203,c_Groups_Ozero__class_Ozero(X4203),X4202)
        | ~ class_Rings_Olinordered__idom(X4203) )
      & ( ~ c_Orderings_Oord__class_Oless(X4203,c_Groups_Ozero__class_Ozero(X4203),X4202)
        | c_Groups_Osgn__class_Osgn(X4203,X4202) = 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__pos])])]) ).

fof(i_0_2266,plain,
    ! [X2778,X2779,X2780] :
      ( ( X2779 = X2778
        | c_Orderings_Oord__class_Oless(X2780,X2779,X2778)
        | c_Orderings_Oord__class_Oless(X2780,X2778,X2779)
        | ~ class_Orderings_Olinorder(X2780) )
      & ( ~ c_Orderings_Oord__class_Oless(X2780,X2779,X2778)
        | X2779 != X2778
        | ~ class_Orderings_Olinorder(X2780) )
      & ( ~ c_Orderings_Oord__class_Oless(X2780,X2778,X2779)
        | X2779 != X2778
        | ~ class_Orderings_Olinorder(X2780) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_2267,plain,
    ! [X3449,X3450,X3451] :
      ( ~ class_Rings_Olinordered__idom(X3451)
      | X3450 = X3449
      | c_Orderings_Oord__class_Oless(X3451,X3450,X3449)
      | c_Orderings_Oord__class_Oless(X3451,X3449,X3450) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])]) ).

fof(i_0_2268,plain,
    ! [X2770,X2771,X2772] :
      ( ~ class_Orderings_Olinorder(X2772)
      | c_Orderings_Oord__class_Oless(X2772,X2771,X2770)
      | X2771 = X2770
      | c_Orderings_Oord__class_Oless(X2772,X2770,X2771) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_2269,plain,
    ! [X2764,X2765,X2766] :
      ( ( c_Orderings_Oord__class_Oless(X2766,X2764,X2765)
        | X2764 = X2765
        | c_Orderings_Oord__class_Oless(X2766,X2765,X2764)
        | ~ class_Orderings_Olinorder(X2766) )
      & ( X2764 != X2765
        | ~ c_Orderings_Oord__class_Oless(X2766,X2764,X2765)
        | c_Orderings_Oord__class_Oless(X2766,X2765,X2764)
        | ~ class_Orderings_Olinorder(X2766) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])])]) ).

fof(i_0_2270,plain,
    ! [X2761,X2762,X2763] :
      ( ~ class_Orderings_Olinorder(X2763)
      | X2762 = X2761
      | c_Orderings_Oord__class_Oless(X2763,X2762,X2761)
      | c_Orderings_Oord__class_Oless(X2763,X2761,X2762) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])]) ).

fof(i_0_2271,plain,
    ! [X2710,X2711,X2712] :
      ( ~ class_Orderings_Olinorder(X2712)
      | c_Orderings_Oord__class_Oless(X2712,X2711,X2710)
      | X2711 = X2710
      | c_Orderings_Oord__class_Oless(X2712,X2710,X2711) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1448])]) ).

fof(i_0_2272,plain,
    ! [X2818,X2819] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2819)
      | ~ c_Orderings_Oord__class_Oless(X2819,c_Groups_Ozero__class_Ozero(X2819),X2818)
      | c_Groups_Oabs__class_Oabs(X2819,X2818) = X2818 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(i_0_2273,plain,
    ! [X3091,X3092] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3092)
      | ~ c_Orderings_Oord__class_Oless__eq(X3092,c_Groups_Ozero__class_Ozero(X3092),X3091)
      | c_Groups_Oabs__class_Oabs(X3092,X3091) = X3091 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

fof(i_0_2274,plain,
    ! [X2847,X2848,X2849] :
      ( ~ class_Orderings_Olinorder(X2849)
      | c_Orderings_Oord__class_Oless__eq(X2849,X2848,X2847)
      | c_Orderings_Oord__class_Oless(X2849,X2847,X2848) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1449])]) ).

fof(i_0_2275,plain,
    ! [X2832,X2833,X2834] :
      ( ~ class_Orderings_Olinorder(X2834)
      | c_Orderings_Oord__class_Oless__eq(X2834,X2833,X2832)
      | c_Orderings_Oord__class_Oless(X2834,X2832,X2833) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_2276,plain,
    ! [X2844,X2845,X2846] :
      ( ~ class_Orderings_Olinorder(X2846)
      | c_Orderings_Oord__class_Oless(X2846,X2845,X2844)
      | c_Orderings_Oord__class_Oless__eq(X2846,X2844,X2845) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1450])]) ).

fof(i_0_2277,plain,
    ! [X3153,X3154,X3155] :
      ( ~ class_Orderings_Olinorder(X3155)
      | c_Orderings_Oord__class_Oless__eq(X3155,X3154,X3153)
      | c_Orderings_Oord__class_Oless__eq(X3155,X3153,X3154) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1451])]) ).

fof(i_0_2278,plain,
    ! [X3101,X3102,X3103] :
      ( ~ class_Orderings_Olinorder(X3103)
      | c_Orderings_Oord__class_Oless__eq(X3103,X3102,X3101)
      | c_Orderings_Oord__class_Oless__eq(X3103,X3101,X3102) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_2279,plain,
    ! [X3712,X3713,X3714] :
      ( ~ class_Rings_Ocomm__semiring__1(X3714)
      | c_Groups_Oplus__class_Oplus(X3714,X3713,X3712) = c_Groups_Oplus__class_Oplus(X3714,X3712,X3713) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_2280,plain,
    ! [X4580,X4581,X4582] :
      ( ~ class_Rings_Odivision__ring(X4582)
      | c_Groups_Otimes__class_Otimes(X4582,X4581,X4580) != c_Groups_Oone__class_Oone(X4582)
      | c_Rings_Oinverse__class_Oinverse(X4582,X4581) = X4580 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).

fof(i_0_2281,plain,
    ! [X2791,X2792,X2793] :
      ( ~ class_Groups_Ogroup__add(X2793)
      | c_Groups_Oplus__class_Oplus(X2793,X2792,X2791) != c_Groups_Ozero__class_Ozero(X2793)
      | c_Groups_Ouminus__class_Ouminus(X2793,X2792) = X2791 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_2282,plain,
    ! [X2798,X2799,X2800] :
      ( ( X2799 != c_Groups_Ouminus__class_Ouminus(X2800,X2798)
        | c_Groups_Oplus__class_Oplus(X2800,X2799,X2798) = c_Groups_Ozero__class_Ozero(X2800)
        | ~ class_Groups_Ogroup__add(X2800) )
      & ( c_Groups_Oplus__class_Oplus(X2800,X2799,X2798) != c_Groups_Ozero__class_Ozero(X2800)
        | X2799 = c_Groups_Ouminus__class_Ouminus(X2800,X2798)
        | ~ class_Groups_Ogroup__add(X2800) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_2283,plain,
    ! [X2696,X2697,X2698] :
      ( ( c_Groups_Oplus__class_Oplus(X2698,X2697,X2696) != c_Groups_Ozero__class_Ozero(X2698)
        | X2696 = c_Groups_Ouminus__class_Ouminus(X2698,X2697)
        | ~ class_Groups_Ogroup__add(X2698) )
      & ( X2696 != c_Groups_Ouminus__class_Ouminus(X2698,X2697)
        | c_Groups_Oplus__class_Oplus(X2698,X2697,X2696) = c_Groups_Ozero__class_Ozero(X2698)
        | ~ class_Groups_Ogroup__add(X2698) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).

fof(i_0_2284,plain,
    ! [X3038,X3039] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3039)
      | c_Orderings_Oord__class_Oless__eq(X3039,c_Groups_Ouminus__class_Ouminus(X3039,X3038),c_Groups_Oabs__class_Oabs(X3039,X3038)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).

fof(i_0_2285,plain,
    ! [X4272] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4272,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4272) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4272) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4272,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4272) = X4272 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1452])]) ).

fof(i_0_2286,plain,
    ! [X2655] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2655,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2655) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2655) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2655,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2655) = X2655 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1453])]) ).

fof(i_0_2287,plain,
    ! [X2654] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2654,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2654) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2654) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2654,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2654) = X2654 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1454])]) ).

fof(i_0_2288,plain,
    ! [X3406] :
      ( ~ class_Rings_Olinordered__semidom(X3406)
      | ~ c_Orderings_Oord__class_Oless(X3406,c_Groups_Oone__class_Oone(X3406),c_Groups_Ozero__class_Ozero(X3406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1455])]) ).

fof(i_0_2289,plain,
    ! [X3397] :
      ( ~ class_Rings_Olinordered__semidom(X3397)
      | ~ c_Orderings_Oord__class_Oless__eq(X3397,c_Groups_Oone__class_Oone(X3397),c_Groups_Ozero__class_Ozero(X3397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1456])]) ).

cnf(i_0_2290,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[i_0_1457]) ).

fof(i_0_2291,plain,
    ! [X4492,X4493,X4494] :
      ( ~ class_Rings_Ono__zero__divisors(X4494)
      | c_Groups_Otimes__class_Otimes(X4494,X4493,X4492) != c_Groups_Ozero__class_Ozero(X4494)
      | X4493 = c_Groups_Ozero__class_Ozero(X4494)
      | X4492 = c_Groups_Ozero__class_Ozero(X4494) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_2292,plain,
    ! [X4489,X4490,X4491] :
      ( ~ class_Rings_Ono__zero__divisors(X4491)
      | X4490 = c_Groups_Ozero__class_Ozero(X4491)
      | X4489 = c_Groups_Ozero__class_Ozero(X4491)
      | c_Groups_Otimes__class_Otimes(X4491,X4490,X4489) != c_Groups_Ozero__class_Ozero(X4491) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_2293,plain,
    ! [X4486,X4487,X4488] :
      ( ( c_Groups_Otimes__class_Otimes(X4488,X4487,X4486) != c_Groups_Ozero__class_Ozero(X4488)
        | X4487 = c_Groups_Ozero__class_Ozero(X4488)
        | X4486 = c_Groups_Ozero__class_Ozero(X4488)
        | ~ class_Rings_Oring__no__zero__divisors(X4488) )
      & ( X4487 != c_Groups_Ozero__class_Ozero(X4488)
        | c_Groups_Otimes__class_Otimes(X4488,X4487,X4486) = c_Groups_Ozero__class_Ozero(X4488)
        | ~ class_Rings_Oring__no__zero__divisors(X4488) )
      & ( X4486 != c_Groups_Ozero__class_Ozero(X4488)
        | c_Groups_Otimes__class_Otimes(X4488,X4487,X4486) = c_Groups_Ozero__class_Ozero(X4488)
        | ~ class_Rings_Oring__no__zero__divisors(X4488) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_2294,plain,
    ! [X4308,X4309] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4309,X4308)
      | X4309 = X4308
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X4308,X4309) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_2295,plain,
    ! [X3535,X3536] :
      ( ( X3536 = X3535
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3536,X3535)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3535,X3536) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3536,X3535)
        | X3536 != X3535 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3535,X3536)
        | X3536 != X3535 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_2296,plain,
    ! [X3513,X3514] :
      ( X3514 = X3513
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3514,X3513)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3513,X3514) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1458])]) ).

fof(i_0_2297,plain,
    ! [X4270] :
      ( ( X4270 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4270) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4270)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4270) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X4270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4270)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4270) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X4270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])])]) ).

fof(i_0_2298,plain,
    ! [X4355] :
      ( ( X4355 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4355) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4355)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4355) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X4355 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4355)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4355) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | X4355 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1460])])]) ).

fof(i_0_2299,plain,
    ! [X4354] :
      ( ( X4354 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4354) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4354)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4354) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | X4354 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4354)
        | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4354) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | X4354 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1461])])]) ).

fof(i_0_2300,plain,
    ! [X3682,X3683,X3684] :
      ( ( c_Rings_Oinverse__class_Odivide(X3684,X3682,X3683) != c_Groups_Oone__class_Oone(X3684)
        | X3682 = X3683
        | X3683 = c_Groups_Ozero__class_Ozero(X3684)
        | ~ class_Rings_Odivision__ring(X3684) )
      & ( X3682 != X3683
        | c_Rings_Oinverse__class_Odivide(X3684,X3682,X3683) = c_Groups_Oone__class_Oone(X3684)
        | X3683 = c_Groups_Ozero__class_Ozero(X3684)
        | ~ class_Rings_Odivision__ring(X3684) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_2301,plain,
    ! [X4301,X4302] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4302,X4301)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4301,X4302) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_2302,plain,
    ! [X3220,X3221] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3221,X3220)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3220,X3221) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_2303,plain,
    ! [X3162,X3163] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3163,X3162)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3162,X3163) ),
    inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).

fof(i_0_2304,plain,
    ! [X3335,X3336] :
      ( ~ class_Groups_Oab__group__add(X3336)
      | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3336),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3336)),X3335) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3336),X3335) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).

fof(i_0_2305,plain,
    ! [X4292,X4293] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4293,X4292) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4292,X4293),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_2306,plain,
    ! [X3169,X3170] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3170,X3169) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3169,X3170),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_2307,plain,
    ! [X3745,X3746] :
      ( ( c_Groups_Oplus__class_Oplus(X3746,X3745,X3745) != c_Groups_Ozero__class_Ozero(X3746)
        | X3745 = c_Groups_Ozero__class_Ozero(X3746)
        | ~ class_Groups_Olinordered__ab__group__add(X3746) )
      & ( X3745 != c_Groups_Ozero__class_Ozero(X3746)
        | c_Groups_Oplus__class_Oplus(X3746,X3745,X3745) = c_Groups_Ozero__class_Ozero(X3746)
        | ~ class_Groups_Olinordered__ab__group__add(X3746) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_2308,plain,
    ! [X2999,X3000] :
      ( ( c_Groups_Ozero__class_Ozero(X3000) != c_Groups_Oplus__class_Oplus(X3000,X2999,X2999)
        | X2999 = c_Groups_Ozero__class_Ozero(X3000)
        | ~ class_Groups_Olinordered__ab__group__add(X3000) )
      & ( X2999 != c_Groups_Ozero__class_Ozero(X3000)
        | c_Groups_Ozero__class_Ozero(X3000) = c_Groups_Oplus__class_Oplus(X3000,X2999,X2999)
        | ~ class_Groups_Olinordered__ab__group__add(X3000) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_2309,plain,
    ! [X4352] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4352)
      | c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4352) = 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_2310,plain,
    ! [X3012,X3013,X3014] :
      ( ( c_Groups_Ominus__class_Ominus(X3014,X3013,X3012) != c_Groups_Ozero__class_Ozero(X3014)
        | X3013 = X3012
        | ~ class_Groups_Ogroup__add(X3014) )
      & ( X3013 != X3012
        | c_Groups_Ominus__class_Ominus(X3014,X3013,X3012) = c_Groups_Ozero__class_Ozero(X3014)
        | ~ class_Groups_Ogroup__add(X3014) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).

fof(i_0_2311,plain,
    ! [X3009,X3010,X3011] :
      ( ( X3010 != X3009
        | c_Groups_Ominus__class_Ominus(X3011,X3010,X3009) = c_Groups_Ozero__class_Ozero(X3011)
        | ~ class_Groups_Oab__group__add(X3011) )
      & ( c_Groups_Ominus__class_Ominus(X3011,X3010,X3009) != c_Groups_Ozero__class_Ozero(X3011)
        | X3010 = X3009
        | ~ class_Groups_Oab__group__add(X3011) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).

fof(i_0_2312,plain,
    ! [X2699,X2700] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2700,X2699) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X2699 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2700) )
      & ( X2699 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2700)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2700,X2699) = 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_2313,plain,
    ! [X3742,X3743,X3744] :
      ( ( X3743 != c_Groups_Oplus__class_Oplus(X3744,X3743,X3742)
        | X3742 = c_Groups_Ozero__class_Ozero(X3744)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3744) )
      & ( X3742 != c_Groups_Ozero__class_Ozero(X3744)
        | X3743 = c_Groups_Oplus__class_Oplus(X3744,X3743,X3742)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3744) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_2314,plain,
    ! [X3415,X3416] :
      ( ( c_Polynomial_Opoly(X3416,X3415) != c_Polynomial_Opoly(X3416,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3416)))
        | X3415 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3416))
        | ~ class_Int_Oring__char__0(X3416)
        | ~ class_Rings_Oidom(X3416) )
      & ( X3415 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3416))
        | c_Polynomial_Opoly(X3416,X3415) = c_Polynomial_Opoly(X3416,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3416)))
        | ~ class_Int_Oring__char__0(X3416)
        | ~ class_Rings_Oidom(X3416) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).

fof(i_0_2315,plain,
    ! [X4561,X4562] :
      ( ~ class_Fields_Ofield(X4562)
      | X4561 = c_Groups_Ozero__class_Ozero(X4562)
      | c_Groups_Otimes__class_Otimes(X4562,c_Rings_Oinverse__class_Oinverse(X4562,X4561),X4561) = c_Groups_Oone__class_Oone(X4562) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).

fof(i_0_2316,plain,
    ! [X4585,X4586] :
      ( ~ class_Rings_Odivision__ring(X4586)
      | X4585 = c_Groups_Ozero__class_Ozero(X4586)
      | c_Groups_Otimes__class_Otimes(X4586,c_Rings_Oinverse__class_Oinverse(X4586,X4585),X4585) = c_Groups_Oone__class_Oone(X4586) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).

fof(i_0_2317,plain,
    ! [X4583,X4584] :
      ( ~ class_Rings_Odivision__ring(X4584)
      | X4583 = c_Groups_Ozero__class_Ozero(X4584)
      | c_Groups_Otimes__class_Otimes(X4584,X4583,c_Rings_Oinverse__class_Oinverse(X4584,X4583)) = c_Groups_Oone__class_Oone(X4584) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).

fof(i_0_2318,plain,
    ! [X2758,X2759,X2760] :
      ( ~ class_Orderings_Oorder(X2760)
      | ~ c_Orderings_Oord__class_Oless(X2760,X2759,X2758)
      | X2759 != X2758 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_2319,plain,
    ! [X2749,X2750,X2751] :
      ( ~ class_Orderings_Oorder(X2751)
      | ~ c_Orderings_Oord__class_Oless(X2751,X2750,X2749)
      | X2750 != X2749 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_2320,plain,
    ! [X2746,X2747,X2748] :
      ( ~ class_Orderings_Oorder(X2748)
      | ~ c_Orderings_Oord__class_Oless(X2748,X2747,X2746)
      | X2746 != X2747 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_2321,plain,
    ! [X4340] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4340) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4340,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4340,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4340) = 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_2322,plain,
    ! [X4339] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4339)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4339,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4339,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4339) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

fof(i_0_2323,plain,
    ! [X4177,X4178] :
      ( ~ class_Fields_Ofield__inverse__zero(X4178)
      | ~ class_Int_Onumber__ring(X4178)
      | c_Rings_Oinverse__class_Odivide(X4178,X4177,c_Int_Onumber__class_Onumber__of(X4178,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X4178) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_2324,plain,
    ! [X3883] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3883,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | c_RComplete_Onatfloor(X3883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).

fof(i_0_2325,plain,
    ! [X3861] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3861,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | c_RComplete_Onatceiling(X3861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).

fof(i_0_2326,plain,
    ! [X3539] :
      ( ( X3539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3539) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3539)
        | X3539 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_2327,plain,
    ! [X3087,X3088] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3088)
      | c_Orderings_Oord__class_Oless__eq(X3088,c_Groups_Ozero__class_Ozero(X3088),c_Groups_Oabs__class_Oabs(X3088,X3087)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).

fof(i_0_2328,plain,
    ! [X2781,X2782] :
      ( ~ class_Orderings_Opreorder(X2782)
      | ~ c_Orderings_Oord__class_Oless(X2782,X2781,X2781) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1462])]) ).

fof(i_0_2329,plain,
    ! [X4618,X4619] :
      ( ~ class_Rings_Odivision__ring(X4619)
      | X4618 = c_Groups_Ozero__class_Ozero(X4619)
      | c_Rings_Oinverse__class_Oinverse(X4619,c_Groups_Ouminus__class_Ouminus(X4619,X4618)) = c_Groups_Ouminus__class_Ouminus(X4619,c_Rings_Oinverse__class_Oinverse(X4619,X4618)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).

fof(i_0_2330,plain,
    ! [X4620,X4621] :
      ( ~ class_Fields_Olinordered__field(X4621)
      | X4620 = c_Groups_Ozero__class_Ozero(X4621)
      | c_Groups_Oabs__class_Oabs(X4621,c_Rings_Oinverse__class_Oinverse(X4621,X4620)) = c_Rings_Oinverse__class_Oinverse(X4621,c_Groups_Oabs__class_Oabs(X4621,X4620)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__inverse])]) ).

fof(i_0_2331,plain,
    ! [X3405] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X3405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3405 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3405,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).

cnf(i_0_2332,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1463]) ).

cnf(i_0_2333,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1464]) ).

cnf(i_0_2334,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_1465]) ).

cnf(i_0_2335,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[i_0_1466]) ).

cnf(i_0_2336,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[i_0_1467]) ).

cnf(i_0_2337,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[i_0_1468]) ).

fof(i_0_2338,plain,
    ! [X2796,X2797] :
      ( ~ class_Groups_Ogroup__add(X2797)
      | c_Groups_Oplus__class_Oplus(X2797,c_Groups_Ouminus__class_Ouminus(X2797,X2796),X2796) = c_Groups_Ozero__class_Ozero(X2797) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_2339,plain,
    ! [X2794,X2795] :
      ( ~ class_Groups_Oab__group__add(X2795)
      | c_Groups_Oplus__class_Oplus(X2795,c_Groups_Ouminus__class_Ouminus(X2795,X2794),X2794) = c_Groups_Ozero__class_Ozero(X2795) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_2340,plain,
    ! [X2801,X2802] :
      ( ~ class_Groups_Ogroup__add(X2802)
      | c_Groups_Oplus__class_Oplus(X2802,X2801,c_Groups_Ouminus__class_Ouminus(X2802,X2801)) = c_Groups_Ozero__class_Ozero(X2802) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_2341,plain,
    ! [X3400,X3401] :
      ( ( X3401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400) = 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_2342,plain,
    ! [X4523,X4524] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(X4524)
      | X4523 = c_Groups_Ozero__class_Ozero(X4524)
      | c_RealVector_Onorm__class_Onorm(X4524,c_Rings_Oinverse__class_Oinverse(X4524,X4523)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4524,X4523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__inverse])]) ).

fof(i_0_2343,plain,
    ! [X3509,X3510] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3510,X3509)
      | X3509 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).

cnf(i_0_2344,plain,
    c_Nat_OSuc(X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_1469]) ).

cnf(i_0_2345,plain,
    X1 != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[i_0_1470]) ).

fof(i_0_2346,plain,
    ! [X4158,X4159] :
      ( ~ class_Int_Onumber__ring(X4159)
      | ~ class_RealVector_Oreal__normed__algebra__1(X4159)
      | c_RealVector_Onorm__class_Onorm(X4159,c_Int_Onumber__class_Onumber__of(X4159,X4158)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X4158)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__number__of])]) ).

fof(i_0_2347,plain,
    ! [X3093,X3094] :
      ( ~ class_RealVector_Oreal__normed__vector(X3094)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3094,X3093)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).

fof(i_0_2348,plain,
    ! [X3398,X3399] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3399,X3398) != X3399
      | X3398 = 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_2349,plain,
    ! [X3543] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3543,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1471]) ).

fof(i_0_2350,plain,
    ! [X3530] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1472]) ).

fof(i_0_2351,plain,
    ! [X3480] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3480,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[i_0_1473]) ).

fof(i_0_2352,plain,
    ! [X4349] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X4349) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4349,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4349)),
    inference(variable_rename,[status(thm)],[fact_real__sgn__eq]) ).

fof(i_0_2353,plain,
    ! [X3860] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3860,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X3860))),
    inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).

fof(i_0_2354,plain,
    ! [X3330,X3331] :
      ( ~ class_Rings_Ocomm__semiring__1(X3331)
      | hAPP(c_Polynomial_Opoly(X3331,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3331))),X3330) = c_Groups_Oone__class_Oone(X3331) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).

fof(i_0_2355,plain,
    ! [X2773,X2774] :
      ( ~ class_Rings_Ocomm__semiring__0(X2774)
      | hAPP(c_Polynomial_Opoly(X2774,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2774))),X2773) = c_Groups_Ozero__class_Ozero(X2774) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).

fof(i_0_2356,plain,
    ! [X2594,X2595] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2595)
      | c_Orderings_Oord__class_Oless__eq(X2595,X2594,c_Groups_Oabs__class_Oabs(X2595,X2594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).

fof(i_0_2357,plain,
    ! [X3507,X3508] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3508,X3507)
      | X3507 != X3508 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

fof(i_0_2358,plain,
    ! [X3505,X3506] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3506,X3505)
      | X3506 != X3505 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_2359,plain,
    ! [X4397,X4398] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X4398)
      | c_Rings_Oinverse__class_Oinverse(X4398,c_Groups_Ouminus__class_Ouminus(X4398,X4397)) = c_Groups_Ouminus__class_Ouminus(X4398,c_Rings_Oinverse__class_Oinverse(X4398,X4397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).

fof(i_0_2360,plain,
    ! [X4162,X4163] :
      ( ~ class_RealVector_Oreal__normed__vector(X4163)
      | c_Groups_Osgn__class_Osgn(X4163,c_Groups_Ouminus__class_Ouminus(X4163,X4162)) = c_Groups_Ouminus__class_Ouminus(X4163,c_Groups_Osgn__class_Osgn(X4163,X4162)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__minus])]) ).

fof(i_0_2361,plain,
    ! [X3419,X3420] :
      ( ~ class_Groups_Ocomm__monoid__add(X3420)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3420),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3420)),X3419) = X3419 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).

fof(i_0_2362,plain,
    ! [X3421,X3422] :
      ( ~ class_Groups_Oab__group__add(X3422)
      | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3422),X3421,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3422))) = X3421 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).

fof(i_0_2363,plain,
    ! [X3417,X3418] :
      ( ~ class_Groups_Ocomm__monoid__add(X3418)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3418),X3417,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3418))) = X3417 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).

fof(i_0_2364,plain,
    ! [X2475] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X2475)),v_r),
    inference(variable_rename,[status(thm)],[fact_g_I1_J]) ).

fof(i_0_2365,plain,
    ! [X2616,X2617] :
      ( ~ c_SEQ_Osubseq(X2617)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2616,hAPP(X2617,X2616)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_seq__suble])]) ).

fof(i_0_2366,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_2367,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk22_0),v_r)
    & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk22_0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk21_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_mth1])]) ).

fof(i_0_2368,plain,
    ! [X4149,X4150] :
      ( ~ class_Int_Onumber__ring(X4150)
      | c_Groups_Oplus__class_Oplus(X4150,c_Int_Onumber__class_Onumber__of(X4150,c_Int_OPls),X4149) = X4149 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_2369,plain,
    ! [X4151,X4152] :
      ( ~ class_Int_Onumber__ring(X4152)
      | c_Groups_Oplus__class_Oplus(X4152,X4151,c_Int_Onumber__class_Onumber__of(X4152,c_Int_OPls)) = X4151 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

cnf(i_0_2370,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1474]) ).

cnf(i_0_2371,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_1475]) ).

fof(i_0_2372,plain,
    ! [X4107,X4108] :
      ( ~ class_Int_Onumber__ring(X4108)
      | c_Int_Onumber__class_Onumber__of(X4108,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4107)) = c_Groups_Ouminus__class_Ouminus(X4108,c_Int_Onumber__class_Onumber__of(X4108,X4107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_2373,plain,
    ! [X4105,X4106] :
      ( ~ class_Int_Onumber__ring(X4106)
      | c_Groups_Ouminus__class_Ouminus(X4106,c_Int_Onumber__class_Onumber__of(X4106,X4105)) = c_Int_Onumber__class_Onumber__of(X4106,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4105)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_2374,plain,
    ! [X3542] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3542,X3542),
    inference(variable_rename,[status(thm)],[i_0_1476]) ).

fof(i_0_2375,plain,
    ! [X3511] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3511,X3511),
    inference(variable_rename,[status(thm)],[i_0_1477]) ).

fof(i_0_2376,plain,
    ! [X4579] :
      ( X4579 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4579),X4579) = 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_2377,plain,
    ! [X2803,X2804] :
      ( ~ class_Groups_Ogroup__add(X2804)
      | c_Groups_Ominus__class_Ominus(X2804,c_Groups_Ozero__class_Ozero(X2804),X2803) = c_Groups_Ouminus__class_Ouminus(X2804,X2803) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).

fof(i_0_2378,plain,
    ! [X4622,X4623] :
      ( ~ class_Fields_Ofield(X4623)
      | c_Rings_Oinverse__class_Oinverse(X4623,X4622) = c_Rings_Oinverse__class_Odivide(X4623,c_Groups_Oone__class_Oone(X4623),X4622) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__class_Onormalizing__field__rules_I2_J])]) ).

fof(i_0_2379,plain,
    ! [X4624,X4625] :
      ( ~ class_Rings_Odivision__ring(X4625)
      | c_Rings_Oinverse__class_Oinverse(X4625,X4624) = c_Rings_Oinverse__class_Odivide(X4625,c_Groups_Oone__class_Oone(X4625),X4624) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide])]) ).

fof(i_0_2380,plain,
    ! [X3485] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X3485)),
    inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).

fof(i_0_2381,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_2382,plain,
    ! [X4281] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4281),X4281) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_2383,plain,
    ! [X3678,X3679] :
      ( ( X3678 != c_Groups_Ozero__class_Ozero(X3679)
        | c_Rings_Oinverse__class_Odivide(X3679,X3678,X3678) = c_Groups_Ozero__class_Ozero(X3679)
        | ~ class_Rings_Odivision__ring__inverse__zero(X3679) )
      & ( X3678 = c_Groups_Ozero__class_Ozero(X3679)
        | c_Rings_Oinverse__class_Odivide(X3679,X3678,X3678) = c_Groups_Oone__class_Oone(X3679)
        | ~ class_Rings_Odivision__ring__inverse__zero(X3679) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_2384,plain,
    ! [X3407] :
      ( ~ class_Rings_Olinordered__semidom(X3407)
      | c_Orderings_Oord__class_Oless(X3407,c_Groups_Ozero__class_Ozero(X3407),c_Groups_Oone__class_Oone(X3407)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_2385,plain,
    ! [X3396] :
      ( ~ class_Rings_Olinordered__semidom(X3396)
      | c_Orderings_Oord__class_Oless__eq(X3396,c_Groups_Ozero__class_Ozero(X3396),c_Groups_Oone__class_Oone(X3396)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_2386,plain,
    ! [X4482,X4483] :
      ( ~ class_Rings_Omult__zero(X4483)
      | c_Groups_Otimes__class_Otimes(X4483,c_Groups_Ozero__class_Ozero(X4483),X4482) = c_Groups_Ozero__class_Ozero(X4483) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).

fof(i_0_2387,plain,
    ! [X4501,X4502] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4502)
      | c_Groups_Otimes__class_Otimes(X4502,c_Groups_Ozero__class_Ozero(X4502),X4501) = c_Groups_Ozero__class_Ozero(X4502) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).

fof(i_0_2388,plain,
    ! [X4499,X4500] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4500)
      | c_Groups_Otimes__class_Otimes(X4500,c_Groups_Ozero__class_Ozero(X4500),X4499) = c_Groups_Ozero__class_Ozero(X4500) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).

fof(i_0_2389,plain,
    ! [X4552,X4553] :
      ( ~ class_Rings_Ocomm__semiring__1(X4553)
      | c_Groups_Otimes__class_Otimes(X4553,c_Groups_Ozero__class_Ozero(X4553),X4552) = c_Groups_Ozero__class_Ozero(X4553) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

fof(i_0_2390,plain,
    ! [X3945,X3946] :
      ( ~ class_Divides_Osemiring__div(X3946)
      | c_Divides_Odiv__class_Odiv(X3946,c_Groups_Ozero__class_Ozero(X3946),X3945) = c_Groups_Ozero__class_Ozero(X3946) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).

fof(i_0_2391,plain,
    ! [X3567,X3568] :
      ( ~ class_Rings_Odivision__ring(X3568)
      | c_Rings_Oinverse__class_Odivide(X3568,c_Groups_Ozero__class_Ozero(X3568),X3567) = c_Groups_Ozero__class_Ozero(X3568) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_2392,plain,
    ! [X3563,X3564] :
      ( ~ class_RealVector_Oreal__normed__field(X3564)
      | c_Rings_Oinverse__class_Odivide(X3564,c_Groups_Ozero__class_Ozero(X3564),X3563) = c_Groups_Ozero__class_Ozero(X3564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ozero])]) ).

fof(i_0_2393,plain,
    ! [X4484,X4485] :
      ( ~ class_Rings_Omult__zero(X4485)
      | c_Groups_Otimes__class_Otimes(X4485,X4484,c_Groups_Ozero__class_Ozero(X4485)) = c_Groups_Ozero__class_Ozero(X4485) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).

fof(i_0_2394,plain,
    ! [X4497,X4498] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4498)
      | c_Groups_Otimes__class_Otimes(X4498,X4497,c_Groups_Ozero__class_Ozero(X4498)) = c_Groups_Ozero__class_Ozero(X4498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).

fof(i_0_2395,plain,
    ! [X4495,X4496] :
      ( ~ class_RealVector_Oreal__normed__algebra(X4496)
      | c_Groups_Otimes__class_Otimes(X4496,X4495,c_Groups_Ozero__class_Ozero(X4496)) = c_Groups_Ozero__class_Ozero(X4496) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).

fof(i_0_2396,plain,
    ! [X4550,X4551] :
      ( ~ class_Rings_Ocomm__semiring__1(X4551)
      | c_Groups_Otimes__class_Otimes(X4551,X4550,c_Groups_Ozero__class_Ozero(X4551)) = c_Groups_Ozero__class_Ozero(X4551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_2397,plain,
    ! [X3947,X3948] :
      ( ~ class_Divides_Osemiring__div(X3948)
      | c_Divides_Odiv__class_Odiv(X3948,X3947,c_Groups_Ozero__class_Ozero(X3948)) = c_Groups_Ozero__class_Ozero(X3948) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).

fof(i_0_2398,plain,
    ! [X3565,X3566] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X3566)
      | c_Rings_Oinverse__class_Odivide(X3566,X3565,c_Groups_Ozero__class_Ozero(X3566)) = c_Groups_Ozero__class_Ozero(X3566) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_2399,plain,
    ! [X3956,X3957] :
      ( ~ class_Divides_Osemiring__div(X3957)
      | X3956 = c_Groups_Ozero__class_Ozero(X3957)
      | c_Divides_Odiv__class_Odiv(X3957,X3956,X3956) = c_Groups_Oone__class_Oone(X3957) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).

fof(i_0_2400,plain,
    ! [X3680,X3681] :
      ( ~ class_Rings_Odivision__ring(X3681)
      | X3680 = c_Groups_Ozero__class_Ozero(X3681)
      | c_Rings_Oinverse__class_Odivide(X3681,X3680,X3680) = c_Groups_Oone__class_Oone(X3681) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_2401,plain,
    ! [X4286] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4286)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4286)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_2402,plain,
    ! [X4572,X4573] :
      ( ~ class_Groups_Ocomm__monoid__mult(X4573)
      | c_Groups_Otimes__class_Otimes(X4573,c_Groups_Oone__class_Oone(X4573),X4572) = X4572 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_2403,plain,
    ! [X4570,X4571] :
      ( ~ class_Groups_Omonoid__mult(X4571)
      | c_Groups_Otimes__class_Otimes(X4571,c_Groups_Oone__class_Oone(X4571),X4570) = X4570 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_2404,plain,
    ! [X4566,X4567] :
      ( ~ class_Rings_Ocomm__semiring__1(X4567)
      | c_Groups_Otimes__class_Otimes(X4567,c_Groups_Oone__class_Oone(X4567),X4566) = X4566 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_2405,plain,
    ! [X3738,X3739] :
      ( ~ class_Rings_Ocomm__semiring__1(X3739)
      | c_Groups_Oplus__class_Oplus(X3739,c_Groups_Ozero__class_Ozero(X3739),X3738) = X3738 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_2406,plain,
    ! [X2997,X2998] :
      ( ~ class_Groups_Ocomm__monoid__add(X2998)
      | c_Groups_Oplus__class_Oplus(X2998,c_Groups_Ozero__class_Ozero(X2998),X2997) = X2997 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_2407,plain,
    ! [X2995,X2996] :
      ( ~ class_Groups_Omonoid__add(X2996)
      | c_Groups_Oplus__class_Oplus(X2996,c_Groups_Ozero__class_Ozero(X2996),X2995) = X2995 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_2408,plain,
    ! [X4576,X4577] :
      ( ~ class_Groups_Ocomm__monoid__mult(X4577)
      | c_Groups_Otimes__class_Otimes(X4577,X4576,c_Groups_Oone__class_Oone(X4577)) = X4576 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_2409,plain,
    ! [X4574,X4575] :
      ( ~ class_Groups_Omonoid__mult(X4575)
      | c_Groups_Otimes__class_Otimes(X4575,X4574,c_Groups_Oone__class_Oone(X4575)) = X4574 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_2410,plain,
    ! [X4568,X4569] :
      ( ~ class_Rings_Ocomm__semiring__1(X4569)
      | c_Groups_Otimes__class_Otimes(X4569,X4568,c_Groups_Oone__class_Oone(X4569)) = X4568 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_2411,plain,
    ! [X3949,X3950] :
      ( ~ class_Divides_Osemiring__div(X3950)
      | c_Divides_Odiv__class_Odiv(X3950,X3949,c_Groups_Oone__class_Oone(X3950)) = X3949 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).

fof(i_0_2412,plain,
    ! [X3585,X3586] :
      ( ~ class_Rings_Odivision__ring(X3586)
      | c_Rings_Oinverse__class_Odivide(X3586,X3585,c_Groups_Oone__class_Oone(X3586)) = X3585 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_2413,plain,
    ! [X3005,X3006] :
      ( ~ class_Groups_Ogroup__add(X3006)
      | c_Groups_Ominus__class_Ominus(X3006,X3005,c_Groups_Ozero__class_Ozero(X3006)) = X3005 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).

fof(i_0_2414,plain,
    ! [X3740,X3741] :
      ( ~ class_Rings_Ocomm__semiring__1(X3741)
      | c_Groups_Oplus__class_Oplus(X3741,X3740,c_Groups_Ozero__class_Ozero(X3741)) = X3740 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_2415,plain,
    ! [X3003,X3004] :
      ( ~ class_Groups_Ocomm__monoid__add(X3004)
      | c_Groups_Oplus__class_Oplus(X3004,X3003,c_Groups_Ozero__class_Ozero(X3004)) = X3003 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_2416,plain,
    ! [X3001,X3002] :
      ( ~ class_Groups_Omonoid__add(X3002)
      | c_Groups_Oplus__class_Oplus(X3002,X3001,c_Groups_Ozero__class_Ozero(X3002)) = X3001 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_2417,plain,
    ! [X3007,X3008] :
      ( ~ class_Groups_Ogroup__add(X3008)
      | c_Groups_Ominus__class_Ominus(X3008,X3007,X3007) = c_Groups_Ozero__class_Ozero(X3008) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).

fof(i_0_2418,plain,
    ! [X3107,X3108,X3109] :
      ( ~ class_Orderings_Opreorder(X3109)
      | X3108 != X3107
      | c_Orderings_Oord__class_Oless__eq(X3109,X3108,X3107) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_2419,plain,
    ! [X4512,X4513,X4514] :
      ( ~ class_Rings_Odivision__ring(X4514)
      | c_Rings_Oinverse__class_Oinverse(X4514,X4513) != c_Rings_Oinverse__class_Oinverse(X4514,X4512)
      | X4513 = c_Groups_Ozero__class_Ozero(X4514)
      | X4512 = c_Groups_Ozero__class_Ozero(X4514)
      | X4513 = X4512 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).

fof(i_0_2420,plain,
    ! [X3880] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X3880)),
    inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).

fof(i_0_2421,plain,
    ! [X3857] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X3857)),
    inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).

fof(i_0_2422,plain,
    ! [X2618,X2619] :
      ( ~ class_Orderings_Opreorder(X2619)
      | c_Orderings_Oord__class_Oless__eq(X2619,X2618,X2618) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

cnf(i_0_2423,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).

fof(i_0_2424,plain,
    ! [X4160,X4161] :
      ( ~ class_Rings_Olinordered__idom(X4161)
      | c_Groups_Osgn__class_Osgn(X4161,c_Groups_Osgn__class_Osgn(X4161,X4160)) = c_Groups_Osgn__class_Osgn(X4161,X4160) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_2425,plain,
    ! [X2988,X2989] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2989)
      | c_Groups_Oabs__class_Oabs(X2989,c_Groups_Ouminus__class_Ouminus(X2989,X2988)) = c_Groups_Oabs__class_Oabs(X2989,X2988) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).

fof(i_0_2426,plain,
    ! [X2549,X2550] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X2550)
      | c_Groups_Oabs__class_Oabs(X2550,c_Groups_Oabs__class_Oabs(X2550,X2549)) = c_Groups_Oabs__class_Oabs(X2550,X2549) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).

fof(i_0_2427,plain,
    ! [X2986,X2987] :
      ( ~ class_RealVector_Oreal__normed__vector(X2987)
      | c_RealVector_Onorm__class_Onorm(X2987,c_Groups_Ouminus__class_Ouminus(X2987,X2986)) = c_RealVector_Onorm__class_Onorm(X2987,X2986) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).

fof(i_0_2428,plain,
    ! [X4119,X4120,X4121] :
      ( ( c_Int_Onumber__class_Onumber__of(X4121,X4120) != c_Int_Onumber__class_Onumber__of(X4121,X4119)
        | X4120 = X4119
        | ~ class_Int_Onumber__ring(X4121)
        | ~ class_Int_Oring__char__0(X4121) )
      & ( X4120 != X4119
        | c_Int_Onumber__class_Onumber__of(X4121,X4120) = c_Int_Onumber__class_Onumber__of(X4121,X4119)
        | ~ class_Int_Onumber__ring(X4121)
        | ~ class_Int_Oring__char__0(X4121) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_2429,plain,
    ! [X3225,X3226,X3227] :
      ( ( c_Polynomial_Opoly(X3227,X3226) != c_Polynomial_Opoly(X3227,X3225)
        | X3226 = X3225
        | ~ class_Int_Oring__char__0(X3227)
        | ~ class_Rings_Oidom(X3227) )
      & ( X3226 != X3225
        | c_Polynomial_Opoly(X3227,X3226) = c_Polynomial_Opoly(X3227,X3225)
        | ~ class_Int_Oring__char__0(X3227)
        | ~ class_Rings_Oidom(X3227) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).

fof(i_0_2430,plain,
    ! [X3490] :
      ( X3490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3490) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_2431,plain,
    ! [X2605,X2606] :
      ( ~ class_RealVector_Oreal__normed__vector(X2606)
      | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2606,X2605)) = c_RealVector_Onorm__class_Onorm(X2606,X2605) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).

fof(i_0_2432,plain,
    ! [X4265] :
      ( X4265 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4265,X4265) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).

fof(i_0_2433,plain,
    ! [X4222] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4222) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).

fof(i_0_2434,plain,
    ! [X3414] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).

fof(i_0_2435,plain,
    ! [X4214,X4215] :
      ( ( X4214 != c_Groups_Ozero__class_Ozero(X4215)
        | c_RealVector_Onorm__class_Onorm(X4215,c_Groups_Osgn__class_Osgn(X4215,X4214)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ class_RealVector_Oreal__normed__vector(X4215) )
      & ( X4214 = c_Groups_Ozero__class_Ozero(X4215)
        | c_RealVector_Onorm__class_Onorm(X4215,c_Groups_Osgn__class_Osgn(X4215,X4214)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
        | ~ class_RealVector_Oreal__normed__vector(X4215) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__sgn])])]) ).

fof(i_0_2436,plain,
    ! [X4565] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4565) = X4565,
    inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).

fof(i_0_2437,plain,
    ! [X4323] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4323) = X4323,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_2438,plain,
    ! [X3403] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3403) = X3403,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_2439,plain,
    ! [X3413] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3413,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3413,
    inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(i_0_2440,plain,
    ! [X4322] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4322,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4322,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_2441,plain,
    ! [X3402] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3402,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3402,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_2442,plain,
    ! [X3218,X3219] :
      ( X3219 != X3218
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3219,X3218) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_2443,plain,
    ! [X3404] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3404),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_2444,plain,
    ! [X3313] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3313),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_2445,plain,
    ! [X3320] :
      ( ~ class_Groups_Oab__group__add(X3320)
      | c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3320),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3320))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3320)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).

cnf(i_0_2446,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_1475]) ).

cnf(i_0_2447,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_1474]) ).

fof(i_0_2448,plain,
    ! [X3412] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3412,X3412) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).

fof(i_0_2449,plain,
    ! [X3994,X3995,X3996] :
      ( ( c_Groups_Ouminus__class_Ouminus(X3996,X3995) != c_Groups_Ouminus__class_Ouminus(X3996,X3994)
        | X3995 = X3994
        | ~ class_Lattices_Oboolean__algebra(X3996) )
      & ( X3995 != X3994
        | c_Groups_Ouminus__class_Ouminus(X3996,X3995) = c_Groups_Ouminus__class_Ouminus(X3996,X3994)
        | ~ class_Lattices_Oboolean__algebra(X3996) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_2450,plain,
    ! [X2690,X2691,X2692] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2692,X2691) != c_Groups_Ouminus__class_Ouminus(X2692,X2690)
        | X2691 = X2690
        | ~ class_Groups_Ogroup__add(X2692) )
      & ( X2691 != X2690
        | c_Groups_Ouminus__class_Ouminus(X2692,X2691) = c_Groups_Ouminus__class_Ouminus(X2692,X2690)
        | ~ class_Groups_Ogroup__add(X2692) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_2451,plain,
    ! [X4508,X4509] :
      ( ~ class_Rings_Odivision__ring(X4509)
      | X4508 = c_Groups_Ozero__class_Ozero(X4509)
      | c_Rings_Oinverse__class_Oinverse(X4509,c_Rings_Oinverse__class_Oinverse(X4509,X4508)) = X4508 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).

fof(i_0_2452,plain,
    ! [X4300] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4300,X4300),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_2453,plain,
    ! [X3224] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3224,X3224),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_2454,plain,
    ! [X3161] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3161,X3161),
    inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).

fof(i_0_2455,plain,
    ! [X4156] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X4156) = X4156,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_2456,plain,
    ! [X4153] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4153,c_Int_OPls) = X4153,
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(i_0_2457,plain,
    ! [X4154] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4154,c_Int_OPls) = X4154,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

cnf(i_0_2458,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

fof(i_0_2459,plain,
    ! [X4001,X4002] :
      ( ~ class_Lattices_Oboolean__algebra(X4002)
      | c_Groups_Ouminus__class_Ouminus(X4002,c_Groups_Ouminus__class_Ouminus(X4002,X4001)) = X4001 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_2460,plain,
    ! [X2656,X2657] :
      ( ~ class_Groups_Ogroup__add(X2657)
      | c_Groups_Ouminus__class_Ouminus(X2657,c_Groups_Ouminus__class_Ouminus(X2657,X2656)) = X2656 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_2461,plain,
    ! [X3596] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X3596)) = c_RealDef_Oreal(tc_Nat_Onat,X3596),
    inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).

fof(i_0_2462,plain,
    ! [X2684,X2685,X2686] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2686,X2685) != X2684
        | c_Groups_Ouminus__class_Ouminus(X2686,X2684) = X2685
        | ~ class_Groups_Ogroup__add(X2686) )
      & ( c_Groups_Ouminus__class_Ouminus(X2686,X2684) != X2685
        | c_Groups_Ouminus__class_Ouminus(X2686,X2685) = X2684
        | ~ class_Groups_Ogroup__add(X2686) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_2463,plain,
    ! [X2670,X2671,X2672] :
      ( ( X2671 != c_Groups_Ouminus__class_Ouminus(X2672,X2670)
        | X2670 = c_Groups_Ouminus__class_Ouminus(X2672,X2671)
        | ~ class_Groups_Ogroup__add(X2672) )
      & ( X2670 != c_Groups_Ouminus__class_Ouminus(X2672,X2671)
        | X2671 = c_Groups_Ouminus__class_Ouminus(X2672,X2670)
        | ~ class_Groups_Ogroup__add(X2672) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_2464,plain,
    ! [X3851,X3852] :
      ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3852,X3851) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X3851 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3852))
        | ~ class_Groups_Ozero(X3852) )
      & ( X3851 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3852))
        | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3852,X3851) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ class_Groups_Ozero(X3852) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).

fof(i_0_2465,plain,
    ! [X3558,X3559] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,X3559) != c_RealDef_Oreal(tc_Nat_Onat,X3558)
        | X3559 = X3558 )
      & ( X3559 != X3558
        | c_RealDef_Oreal(tc_Nat_Onat,X3559) = c_RealDef_Oreal(tc_Nat_Onat,X3558) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).

fof(i_0_2466,plain,
    ! [X2662,X2663] :
      ( ( c_Groups_Ozero__class_Ozero(X2663) != c_Groups_Ouminus__class_Ouminus(X2663,X2662)
        | c_Groups_Ozero__class_Ozero(X2663) = X2662
        | ~ class_Groups_Ogroup__add(X2663) )
      & ( c_Groups_Ozero__class_Ozero(X2663) != X2662
        | c_Groups_Ozero__class_Ozero(X2663) = c_Groups_Ouminus__class_Ouminus(X2663,X2662)
        | ~ class_Groups_Ogroup__add(X2663) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_2467,plain,
    ! [X4563,X4564] :
      ( ( c_Rings_Oinverse__class_Oinverse(X4564,X4563) != c_Groups_Oone__class_Oone(X4564)
        | X4563 = c_Groups_Oone__class_Oone(X4564)
        | ~ class_Fields_Ofield__inverse__zero(X4564) )
      & ( X4563 != c_Groups_Oone__class_Oone(X4564)
        | c_Rings_Oinverse__class_Oinverse(X4564,X4563) = c_Groups_Oone__class_Oone(X4564)
        | ~ class_Fields_Ofield__inverse__zero(X4564) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).

fof(i_0_2468,plain,
    ! [X4510,X4511] :
      ( ~ class_Rings_Odivision__ring(X4511)
      | c_Rings_Oinverse__class_Oinverse(X4511,X4510) != c_Groups_Ozero__class_Ozero(X4511)
      | X4510 = c_Groups_Ozero__class_Ozero(X4511) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).

fof(i_0_2469,plain,
    ! [X4506,X4507] :
      ( ~ class_Rings_Odivision__ring(X4507)
      | X4506 = c_Groups_Ozero__class_Ozero(X4507)
      | c_Rings_Oinverse__class_Oinverse(X4507,X4506) != c_Groups_Ozero__class_Ozero(X4507) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).

fof(i_0_2470,plain,
    ! [X4504,X4505] :
      ( ( c_Rings_Oinverse__class_Oinverse(X4505,X4504) != c_Groups_Ozero__class_Ozero(X4505)
        | X4504 = c_Groups_Ozero__class_Ozero(X4505)
        | ~ class_Rings_Odivision__ring__inverse__zero(X4505) )
      & ( X4504 != c_Groups_Ozero__class_Ozero(X4505)
        | c_Rings_Oinverse__class_Oinverse(X4505,X4504) = c_Groups_Ozero__class_Ozero(X4505)
        | ~ class_Rings_Odivision__ring__inverse__zero(X4505) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).

fof(i_0_2471,plain,
    ! [X4168,X4169] :
      ( ( c_Groups_Osgn__class_Osgn(X4169,X4168) != c_Groups_Ozero__class_Ozero(X4169)
        | X4168 = c_Groups_Ozero__class_Ozero(X4169)
        | ~ class_Rings_Olinordered__idom(X4169) )
      & ( X4168 != c_Groups_Ozero__class_Ozero(X4169)
        | c_Groups_Osgn__class_Osgn(X4169,X4168) = c_Groups_Ozero__class_Ozero(X4169)
        | ~ class_Rings_Olinordered__idom(X4169) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_2472,plain,
    ! [X4166,X4167] :
      ( ( c_Groups_Osgn__class_Osgn(X4167,X4166) != c_Groups_Ozero__class_Ozero(X4167)
        | X4166 = c_Groups_Ozero__class_Ozero(X4167)
        | ~ class_RealVector_Oreal__normed__vector(X4167) )
      & ( X4166 != c_Groups_Ozero__class_Ozero(X4167)
        | c_Groups_Osgn__class_Osgn(X4167,X4166) = c_Groups_Ozero__class_Ozero(X4167)
        | ~ class_RealVector_Oreal__normed__vector(X4167) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff])])]) ).

fof(i_0_2473,plain,
    ! [X2678,X2679] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2679,X2678) != c_Groups_Ozero__class_Ozero(X2679)
        | X2678 = c_Groups_Ozero__class_Ozero(X2679)
        | ~ class_Groups_Ogroup__add(X2679) )
      & ( X2678 != c_Groups_Ozero__class_Ozero(X2679)
        | c_Groups_Ouminus__class_Ouminus(X2679,X2678) = c_Groups_Ozero__class_Ozero(X2679)
        | ~ class_Groups_Ogroup__add(X2679) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_2474,plain,
    ! [X3016,X3017] :
      ( ( c_Groups_Oabs__class_Oabs(X3017,X3016) != c_Groups_Ozero__class_Ozero(X3017)
        | X3016 = c_Groups_Ozero__class_Ozero(X3017)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3017) )
      & ( X3016 != c_Groups_Ozero__class_Ozero(X3017)
        | c_Groups_Oabs__class_Oabs(X3017,X3016) = c_Groups_Ozero__class_Ozero(X3017)
        | ~ class_Groups_Oordered__ab__group__add__abs(X3017) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).

fof(i_0_2475,plain,
    ! [X4347] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X4347)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4347),
    inference(variable_rename,[status(thm)],[fact_natfloor__number__of__eq]) ).

fof(i_0_2476,plain,
    ! [X4348] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X4348)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4348),
    inference(variable_rename,[status(thm)],[fact_natceiling__number__of__eq]) ).

fof(i_0_2477,plain,
    ! [X2893,X2894] :
      ( ( c_RealVector_Onorm__class_Onorm(X2894,X2893) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X2893 = c_Groups_Ozero__class_Ozero(X2894)
        | ~ class_RealVector_Oreal__normed__vector(X2894) )
      & ( X2893 != c_Groups_Ozero__class_Ozero(X2894)
        | c_RealVector_Onorm__class_Onorm(X2894,X2893) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ class_RealVector_Oreal__normed__vector(X2894) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).

fof(i_0_2478,plain,
    ! [X4844,X4845] :
      ( ~ class_Groups_Ouminus(X4845)
      | class_Groups_Ouminus(tc_fun(X4844,X4845)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_2479,plain,
    ! [X4846,X4847] :
      ( ~ class_Groups_Ominus(X4847)
      | class_Groups_Ominus(tc_fun(X4846,X4847)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).

fof(i_0_2480,plain,
    ! [X4836,X4837] :
      ( ~ class_Lattices_Oboolean__algebra(X4837)
      | class_Lattices_Oboolean__algebra(tc_fun(X4836,X4837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_2481,plain,
    ! [X4842,X4843] :
      ( ~ class_Orderings_Oord(X4843)
      | class_Orderings_Oord(tc_fun(X4842,X4843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_2482,plain,
    ! [X4840,X4841] :
      ( ~ class_Orderings_Oorder(X4841)
      | class_Orderings_Oorder(tc_fun(X4840,X4841)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_2483,plain,
    ! [X4838,X4839] :
      ( ~ class_Orderings_Opreorder(X4839)
      | class_Orderings_Opreorder(tc_fun(X4838,X4839)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_2484,plain,
    ! [X4287] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4287)) = X4287,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_2485,plain,
    ! [X2682,X2683] :
      ( ( c_Groups_Ouminus__class_Ouminus(X2683,X2682) != X2682
        | X2682 = c_Groups_Ozero__class_Ozero(X2683)
        | ~ class_Groups_Olinordered__ab__group__add(X2683) )
      & ( X2682 != c_Groups_Ozero__class_Ozero(X2683)
        | c_Groups_Ouminus__class_Ouminus(X2683,X2682) = X2682
        | ~ class_Groups_Olinordered__ab__group__add(X2683) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_2486,plain,
    ! [X2668,X2669] :
      ( ( X2668 != c_Groups_Ouminus__class_Ouminus(X2669,X2668)
        | X2668 = c_Groups_Ozero__class_Ozero(X2669)
        | ~ class_Groups_Olinordered__ab__group__add(X2669) )
      & ( X2668 != c_Groups_Ozero__class_Ozero(X2669)
        | X2668 = c_Groups_Ouminus__class_Ouminus(X2669,X2668)
        | ~ class_Groups_Olinordered__ab__group__add(X2669) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_2487,plain,
    ! [X4578] :
      ( ~ class_Rings_Odivision__ring(X4578)
      | c_Rings_Oinverse__class_Oinverse(X4578,c_Groups_Oone__class_Oone(X4578)) = c_Groups_Oone__class_Oone(X4578) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).

fof(i_0_2488,plain,
    ! [X4503] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X4503)
      | c_Rings_Oinverse__class_Oinverse(X4503,c_Groups_Ozero__class_Ozero(X4503)) = c_Groups_Ozero__class_Ozero(X4503) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).

fof(i_0_2489,plain,
    ! [X4557] :
      ( ~ class_Fields_Ofield__inverse__zero(X4557)
      | c_Rings_Oinverse__class_Oinverse(X4557,c_Groups_Ozero__class_Ozero(X4557)) = c_Groups_Ozero__class_Ozero(X4557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).

fof(i_0_2490,plain,
    ! [X4038] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X4038)
      | c_Groups_Osgn__class_Osgn(X4038,c_Groups_Oone__class_Oone(X4038)) = c_Groups_Oone__class_Oone(X4038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__one])]) ).

fof(i_0_2491,plain,
    ! [X4164] :
      ( ~ class_Groups_Osgn__if(X4164)
      | c_Groups_Osgn__class_Osgn(X4164,c_Groups_Ozero__class_Ozero(X4164)) = c_Groups_Ozero__class_Ozero(X4164) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_2492,plain,
    ! [X4165] :
      ( ~ class_RealVector_Oreal__normed__vector(X4165)
      | c_Groups_Osgn__class_Osgn(X4165,c_Groups_Ozero__class_Ozero(X4165)) = c_Groups_Ozero__class_Ozero(X4165) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero])]) ).

fof(i_0_2493,plain,
    ! [X2651] :
      ( ~ class_Groups_Ogroup__add(X2651)
      | c_Groups_Ouminus__class_Ouminus(X2651,c_Groups_Ozero__class_Ozero(X2651)) = c_Groups_Ozero__class_Ozero(X2651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_2494,plain,
    ! [X3334] :
      ( ~ class_Rings_Olinordered__idom(X3334)
      | c_Groups_Oabs__class_Oabs(X3334,c_Groups_Oone__class_Oone(X3334)) = c_Groups_Oone__class_Oone(X3334) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_2495,plain,
    ! [X3015] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X3015)
      | c_Groups_Oabs__class_Oabs(X3015,c_Groups_Ozero__class_Ozero(X3015)) = c_Groups_Ozero__class_Ozero(X3015) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).

fof(i_0_2496,plain,
    ! [X3323] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X3323)
      | c_RealVector_Onorm__class_Onorm(X3323,c_Groups_Oone__class_Oone(X3323)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).

fof(i_0_2497,plain,
    ! [X2895] :
      ( ~ class_RealVector_Oreal__normed__vector(X2895)
      | c_RealVector_Onorm__class_Onorm(X2895,c_Groups_Ozero__class_Ozero(X2895)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).

fof(i_0_2498,plain,
    ! [X3879] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X3879)) = X3879,
    inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).

fof(i_0_2499,plain,
    ! [X3856] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X3856)) = X3856,
    inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).

fof(i_0_2500,plain,
    ! [X3589] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,X3589) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X3589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X3589 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_RealDef_Oreal(tc_Nat_Onat,X3589) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff])]) ).

fof(i_0_2501,plain,
    ! [X2514] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2514) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2514),
    inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).

fof(i_0_2502,plain,
    ! [X4070] :
      ( ~ class_Int_Onumber__ring(X4070)
      | c_Int_Onumber__class_Onumber__of(X4070,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X4070) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_2503,plain,
    ! [X4174] :
      ( ~ class_Int_Onumber__ring(X4174)
      | c_Groups_Ozero__class_Ozero(X4174) = c_Int_Onumber__class_Onumber__of(X4174,c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_2504,plain,
    ! [X3333] :
      ( ~ class_Rings_Ozero__neq__one(X3333)
      | c_Groups_Ozero__class_Ozero(X3333) != c_Groups_Oone__class_Oone(X3333) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_2505,plain,
    ! [X3332] :
      ( ~ class_Rings_Ozero__neq__one(X3332)
      | c_Groups_Oone__class_Oone(X3332) != c_Groups_Ozero__class_Ozero(X3332) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_2506,plain,
    ! [X4271] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X4271),
    inference(variable_rename,[status(thm)],[fact_complex__i__not__number__of]) ).

fof(i_0_2507,plain,
    ! [X4835] :
      ( ~ class_Groups_Ocancel__comm__monoid__add(X4835)
      | class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X4835)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).

fof(i_0_2508,plain,
    ! [X4852] :
      ( ~ class_Rings_Olinordered__idom(X4852)
      | class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X4852)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).

fof(i_0_2509,plain,
    ! [X4851] :
      ( ~ class_Rings_Olinordered__idom(X4851)
      | class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X4851)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).

fof(i_0_2510,plain,
    ! [X4861] :
      ( ~ class_Rings_Olinordered__idom(X4861)
      | class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X4861)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).

fof(i_0_2511,plain,
    ! [X4867] :
      ( ~ class_Rings_Olinordered__idom(X4867)
      | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X4867)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).

fof(i_0_2512,plain,
    ! [X4878] :
      ( ~ class_Rings_Olinordered__idom(X4878)
      | class_Rings_Oordered__ring(tc_Polynomial_Opoly(X4878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).

fof(i_0_2513,plain,
    ! [X4858] :
      ( ~ class_Rings_Olinordered__idom(X4858)
      | class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X4858)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).

fof(i_0_2514,plain,
    ! [X4859] :
      ( ~ class_Rings_Olinordered__idom(X4859)
      | class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X4859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).

fof(i_0_2515,plain,
    ! [X4870] :
      ( ~ class_Rings_Olinordered__idom(X4870)
      | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X4870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).

fof(i_0_2516,plain,
    ! [X4865] :
      ( ~ class_Rings_Ocomm__semiring__1(X4865)
      | class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X4865)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).

fof(i_0_2517,plain,
    ! [X4881] :
      ( ~ class_Rings_Ocomm__semiring__1(X4881)
      | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X4881)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).

fof(i_0_2518,plain,
    ! [X4868] :
      ( ~ class_Rings_Oidom(X4868)
      | class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X4868)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).

fof(i_0_2519,plain,
    ! [X4860] :
      ( ~ class_Rings_Oidom(X4860)
      | class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X4860)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).

fof(i_0_2520,plain,
    ! [X4885] :
      ( ~ class_Rings_Ocomm__semiring__0(X4885)
      | class_Rings_Omult__zero(tc_Polynomial_Opoly(X4885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).

fof(i_0_2521,plain,
    ! [X4875] :
      ( ~ class_Rings_Ocomm__semiring__0(X4875)
      | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X4875)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).

fof(i_0_2522,plain,
    ! [X4890] :
      ( ~ class_Rings_Ocomm__semiring__0(X4890)
      | class_Rings_Osemiring(tc_Polynomial_Opoly(X4890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).

fof(i_0_2523,plain,
    ! [X4897] :
      ( ~ class_Rings_Ocomm__ring(X4897)
      | class_Rings_Oring(tc_Polynomial_Opoly(X4897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).

fof(i_0_2524,plain,
    ! [X4893] :
      ( ~ class_Rings_Olinordered__idom(X4893)
      | class_Groups_Osgn__if(tc_Polynomial_Opoly(X4893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if])]) ).

fof(i_0_2525,plain,
    ! [X4899] :
      ( ~ class_Rings_Ocomm__ring__1(X4899)
      | class_Int_Onumber(tc_Polynomial_Opoly(X4899)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber])]) ).

fof(i_0_2526,plain,
    ! [X4889] :
      ( ~ class_Rings_Ocomm__ring__1(X4889)
      | class_Int_Onumber__ring(tc_Polynomial_Opoly(X4889)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Onumber__ring])]) ).

fof(i_0_2527,plain,
    ! [X4892] :
      ( ~ class_Groups_Oab__group__add(X4892)
      | class_Groups_Ouminus(tc_Polynomial_Opoly(X4892)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).

fof(i_0_2528,plain,
    ! [X4895] :
      ( ~ class_Groups_Oab__group__add(X4895)
      | class_Groups_Ominus(tc_Polynomial_Opoly(X4895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])]) ).

fof(i_0_2529,plain,
    ! [X4874] :
      ( ~ class_Fields_Ofield(X4874)
      | class_Divides_Osemiring__div(tc_Polynomial_Opoly(X4874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])]) ).

fof(i_0_2530,plain,
    ! [X4848] :
      ( ~ class_Rings_Oidom(X4848)
      | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X4848)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).

fof(i_0_2531,plain,
    ! [X4882] :
      ( ~ class_Rings_Ocomm__ring__1(X4882)
      | class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X4882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).

fof(i_0_2532,plain,
    ! [X4864] :
      ( ~ class_Rings_Olinordered__idom(X4864)
      | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X4864)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).

fof(i_0_2533,plain,
    ! [X4877] :
      ( ~ class_Rings_Ocomm__semiring__1(X4877)
      | class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X4877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).

fof(i_0_2534,plain,
    ! [X4872] :
      ( ~ class_Rings_Ocomm__semiring__1(X4872)
      | class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X4872)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).

fof(i_0_2535,plain,
    ! [X4900] :
      ( ~ class_Rings_Ocomm__semiring__1(X4900)
      | class_Groups_Oone(tc_Polynomial_Opoly(X4900)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).

fof(i_0_2536,plain,
    ! [X4871] :
      ( ~ class_Rings_Olinordered__idom(X4871)
      | class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X4871)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).

fof(i_0_2537,plain,
    ! [X4898] :
      ( ~ class_Rings_Oidom(X4898)
      | class_Rings_Oidom(tc_Polynomial_Opoly(X4898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).

fof(i_0_2538,plain,
    ! [X4888] :
      ( ~ class_Rings_Olinordered__idom(X4888)
      | class_Int_Oring__char__0(tc_Polynomial_Opoly(X4888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).

fof(i_0_2539,plain,
    ! [X4869] :
      ( ~ class_Groups_Ocomm__monoid__add(X4869)
      | class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X4869)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).

fof(i_0_2540,plain,
    ! [X4883] :
      ( ~ class_Groups_Ocomm__monoid__add(X4883)
      | class_Groups_Omonoid__add(tc_Polynomial_Opoly(X4883)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).

fof(i_0_2541,plain,
    ! [X4849] :
      ( ~ class_Rings_Olinordered__idom(X4849)
      | class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X4849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).

fof(i_0_2542,plain,
    ! [X4855] :
      ( ~ class_Rings_Olinordered__idom(X4855)
      | class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X4855)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).

fof(i_0_2543,plain,
    ! [X4891] :
      ( ~ class_Rings_Olinordered__idom(X4891)
      | class_Orderings_Oord(tc_Polynomial_Opoly(X4891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).

fof(i_0_2544,plain,
    ! [X4887] :
      ( ~ class_Rings_Olinordered__idom(X4887)
      | class_Orderings_Oorder(tc_Polynomial_Opoly(X4887)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).

fof(i_0_2545,plain,
    ! [X4880] :
      ( ~ class_Rings_Olinordered__idom(X4880)
      | class_Orderings_Olinorder(tc_Polynomial_Opoly(X4880)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).

fof(i_0_2546,plain,
    ! [X4856] :
      ( ~ class_Rings_Olinordered__idom(X4856)
      | class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X4856)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).

fof(i_0_2547,plain,
    ! [X4896] :
      ( ~ class_Groups_Ozero(X4896)
      | class_Groups_Ozero(tc_Polynomial_Opoly(X4896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).

fof(i_0_2548,plain,
    ! [X4894] :
      ( ~ class_Rings_Olinordered__idom(X4894)
      | class_Groups_Oabs__if(tc_Polynomial_Opoly(X4894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if])]) ).

fof(i_0_2549,plain,
    ! [X4873] :
      ( ~ class_Rings_Ocomm__semiring__0(X4873)
      | class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X4873)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).

fof(i_0_2550,plain,
    ! [X4886] :
      ( ~ class_Rings_Ocomm__ring(X4886)
      | class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X4886)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).

fof(i_0_2551,plain,
    ! [X4879] :
      ( ~ class_Rings_Olinordered__idom(X4879)
      | class_Orderings_Opreorder(tc_Polynomial_Opoly(X4879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).

fof(i_0_2552,plain,
    ! [X4884] :
      ( ~ class_Groups_Oab__group__add(X4884)
      | class_Groups_Ogroup__add(tc_Polynomial_Opoly(X4884)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).

fof(i_0_2553,plain,
    ! [X4862] :
      ( ~ class_Rings_Olinordered__idom(X4862)
      | class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X4862)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).

fof(i_0_2554,plain,
    ! [X4853] :
      ( ~ class_Rings_Olinordered__idom(X4853)
      | class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X4853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).

fof(i_0_2555,plain,
    ! [X4850] :
      ( ~ class_Rings_Olinordered__idom(X4850)
      | class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X4850)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).

fof(i_0_2556,plain,
    ! [X4876] :
      ( ~ class_Groups_Oab__group__add(X4876)
      | class_Groups_Oab__group__add(tc_Polynomial_Opoly(X4876)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).

fof(i_0_2557,plain,
    ! [X4866] :
      ( ~ class_Groups_Ocomm__monoid__add(X4866)
      | class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X4866)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).

fof(i_0_2558,plain,
    ! [X4857] :
      ( ~ class_Groups_Ocancel__comm__monoid__add(X4857)
      | class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X4857)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).

fof(i_0_2559,plain,
    ! [X4863] :
      ( ~ class_Groups_Ocancel__comm__monoid__add(X4863)
      | class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X4863)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).

fof(i_0_2560,plain,
    ! [X4854] :
      ( ~ class_Rings_Olinordered__idom(X4854)
      | class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X4854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])]) ).

fof(i_0_2561,plain,
    ! [X4396] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4396) = X4396,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

cnf(i_0_2562,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_1479]),c_0_1479]),c_0_1479]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2563,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),
    inference(split_conjunct,[status(thm)],[i_0_1482]),
    [final] ).

cnf(i_0_2564,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1483,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2565,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1484,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2566,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1485,c_0_1479]),c_0_1479]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2567,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4)),X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1486,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2568,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)),
    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_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2569,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),X2),
    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_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2570,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)),
    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_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2571,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(rw,[status(thm)],[i_0_1490,c_0_1480]),
    [final] ).

cnf(i_0_2572,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),esk45_0)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1491,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2573,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1492,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2574,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1493,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2575,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1494,c_0_1479]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2576,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1495,c_0_1479]),c_0_1479]),c_0_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2577,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1496,c_0_1479]),c_0_1479]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2578,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1497,c_0_1479]),c_0_1479]),c_0_1481]),c_0_1481]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2579,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),v_d____) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1498,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2580,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1499,c_0_1479]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2581,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1500,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2582,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,hAPP(X2,X3),hAPP(X2,esk23_4(X2,X3,X4,X1)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(X4,X3,X5)
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ class_Orderings_Oord(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1501]),
    [final] ).

cnf(i_0_2583,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk47_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1502,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2584,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,esk46_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1503,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2585,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1504,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2586,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,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1505,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2587,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1506,c_0_1480]),
    [final] ).

cnf(i_0_2588,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1507,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2589,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1508,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2590,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1509,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2591,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ class_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)],[i_0_1510,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2592,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ class_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)],[i_0_1511,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2593,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1512,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2594,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1513,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2595,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1514,c_0_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2596,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1515,c_0_1480]),
    [final] ).

cnf(i_0_2597,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1516,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2598,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1517,c_0_1479]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2599,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1518,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2600,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk5_4(X3,X2,X4,X1)),hAPP(X3,esk5_4(X3,X2,X4,X1)))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1519]),
    [final] ).

cnf(i_0_2601,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1520,c_0_1479]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2602,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1521,c_0_1479]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2603,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1522,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2604,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4))))),
    inference(split_conjunct,[status(thm)],[i_0_1523]),
    [final] ).

cnf(i_0_2605,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1524,c_0_1480]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2606,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5)))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1525]),
    [final] ).

cnf(i_0_2607,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(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_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1526]),
    [final] ).

cnf(i_0_2608,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X5))))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1527]),
    [final] ).

cnf(i_0_2609,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)),X4) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)),c_Rings_Oinverse__class_Oinverse(X1,X3)))
    | ~ class_RealVector_Oreal__normed__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1528]),
    [final] ).

cnf(i_0_2610,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3),X2))),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)),esk44_3(X3,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_2611,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
    inference(split_conjunct,[status(thm)],[fact_th31]),
    [final] ).

cnf(i_0_2612,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1530,c_0_1480]),c_0_1481]),
    [final] ).

cnf(i_0_2613,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk39_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1531,c_0_1480]),
    [final] ).

cnf(i_0_2614,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(esk37_0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1532,c_0_1480]),
    [final] ).

cnf(i_0_2615,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk38_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1533,c_0_1480]),
    [final] ).

cnf(i_0_2616,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk36_1(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1534,c_0_1480]),
    [final] ).

cnf(i_0_2617,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
    inference(rw,[status(thm)],[i_0_1535,c_0_1480]),
    [final] ).

cnf(i_0_2618,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1536,c_0_1479]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2619,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1537,c_0_1479]),c_0_1480]),c_0_1480]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2620,plain,
    ( c_Groups_Ominus__class_Ominus(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_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1538,c_0_1481]),
    [final] ).

cnf(i_0_2621,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk29_2(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_RealVector_Oreal__normed__vector(X2)
    | ~ 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_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk28_3(X3,X2,X1))),X1) ),
    inference(rw,[status(thm)],[i_0_1539,c_0_1480]),
    [final] ).

cnf(i_0_2622,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X3,X4)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk33_2(X3,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_RealVector_Oreal__normed__vector(X2)
    | ~ 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_RealVector_Onorm__class_Onorm(X2,hAPP(X3,esk32_3(X3,X2,X1))),X1) ),
    inference(rw,[status(thm)],[i_0_1540,c_0_1480]),
    [final] ).

cnf(i_0_2623,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1541,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2624,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1542,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2625,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk35_2(X2,X1))
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk34_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[i_0_1543,c_0_1480]),
    [final] ).

cnf(i_0_2626,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,X3)),esk31_2(X2,X1))
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X2,esk30_3(X2,X1,X4))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[i_0_1544,c_0_1480]),
    [final] ).

cnf(i_0_2627,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_2628,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_2(X1,X2))
    | ~ class_RealVector_Oreal__normed__vector(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk34_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[i_0_1546,c_0_1480]),
    [final] ).

cnf(i_0_2629,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk31_2(X1,X2))
    | ~ class_RealVector_Oreal__normed__vector(X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,hAPP(X1,esk30_3(X1,X2,X3))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[i_0_1547,c_0_1480]),
    [final] ).

cnf(i_0_2630,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X4)),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1548]),
    [final] ).

cnf(i_0_2631,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | c_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)],[i_0_1549,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2632,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_1550]),
    [final] ).

cnf(i_0_2633,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,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)],[inference(rw,[status(thm)],[i_0_1551,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2634,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1552,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2635,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1553,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2636,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1554,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2637,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1555,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2638,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,esk23_4(X3,X2,X1,X4))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,hAPP(X3,X2))))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X5)
    | ~ class_RealVector_Oreal__normed__vector(X4)
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1501]),
    [final] ).

cnf(i_0_2639,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X3)))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1556]),
    [final] ).

cnf(i_0_2640,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_1557]),
    [final] ).

cnf(i_0_2641,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)))),
    inference(split_conjunct,[status(thm)],[i_0_1558]),
    [final] ).

cnf(i_0_2642,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1559]),
    [final] ).

cnf(i_0_2643,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1560,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2644,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
    inference(split_conjunct,[status(thm)],[fact_e]),
    [final] ).

cnf(i_0_2645,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1561,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2646,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1562,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2647,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1563,c_0_1479]),c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2648,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk8_1(X1))))),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_2649,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) != X6
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1564]),
    [final] ).

cnf(i_0_2650,plain,
    ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X4,X5),X1) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X5),X6)
    | X1 != c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,c_Groups_Ominus__class_Ominus(X2,X3,X4),X5),X6)
    | ~ class_Rings_Oring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1565]),
    [final] ).

cnf(i_0_2651,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) = X6
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1564]),
    [final] ).

cnf(i_0_2652,plain,
    ( X4 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1565]),
    [final] ).

cnf(i_0_2653,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1566,c_0_1481]),
    [final] ).

cnf(i_0_2654,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1567]),
    [final] ).

cnf(i_0_2655,plain,
    ( X1 = X2
    | X3 = X4
    | c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X1,X3),c_Groups_Otimes__class_Otimes(X5,X2,X4)) != c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X1,X4),c_Groups_Otimes__class_Otimes(X5,X2,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1568]),
    [final] ).

cnf(i_0_2656,plain,
    ( X2 = X4
    | X3 = X5
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1569]),
    [final] ).

cnf(i_0_2657,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1570,c_0_1481]),
    [final] ).

cnf(i_0_2658,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1571,c_0_1481]),
    [final] ).

cnf(i_0_2659,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2660,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1573,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2661,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1574,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2662,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1575,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2663,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1576,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2664,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1577,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2665,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1578,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2666,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1579,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2667,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1580,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2668,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1581,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2669,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1582,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2670,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1583,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2671,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1584,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2672,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1585]),
    [final] ).

cnf(i_0_2673,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1586]),
    [final] ).

cnf(i_0_2674,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_1587]),
    [final] ).

cnf(i_0_2675,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_1588]),
    [final] ).

cnf(i_0_2676,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1589,c_0_1481]),
    [final] ).

cnf(i_0_2677,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X2
    | ~ class_Fields_Ofield(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1590,c_0_1481]),
    [final] ).

cnf(i_0_2678,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1591,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2679,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1592,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2680,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(rw,[status(thm)],[i_0_1593,c_0_1480]),
    [final] ).

cnf(i_0_2681,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2)),
    inference(split_conjunct,[status(thm)],[i_0_1594]),
    [final] ).

cnf(i_0_2682,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
    inference(split_conjunct,[status(thm)],[i_0_1595]),
    [final] ).

cnf(i_0_2683,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1596,c_0_1480]),c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2684,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_1597,c_0_1481]),
    [final] ).

cnf(i_0_2685,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_1598,c_0_1481]),
    [final] ).

cnf(i_0_2686,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1) ),
    inference(rw,[status(thm)],[i_0_1599,c_0_1481]),
    [final] ).

cnf(i_0_2687,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_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1) ),
    inference(rw,[status(thm)],[i_0_1600,c_0_1481]),
    [final] ).

cnf(i_0_2688,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2689,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2690,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2691,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2692,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X2)),v_z____)),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_Nat_Onat,esk4_1(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1603]),
    [final] ).

cnf(i_0_2693,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_1604]),
    [final] ).

cnf(i_0_2694,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rw,[status(thm)],[i_0_1605,c_0_1481]),
    [final] ).

cnf(i_0_2695,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X5))
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1606]),
    [final] ).

cnf(i_0_2696,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X5))
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
    inference(split_conjunct,[status(thm)],[i_0_1607]),
    [final] ).

cnf(i_0_2697,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1608,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2698,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
    inference(rw,[status(thm)],[i_0_1609,c_0_1481]),
    [final] ).

cnf(i_0_2699,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
    inference(rw,[status(thm)],[i_0_1610,c_0_1481]),
    [final] ).

cnf(i_0_2700,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1611,c_0_1481]),
    [final] ).

cnf(i_0_2701,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1612,c_0_1481]),
    [final] ).

cnf(i_0_2702,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_1613]),
    [final] ).

cnf(i_0_2703,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_1614]),
    [final] ).

cnf(i_0_2704,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1615]),
    [final] ).

cnf(i_0_2705,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1616]),
    [final] ).

cnf(i_0_2706,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_1617]),
    [final] ).

cnf(i_0_2707,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2708,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1572]),
    [final] ).

cnf(i_0_2709,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1618]),
    [final] ).

cnf(i_0_2710,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1619]),
    [final] ).

cnf(i_0_2711,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Oplus__class_Oplus(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,X4))),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1620]),
    [final] ).

cnf(i_0_2712,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1621]),
    [final] ).

cnf(i_0_2713,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1622,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2714,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1623,c_0_1481]),
    [final] ).

cnf(i_0_2715,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ 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),X1) ),
    inference(rw,[status(thm)],[i_0_1624,c_0_1480]),
    [final] ).

cnf(i_0_2716,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1625]),
    [final] ).

cnf(i_0_2717,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1626]),
    [final] ).

cnf(i_0_2718,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)) = c_Groups_Otimes__class_Otimes(X1,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_1627]),
    [final] ).

cnf(i_0_2719,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3))
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1628]),
    [final] ).

cnf(i_0_2720,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)) = c_Groups_Otimes__class_Otimes(X1,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_1629]),
    [final] ).

cnf(i_0_2721,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1630]),
    [final] ).

cnf(i_0_2722,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1631]),
    [final] ).

cnf(i_0_2723,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1632]),
    [final] ).

cnf(i_0_2724,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
    | ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1633]),
    [final] ).

cnf(i_0_2725,plain,
    ( c_SEQ_Osubseq(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk27_1(X1)),hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk27_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
    inference(rw,[status(thm)],[i_0_1634,c_0_1480]),
    [final] ).

cnf(i_0_2726,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_2727,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk13_0,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1636]),
    [final] ).

cnf(i_0_2728,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_0,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1637]),
    [final] ).

cnf(i_0_2729,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(v_f____,X1)),v_z____)),v_d____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1638]),
    [final] ).

cnf(i_0_2730,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1639,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2731,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1640,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2732,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1641,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2733,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1642,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2734,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1643,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2735,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1644,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2736,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1645,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2737,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1646,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_2738,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | 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),X2) ),
    inference(rw,[status(thm)],[i_0_1647,c_0_1480]),
    [final] ).

cnf(i_0_2739,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[i_0_1648,c_0_1480]),
    [final] ).

cnf(i_0_2740,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2741,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2742,plain,
    ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X4),c_Groups_Otimes__class_Otimes(X3,X2,X5)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X5),c_Groups_Otimes__class_Otimes(X3,X2,X4))
    | X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1569]),
    [final] ).

cnf(i_0_2743,plain,
    ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X4),c_Groups_Otimes__class_Otimes(X3,X2,X5)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X5),c_Groups_Otimes__class_Otimes(X3,X2,X4))
    | X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1568]),
    [final] ).

cnf(i_0_2744,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2745,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2746,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2747,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2748,plain,
    ( c_Groups_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1651]),
    [final] ).

cnf(i_0_2749,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_1652]),
    [final] ).

cnf(i_0_2750,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2751,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2752,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1653]),
    [final] ).

cnf(i_0_2753,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1654]),
    [final] ).

cnf(i_0_2754,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_1655]),
    [final] ).

cnf(i_0_2755,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk12_0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ),
    inference(split_conjunct,[status(thm)],[i_0_1656]),
    [final] ).

cnf(i_0_2756,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X5 = X6
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X4
    | c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X5)) != c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_1657]),
    [final] ).

cnf(i_0_2757,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1658]),
    [final] ).

cnf(i_0_2758,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1659]),
    [final] ).

cnf(i_0_2759,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1660,c_0_1479]),c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2760,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_1661,c_0_1479]),c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2761,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2)
    | ~ class_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)],[i_0_1662,c_0_1481]),
    [final] ).

cnf(i_0_2762,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2)
    | ~ class_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)],[i_0_1663,c_0_1481]),
    [final] ).

cnf(i_0_2763,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
    | ~ class_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)],[i_0_1664,c_0_1481]),
    [final] ).

cnf(i_0_2764,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
    | ~ class_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)],[i_0_1665,c_0_1481]),
    [final] ).

cnf(i_0_2765,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_2766,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1667,c_0_1481]),c_0_1481]),
    [final] ).

cnf(i_0_2767,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1618]),
    [final] ).

cnf(i_0_2768,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1619]),
    [final] ).

cnf(i_0_2769,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1668]),
    [final] ).

cnf(i_0_2770,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1669]),
    [final] ).

cnf(i_0_2771,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1670]),
    [final] ).

cnf(i_0_2772,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1671]),
    [final] ).

cnf(i_0_2773,plain,
    ( c_RComplete_Onatceiling(X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    inference(split_conjunct,[status(thm)],[i_0_1672]),
    [final] ).

cnf(i_0_2774,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1673]),
    [final] ).

cnf(i_0_2775,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1674]),
    [final] ).

cnf(i_0_2776,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1675]),
    [final] ).

cnf(i_0_2777,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1676]),
    [final] ).

cnf(i_0_2778,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1677]),
    [final] ).

cnf(i_0_2779,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))
    | ~ class_Rings_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1678]),
    [final] ).

cnf(i_0_2780,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1679]),
    [final] ).

cnf(i_0_2781,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2782,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2783,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2784,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2785,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_2786,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1680]),
    [final] ).

cnf(i_0_2787,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_1681]),
    [final] ).

cnf(i_0_2788,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_1682]),
    [final] ).

cnf(i_0_2789,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_1683]),
    [final] ).

cnf(i_0_2790,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_1684]),
    [final] ).

cnf(i_0_2791,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_1685]),
    [final] ).

cnf(i_0_2792,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_1686]),
    [final] ).

cnf(i_0_2793,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_1687]),
    [final] ).

cnf(i_0_2794,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_1688]),
    [final] ).

cnf(i_0_2795,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1689,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2796,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1690,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2797,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1691,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2798,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1692,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2799,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1693]),
    [final] ).

cnf(i_0_2800,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))),
    inference(split_conjunct,[status(thm)],[i_0_1694]),
    [final] ).

cnf(i_0_2801,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_1604]),
    [final] ).

cnf(i_0_2802,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(rw,[status(thm)],[i_0_1695,c_0_1481]),
    [final] ).

cnf(i_0_2803,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[i_0_1696,c_0_1480]),
    [final] ).

cnf(i_0_2804,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_1697,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2805,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_1698,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2806,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_1699]),
    [final] ).

cnf(i_0_2807,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_1700,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2808,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_1701,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2809,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_1702]),
    [final] ).

cnf(i_0_2810,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2811,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1703]),
    [final] ).

cnf(i_0_2812,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2813,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1704]),
    [final] ).

cnf(i_0_2814,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1705]),
    [final] ).

cnf(i_0_2815,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1625]),
    [final] ).

cnf(i_0_2816,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_1706]),
    [final] ).

cnf(i_0_2817,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1707]),
    [final] ).

cnf(i_0_2818,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1708]),
    [final] ).

cnf(i_0_2819,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_1709]),
    [final] ).

cnf(i_0_2820,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_1710]),
    [final] ).

cnf(i_0_2821,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1649]),
    [final] ).

cnf(i_0_2822,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1711]),
    [final] ).

cnf(i_0_2823,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1650]),
    [final] ).

cnf(i_0_2824,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1626]),
    [final] ).

cnf(i_0_2825,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1712]),
    [final] ).

cnf(i_0_2826,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_1713]),
    [final] ).

cnf(i_0_2827,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1714]),
    [final] ).

cnf(i_0_2828,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1715]),
    [final] ).

cnf(i_0_2829,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_1716]),
    [final] ).

cnf(i_0_2830,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1717,c_0_1481]),
    [final] ).

cnf(i_0_2831,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(rw,[status(thm)],[i_0_1718,c_0_1481]),
    [final] ).

cnf(i_0_2832,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(rw,[status(thm)],[i_0_1719,c_0_1481]),
    [final] ).

cnf(i_0_2833,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(rw,[status(thm)],[i_0_1720,c_0_1481]),
    [final] ).

cnf(i_0_2834,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk15_3(X2,X1,X3))
    | hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2835,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
    | hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2836,plain,
    ( c_RComplete_Onatfloor(X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    inference(split_conjunct,[status(thm)],[i_0_1721]),
    [final] ).

cnf(i_0_2837,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk15_3(X2,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1601]),
    [final] ).

cnf(i_0_2838,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_1602]),
    [final] ).

cnf(i_0_2839,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
    inference(split_conjunct,[status(thm)],[fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096]),
    [final] ).

cnf(i_0_2840,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1722]),
    [final] ).

cnf(i_0_2841,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_1723]),
    [final] ).

cnf(i_0_2842,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_1724]),
    [final] ).

cnf(i_0_2843,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_1725]),
    [final] ).

cnf(i_0_2844,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_1726]),
    [final] ).

cnf(i_0_2845,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_2846,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X3),c_Groups_Otimes__class_Otimes(X2,X1,X1)) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_2847,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1728]),
    [final] ).

cnf(i_0_2848,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1729]),
    [final] ).

cnf(i_0_2849,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1730]),
    [final] ).

cnf(i_0_2850,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1731]),
    [final] ).

cnf(i_0_2851,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1732]),
    [final] ).

cnf(i_0_2852,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1733]),
    [final] ).

cnf(i_0_2853,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1734]),
    [final] ).

cnf(i_0_2854,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(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_1735]),
    [final] ).

cnf(i_0_2855,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(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_1736]),
    [final] ).

cnf(i_0_2856,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_1737]),
    [final] ).

cnf(i_0_2857,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_1738]),
    [final] ).

cnf(i_0_2858,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1739]),
    [final] ).

cnf(i_0_2859,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1740]),
    [final] ).

cnf(i_0_2860,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1741]),
    [final] ).

cnf(i_0_2861,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1742]),
    [final] ).

cnf(i_0_2862,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1743]),
    [final] ).

cnf(i_0_2863,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[i_0_1744,c_0_1480]),
    [final] ).

cnf(i_0_2864,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1745]),
    [final] ).

cnf(i_0_2865,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X3,X2),c_Divides_Odiv__class_Odiv(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__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1746]),
    [final] ).

cnf(i_0_2866,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1747]),
    [final] ).

cnf(i_0_2867,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_1748]),
    [final] ).

cnf(i_0_2868,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1749]),
    [final] ).

cnf(i_0_2869,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1750]),
    [final] ).

cnf(i_0_2870,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_1751]),
    [final] ).

cnf(i_0_2871,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_1752]),
    [final] ).

cnf(i_0_2872,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1753]),
    [final] ).

cnf(i_0_2873,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1754]),
    [final] ).

cnf(i_0_2874,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_2875,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1756]),
    [final] ).

cnf(i_0_2876,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    inference(split_conjunct,[status(thm)],[i_0_1757]),
    [final] ).

cnf(i_0_2877,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_1758]),
    [final] ).

cnf(i_0_2878,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1759,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_2879,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk40_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),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_1760]),
    [final] ).

cnf(i_0_2880,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1761,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2881,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_2882,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_1763]),
    [final] ).

cnf(i_0_2883,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1762]),
    [final] ).

cnf(i_0_2884,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1763]),
    [final] ).

cnf(i_0_2885,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1764]),
    [final] ).

cnf(i_0_2886,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1765]),
    [final] ).

cnf(i_0_2887,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1766]),
    [final] ).

cnf(i_0_2888,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1767]),
    [final] ).

cnf(i_0_2889,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1768]),
    [final] ).

cnf(i_0_2890,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_2891,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1769]),
    [final] ).

cnf(i_0_2892,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_2893,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_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1771]),
    [final] ).

cnf(i_0_2894,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_2895,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,esk18_0)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_2896,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,v_s____)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_2897,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1755]),
    [final] ).

cnf(i_0_2898,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1775]),
    [final] ).

cnf(i_0_2899,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_1776]),
    [final] ).

cnf(i_0_2900,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2901,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_1778]),
    [final] ).

cnf(i_0_2902,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_1776]),
    [final] ).

cnf(i_0_2903,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_1776]),
    [final] ).

cnf(i_0_2904,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2905,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2906,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_1778]),
    [final] ).

cnf(i_0_2907,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_1778]),
    [final] ).

cnf(i_0_2908,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_1779]),
    [final] ).

cnf(i_0_2909,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_1779]),
    [final] ).

cnf(i_0_2910,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_1779]),
    [final] ).

cnf(i_0_2911,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_1779]),
    [final] ).

cnf(i_0_2912,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2913,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2914,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_1781]),
    [final] ).

cnf(i_0_2915,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_1781]),
    [final] ).

cnf(i_0_2916,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2917,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2918,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_1781]),
    [final] ).

cnf(i_0_2919,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_1781]),
    [final] ).

cnf(i_0_2920,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_1776]),
    [final] ).

cnf(i_0_2921,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2922,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_1778]),
    [final] ).

cnf(i_0_2923,plain,
    ( c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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_1782]),
    [final] ).

cnf(i_0_2924,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1783,c_0_1480]),c_0_1481]),
    [final] ).

cnf(i_0_2925,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_1784,c_0_1479]),
    [final] ).

cnf(i_0_2926,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2))
    | ~ class_RealVector_Oreal__normed__div__algebra(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1785]),
    [final] ).

cnf(i_0_2927,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_1786,c_0_1480]),
    [final] ).

cnf(i_0_2928,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_1787,c_0_1480]),
    [final] ).

cnf(i_0_2929,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    inference(split_conjunct,[status(thm)],[fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096]),
    [final] ).

cnf(i_0_2930,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk10_0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_2931,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1788,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2932,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1789,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2933,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1790]),
    [final] ).

cnf(i_0_2934,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1791]),
    [final] ).

cnf(i_0_2935,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1792]),
    [final] ).

cnf(i_0_2936,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_1793]),
    [final] ).

cnf(i_0_2937,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_1794]),
    [final] ).

cnf(i_0_2938,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_1776]),
    [final] ).

cnf(i_0_2939,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_1776]),
    [final] ).

cnf(i_0_2940,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1795]),
    [final] ).

cnf(i_0_2941,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1796]),
    [final] ).

cnf(i_0_2942,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1795]),
    [final] ).

cnf(i_0_2943,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1797]),
    [final] ).

cnf(i_0_2944,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2945,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1777]),
    [final] ).

cnf(i_0_2946,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1798]),
    [final] ).

cnf(i_0_2947,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_1799]),
    [final] ).

cnf(i_0_2948,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_1800]),
    [final] ).

cnf(i_0_2949,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_1778]),
    [final] ).

cnf(i_0_2950,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_1778]),
    [final] ).

cnf(i_0_2951,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_1801]),
    [final] ).

cnf(i_0_2952,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_1802]),
    [final] ).

cnf(i_0_2953,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_1803]),
    [final] ).

cnf(i_0_2954,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_1804]),
    [final] ).

cnf(i_0_2955,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1805]),
    [final] ).

cnf(i_0_2956,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1806]),
    [final] ).

cnf(i_0_2957,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_1807]),
    [final] ).

cnf(i_0_2958,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_1779]),
    [final] ).

cnf(i_0_2959,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_1808]),
    [final] ).

cnf(i_0_2960,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_1809]),
    [final] ).

cnf(i_0_2961,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_1810]),
    [final] ).

cnf(i_0_2962,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1811]),
    [final] ).

cnf(i_0_2963,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1812]),
    [final] ).

cnf(i_0_2964,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2965,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_1813]),
    [final] ).

cnf(i_0_2966,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_1781]),
    [final] ).

cnf(i_0_2967,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_1814]),
    [final] ).

cnf(i_0_2968,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1815]),
    [final] ).

cnf(i_0_2969,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_1816]),
    [final] ).

cnf(i_0_2970,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_1779]),
    [final] ).

cnf(i_0_2971,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1811]),
    [final] ).

cnf(i_0_2972,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1817]),
    [final] ).

cnf(i_0_2973,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1780]),
    [final] ).

cnf(i_0_2974,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_1818]),
    [final] ).

cnf(i_0_2975,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_1781]),
    [final] ).

cnf(i_0_2976,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_1819]),
    [final] ).

cnf(i_0_2977,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_1820]),
    [final] ).

cnf(i_0_2978,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_1820]),
    [final] ).

cnf(i_0_2979,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_1821]),
    [final] ).

cnf(i_0_2980,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_1682]),
    [final] ).

cnf(i_0_2981,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_1822]),
    [final] ).

cnf(i_0_2982,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_1684]),
    [final] ).

cnf(i_0_2983,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_1823]),
    [final] ).

cnf(i_0_2984,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_1685]),
    [final] ).

cnf(i_0_2985,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_1824]),
    [final] ).

cnf(i_0_2986,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_1687]),
    [final] ).

cnf(i_0_2987,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1825,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2988,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1826,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2989,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1827,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_2990,plain,
    ( c_SEQ_Odecseq(X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk43_2(X2,X1)),hAPP(X2,esk42_2(X2,X1)))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_2991,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1829]),
    [final] ).

cnf(i_0_2992,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_1830]),
    [final] ).

cnf(i_0_2993,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_1831]),
    [final] ).

cnf(i_0_2994,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_1832]),
    [final] ).

cnf(i_0_2995,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_1833]),
    [final] ).

cnf(i_0_2996,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_1834]),
    [final] ).

cnf(i_0_2997,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_1835]),
    [final] ).

cnf(i_0_2998,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(rw,[status(thm)],[i_0_1836,c_0_1480]),
    [final] ).

cnf(i_0_2999,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk9_1(X1))),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_3000,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ),
    inference(split_conjunct,[status(thm)],[i_0_1837]),
    [final] ).

cnf(i_0_3001,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_1838,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3002,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_1839,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3003,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_1840]),
    [final] ).

cnf(i_0_3004,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_1841]),
    [final] ).

cnf(i_0_3005,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_1699]),
    [final] ).

cnf(i_0_3006,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_1842,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3007,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_1843,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3008,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_1844]),
    [final] ).

cnf(i_0_3009,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X3),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1845]),
    [final] ).

cnf(i_0_3010,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1846]),
    [final] ).

cnf(i_0_3011,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1847]),
    [final] ).

cnf(i_0_3012,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_1848]),
    [final] ).

cnf(i_0_3013,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_1702]),
    [final] ).

cnf(i_0_3014,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_1849]),
    [final] ).

cnf(i_0_3015,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk24_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1850,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3016,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1851,c_0_1480]),
    [final] ).

cnf(i_0_3017,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1852]),
    [final] ).

cnf(i_0_3018,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1853]),
    [final] ).

cnf(i_0_3019,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1854]),
    [final] ).

cnf(i_0_3020,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X2),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1855]),
    [final] ).

cnf(i_0_3021,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1856,c_0_1480]),
    [final] ).

cnf(i_0_3022,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1857,c_0_1480]),
    [final] ).

cnf(i_0_3023,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1858,c_0_1481]),
    [final] ).

cnf(i_0_3024,plain,
    ( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_1859,c_0_1481]),
    [final] ).

cnf(i_0_3025,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk24_2(X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1860,c_0_1480]),
    [final] ).

cnf(i_0_3026,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1861,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_3027,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1862,c_0_1479]),c_0_1481]),
    [final] ).

cnf(i_0_3028,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1863]),
    [final] ).

cnf(i_0_3029,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1864]),
    [final] ).

cnf(i_0_3030,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1771]),
    [final] ).

cnf(i_0_3031,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1770]),
    [final] ).

cnf(i_0_3032,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1865]),
    [final] ).

cnf(i_0_3033,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1866]),
    [final] ).

cnf(i_0_3034,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1769]),
    [final] ).

cnf(i_0_3035,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1867]),
    [final] ).

cnf(i_0_3036,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_1820]),
    [final] ).

cnf(i_0_3037,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_1820]),
    [final] ).

cnf(i_0_3038,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_1820]),
    [final] ).

cnf(i_0_3039,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1772]),
    [final] ).

cnf(i_0_3040,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_1820]),
    [final] ).

cnf(i_0_3041,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1868,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3042,plain,
    ( X1 = X3
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1869]),
    [final] ).

cnf(i_0_3043,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1870]),
    [final] ).

cnf(i_0_3044,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
    | ~ class_Fields_Ofield__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1871]),
    [final] ).

cnf(i_0_3045,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1872]),
    [final] ).

cnf(i_0_3046,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1873]),
    [final] ).

cnf(i_0_3047,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1874]),
    [final] ).

cnf(i_0_3048,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1775]),
    [final] ).

cnf(i_0_3049,plain,
    ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1875]),
    [final] ).

cnf(i_0_3050,plain,
    ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1876]),
    [final] ).

cnf(i_0_3051,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ c_SEQ_Osubseq(X1) ),
    inference(rw,[status(thm)],[i_0_1877,c_0_1480]),
    [final] ).

cnf(i_0_3052,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_1878]),
    [final] ).

cnf(i_0_3053,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_1879]),
    [final] ).

cnf(i_0_3054,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_1880]),
    [final] ).

cnf(i_0_3055,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_1881]),
    [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,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_1882]),
    [final] ).

cnf(i_0_3057,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1883,c_0_1480]),
    [final] ).

cnf(i_0_3058,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_1884]),
    [final] ).

cnf(i_0_3059,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_1885]),
    [final] ).

cnf(i_0_3060,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_1886]),
    [final] ).

cnf(i_0_3061,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_1887]),
    [final] ).

cnf(i_0_3062,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_1888]),
    [final] ).

cnf(i_0_3063,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(rw,[status(thm)],[i_0_1889,c_0_1481]),
    [final] ).

cnf(i_0_3064,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(rw,[status(thm)],[i_0_1890,c_0_1481]),
    [final] ).

cnf(i_0_3065,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(rw,[status(thm)],[i_0_1891,c_0_1481]),
    [final] ).

cnf(i_0_3066,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
    inference(split_conjunct,[status(thm)],[i_0_1892]),
    [final] ).

cnf(i_0_3067,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_1893]),
    [final] ).

cnf(i_0_3068,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_1894]),
    [final] ).

cnf(i_0_3069,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_1895]),
    [final] ).

cnf(i_0_3070,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_1896]),
    [final] ).

cnf(i_0_3071,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_1897]),
    [final] ).

cnf(i_0_3072,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_1898]),
    [final] ).

cnf(i_0_3073,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1899]),
    [final] ).

cnf(i_0_3074,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1900]),
    [final] ).

cnf(i_0_3075,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1901,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3076,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1902,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3077,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
    inference(rw,[status(thm)],[i_0_1903,c_0_1480]),
    [final] ).

cnf(i_0_3078,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
    inference(split_conjunct,[status(thm)],[i_0_1904]),
    [final] ).

cnf(i_0_3079,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1905,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3080,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1906,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3081,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1907]),
    [final] ).

cnf(i_0_3082,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1907]),
    [final] ).

cnf(i_0_3083,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3084,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1908]),
    [final] ).

cnf(i_0_3085,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_1909]),
    [final] ).

cnf(i_0_3086,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1910]),
    [final] ).

cnf(i_0_3087,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1756]),
    [final] ).

cnf(i_0_3088,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1757]),
    [final] ).

cnf(i_0_3089,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_1911]),
    [final] ).

cnf(i_0_3090,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
    inference(split_conjunct,[status(thm)],[i_0_1912]),
    [final] ).

cnf(i_0_3091,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
    inference(split_conjunct,[status(thm)],[i_0_1913]),
    [final] ).

cnf(i_0_3092,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[i_0_1914]),
    [final] ).

cnf(i_0_3093,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_1915]),
    [final] ).

cnf(i_0_3094,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_3095,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_1917]),
    [final] ).

cnf(i_0_3096,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_3097,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_1919]),
    [final] ).

cnf(i_0_3098,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1920,c_0_1480]),
    [final] ).

cnf(i_0_3099,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1921,c_0_1480]),
    [final] ).

cnf(i_0_3100,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1922,c_0_1480]),
    [final] ).

cnf(i_0_3101,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1923,c_0_1480]),
    [final] ).

cnf(i_0_3102,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,esk11_0)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1924]),
    [final] ).

cnf(i_0_3103,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_1925]),
    [final] ).

cnf(i_0_3104,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1926,c_0_1480]),
    [final] ).

cnf(i_0_3105,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1927,c_0_1480]),
    [final] ).

cnf(i_0_3106,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1928,c_0_1480]),
    [final] ).

cnf(i_0_3107,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1929,c_0_1480]),
    [final] ).

cnf(i_0_3108,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
    inference(rw,[status(thm)],[i_0_1930,c_0_1480]),
    [final] ).

cnf(i_0_3109,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_1931]),
    [final] ).

cnf(i_0_3110,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_1932]),
    [final] ).

cnf(i_0_3111,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1933,c_0_1480]),
    [final] ).

cnf(i_0_3112,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_1934,c_0_1479]),
    [final] ).

cnf(i_0_3113,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[i_0_1935,c_0_1480]),
    [final] ).

cnf(i_0_3114,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_1936]),
    [final] ).

cnf(i_0_3115,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_1937]),
    [final] ).

cnf(i_0_3116,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1938]),
    [final] ).

cnf(i_0_3117,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_1939]),
    [final] ).

cnf(i_0_3118,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1940,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3119,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_1941]),
    [final] ).

cnf(i_0_3120,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),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_1942]),
    [final] ).

cnf(i_0_3121,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),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_1943]),
    [final] ).

cnf(i_0_3122,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3123,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1945]),
    [final] ).

cnf(i_0_3124,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1946]),
    [final] ).

cnf(i_0_3125,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_1947]),
    [final] ).

cnf(i_0_3126,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_1948]),
    [final] ).

cnf(i_0_3127,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_1948]),
    [final] ).

cnf(i_0_3128,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_1949]),
    [final] ).

cnf(i_0_3129,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_1950]),
    [final] ).

cnf(i_0_3130,plain,
    ( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),c_RealDef_Oreal(tc_Nat_Onat,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1951]),
    [final] ).

cnf(i_0_3131,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(rw,[status(thm)],[i_0_1952,c_0_1480]),
    [final] ).

cnf(i_0_3132,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X5) = c_Groups_Otimes__class_Otimes(X1,X4,X3)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Rings_Oinverse__class_Odivide(X1,X4,X5)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1953]),
    [final] ).

cnf(i_0_3133,plain,
    ( c_Rings_Oinverse__class_Odivide(X1,X2,X5) = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Otimes__class_Otimes(X1,X4,X5)
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1953]),
    [final] ).

cnf(i_0_3134,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1954,c_0_1480]),c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3135,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1955,c_0_1480]),c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3136,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk26_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1956,c_0_1480]),
    [final] ).

cnf(i_0_3137,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_1957]),
    [final] ).

cnf(i_0_3138,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_1957]),
    [final] ).

cnf(i_0_3139,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_1958,c_0_1479]),
    [final] ).

cnf(i_0_3140,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_1959,c_0_1479]),
    [final] ).

cnf(i_0_3141,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_1960,c_0_1479]),
    [final] ).

cnf(i_0_3142,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_1961,c_0_1479]),
    [final] ).

cnf(i_0_3143,plain,
    ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1727]),
    [final] ).

cnf(i_0_3144,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_1962]),
    [final] ).

cnf(i_0_3145,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_1963]),
    [final] ).

cnf(i_0_3146,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_1964]),
    [final] ).

cnf(i_0_3147,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_1965]),
    [final] ).

cnf(i_0_3148,plain,
    ( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1),X3,X4),X5) = c_Groups_Ominus__class_Ominus(X1,hAPP(X3,X5),hAPP(X4,X5))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1966]),
    [final] ).

cnf(i_0_3149,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1)
    | ~ 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,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1967]),
    [final] ).

cnf(i_0_3150,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_1895]),
    [final] ).

cnf(i_0_3151,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_1896]),
    [final] ).

cnf(i_0_3152,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_1893]),
    [final] ).

cnf(i_0_3153,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_1894]),
    [final] ).

cnf(i_0_3154,plain,
    ( c_Groups_Ominus__class_Ominus(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,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1968]),
    [final] ).

cnf(i_0_3155,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_1957]),
    [final] ).

cnf(i_0_3156,plain,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_1969]),
    [final] ).

cnf(i_0_3157,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_1880]),
    [final] ).

cnf(i_0_3158,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_1881]),
    [final] ).

cnf(i_0_3159,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_1882]),
    [final] ).

cnf(i_0_3160,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_1878]),
    [final] ).

cnf(i_0_3161,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_1879]),
    [final] ).

cnf(i_0_3162,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_1970,c_0_1480]),
    [final] ).

cnf(i_0_3163,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(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(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_1971]),
    [final] ).

cnf(i_0_3164,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,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_1972]),
    [final] ).

cnf(i_0_3165,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
    | ~ 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_1973]),
    [final] ).

cnf(i_0_3166,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_1974,c_0_1480]),
    [final] ).

cnf(i_0_3167,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ 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_1975]),
    [final] ).

cnf(i_0_3168,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ 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_1976]),
    [final] ).

cnf(i_0_3169,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_1965]),
    [final] ).

cnf(i_0_3170,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_1964]),
    [final] ).

cnf(i_0_3171,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1899]),
    [final] ).

cnf(i_0_3172,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1900]),
    [final] ).

cnf(i_0_3173,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_1977]),
    [final] ).

cnf(i_0_3174,plain,
    c_Groups_Ominus__class_Ominus(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,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2))),
    inference(split_conjunct,[status(thm)],[i_0_1978]),
    [final] ).

cnf(i_0_3175,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_1979]),
    [final] ).

cnf(i_0_3176,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
    | ~ 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_1973]),
    [final] ).

cnf(i_0_3177,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),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_1972]),
    [final] ).

cnf(i_0_3178,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
    inference(rw,[status(thm)],[i_0_1980,c_0_1480]),
    [final] ).

cnf(i_0_3179,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Int_OPls,
    inference(rw,[status(thm)],[i_0_1981,c_0_1481]),
    [final] ).

cnf(i_0_3180,plain,
    c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[i_0_1982,c_0_1481]),
    [final] ).

cnf(i_0_3181,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[i_0_1983,c_0_1480]),
    [final] ).

cnf(i_0_3182,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[i_0_1984,c_0_1480]),
    [final] ).

cnf(i_0_3183,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_1985]),
    [final] ).

cnf(i_0_3184,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1986,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3185,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk44_3(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_1529]),
    [final] ).

cnf(i_0_3186,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_1987]),
    [final] ).

cnf(i_0_3187,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(rw,[status(thm)],[i_0_1988,c_0_1480]),
    [final] ).

cnf(i_0_3188,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1989]),
    [final] ).

cnf(i_0_3189,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ominus__class_Ominus(X1,X3,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1990]),
    [final] ).

cnf(i_0_3190,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_1991,c_0_1479]),
    [final] ).

cnf(i_0_3191,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_1819]),
    [final] ).

cnf(i_0_3192,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_1819]),
    [final] ).

cnf(i_0_3193,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1992]),
    [final] ).

cnf(i_0_3194,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_1925]),
    [final] ).

cnf(i_0_3195,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_1993]),
    [final] ).

cnf(i_0_3196,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1994,c_0_1480]),
    [final] ).

cnf(i_0_3197,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1995,c_0_1480]),
    [final] ).

cnf(i_0_3198,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1996,c_0_1480]),
    [final] ).

cnf(i_0_3199,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_1919]),
    [final] ).

cnf(i_0_3200,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_1932]),
    [final] ).

cnf(i_0_3201,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1997,c_0_1480]),
    [final] ).

cnf(i_0_3202,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1998,c_0_1480]),
    [final] ).

cnf(i_0_3203,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_1999,c_0_1480]),
    [final] ).

cnf(i_0_3204,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_2000,c_0_1480]),
    [final] ).

cnf(i_0_3205,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1931]),
    [final] ).

cnf(i_0_3206,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_2001,c_0_1480]),
    [final] ).

cnf(i_0_3207,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_2002,c_0_1480]),
    [final] ).

cnf(i_0_3208,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_2003]),
    [final] ).

cnf(i_0_3209,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_2004]),
    [final] ).

cnf(i_0_3210,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = 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_2005]),
    [final] ).

cnf(i_0_3211,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2006]),
    [final] ).

cnf(i_0_3212,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2007]),
    [final] ).

cnf(i_0_3213,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_1909]),
    [final] ).

cnf(i_0_3214,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1936]),
    [final] ).

cnf(i_0_3215,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1937]),
    [final] ).

cnf(i_0_3216,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1938]),
    [final] ).

cnf(i_0_3217,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2008]),
    [final] ).

cnf(i_0_3218,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2009]),
    [final] ).

cnf(i_0_3219,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2010]),
    [final] ).

cnf(i_0_3220,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_2011]),
    [final] ).

cnf(i_0_3221,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_2012]),
    [final] ).

cnf(i_0_3222,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_1519]),
    [final] ).

cnf(i_0_3223,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2013]),
    [final] ).

cnf(i_0_3224,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_2014]),
    [final] ).

cnf(i_0_3225,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_2015]),
    [final] ).

cnf(i_0_3226,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_2016]),
    [final] ).

cnf(i_0_3227,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_2017]),
    [final] ).

cnf(i_0_3228,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_2018]),
    [final] ).

cnf(i_0_3229,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_2019]),
    [final] ).

cnf(i_0_3230,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_2020]),
    [final] ).

cnf(i_0_3231,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_2021]),
    [final] ).

cnf(i_0_3232,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2022,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3233,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2023,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3234,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2024,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3235,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2025,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3236,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | ~ class_RealVector_Oreal__normed__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2026]),
    [final] ).

cnf(i_0_3237,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,X2))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2027]),
    [final] ).

cnf(i_0_3238,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X1,X2))
    | ~ class_RealVector_Oreal__normed__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2028]),
    [final] ).

cnf(i_0_3239,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_2029,c_0_1479]),
    [final] ).

cnf(i_0_3240,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_2030,c_0_1479]),
    [final] ).

cnf(i_0_3241,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_2031,c_0_1479]),
    [final] ).

cnf(i_0_3242,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_2032,c_0_1479]),
    [final] ).

cnf(i_0_3243,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_2033]),
    [final] ).

cnf(i_0_3244,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_2034]),
    [final] ).

cnf(i_0_3245,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_2035]),
    [final] ).

cnf(i_0_3246,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_2036]),
    [final] ).

cnf(i_0_3247,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_2037]),
    [final] ).

cnf(i_0_3248,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_2038]),
    [final] ).

cnf(i_0_3249,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_2039]),
    [final] ).

cnf(i_0_3250,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_2040]),
    [final] ).

cnf(i_0_3251,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_2041]),
    [final] ).

cnf(i_0_3252,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_2042]),
    [final] ).

cnf(i_0_3253,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2043]),
    [final] ).

cnf(i_0_3254,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = 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_2044]),
    [final] ).

cnf(i_0_3255,plain,
    ( c_Groups_Osgn__class_Osgn(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = 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_2045]),
    [final] ).

cnf(i_0_3256,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_2046]),
    [final] ).

cnf(i_0_3257,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_2047]),
    [final] ).

cnf(i_0_3258,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2048]),
    [final] ).

cnf(i_0_3259,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(split_conjunct,[status(thm)],[i_0_2049]),
    [final] ).

cnf(i_0_3260,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2050]),
    [final] ).

cnf(i_0_3261,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_2051]),
    [final] ).

cnf(i_0_3262,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2052]),
    [final] ).

cnf(i_0_3263,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2053]),
    [final] ).

cnf(i_0_3264,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_2054]),
    [final] ).

cnf(i_0_3265,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Ouminus__class_Ouminus(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))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2055]),
    [final] ).

cnf(i_0_3266,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_2056]),
    [final] ).

cnf(i_0_3267,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_2057]),
    [final] ).

cnf(i_0_3268,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_2058]),
    [final] ).

cnf(i_0_3269,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3270,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2060]),
    [final] ).

cnf(i_0_3271,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ 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),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1335]),
    [final] ).

cnf(i_0_3272,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3273,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2061]),
    [final] ).

cnf(i_0_3274,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_1835]),
    [final] ).

cnf(i_0_3275,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) = X2
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2062]),
    [final] ).

cnf(i_0_3276,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2062]),
    [final] ).

cnf(i_0_3277,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_2063]),
    [final] ).

cnf(i_0_3278,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_2064]),
    [final] ).

cnf(i_0_3279,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_2065]),
    [final] ).

cnf(i_0_3280,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_2066]),
    [final] ).

cnf(i_0_3281,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,X4),hAPP(X2,X3))
    | ~ c_SEQ_Odecseq(X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_3282,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != X2 ),
    inference(rw,[status(thm)],[i_0_2067,c_0_1480]),
    [final] ).

cnf(i_0_3283,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk10_0),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
    inference(split_conjunct,[status(thm)],[i_0_1635]),
    [final] ).

cnf(i_0_3284,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
    inference(rw,[status(thm)],[i_0_2068,c_0_1480]),
    [final] ).

cnf(i_0_3285,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(rw,[status(thm)],[i_0_2069,c_0_1480]),
    [final] ).

cnf(i_0_3286,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3))
    | ~ class_Rings_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2070]),
    [final] ).

cnf(i_0_3287,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_1964]),
    [final] ).

cnf(i_0_3288,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3289,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_2071]),
    [final] ).

cnf(i_0_3290,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_2071]),
    [final] ).

cnf(i_0_3291,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2072]),
    [final] ).

cnf(i_0_3292,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1946]),
    [final] ).

cnf(i_0_3293,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_2073]),
    [final] ).

cnf(i_0_3294,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_2073]),
    [final] ).

cnf(i_0_3295,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_2074]),
    [final] ).

cnf(i_0_3296,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_2074]),
    [final] ).

cnf(i_0_3297,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_2075]),
    [final] ).

cnf(i_0_3298,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_2075]),
    [final] ).

cnf(i_0_3299,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_2076]),
    [final] ).

cnf(i_0_3300,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2077]),
    [final] ).

cnf(i_0_3301,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_2078,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3302,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_2079]),
    [final] ).

cnf(i_0_3303,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_2080]),
    [final] ).

cnf(i_0_3304,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2081,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3305,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2082,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3306,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2083,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3307,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2084,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3308,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
    inference(split_conjunct,[status(thm)],[i_0_2085]),
    [final] ).

cnf(i_0_3309,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2086]),
    [final] ).

cnf(i_0_3310,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_2087]),
    [final] ).

cnf(i_0_3311,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_2088]),
    [final] ).

cnf(i_0_3312,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_2089]),
    [final] ).

cnf(i_0_3313,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_1965]),
    [final] ).

cnf(i_0_3314,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2090]),
    [final] ).

cnf(i_0_3315,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_2091]),
    [final] ).

cnf(i_0_3316,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2092]),
    [final] ).

cnf(i_0_3317,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2093]),
    [final] ).

cnf(i_0_3318,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2094]),
    [final] ).

cnf(i_0_3319,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_2095]),
    [final] ).

cnf(i_0_3320,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2096]),
    [final] ).

cnf(i_0_3321,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2097]),
    [final] ).

cnf(i_0_3322,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = 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_2098]),
    [final] ).

cnf(i_0_3323,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_2099]),
    [final] ).

cnf(i_0_3324,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = 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_2100]),
    [final] ).

cnf(i_0_3325,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_2101]),
    [final] ).

cnf(i_0_3326,plain,
    ( c_SEQ_Osubseq(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,esk16_1(X1)),hAPP(X1,esk17_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3327,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_2033]),
    [final] ).

cnf(i_0_3328,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_2034]),
    [final] ).

cnf(i_0_3329,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_2103]),
    [final] ).

cnf(i_0_3330,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_2104]),
    [final] ).

cnf(i_0_3331,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_2105]),
    [final] ).

cnf(i_0_3332,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_2106]),
    [final] ).

cnf(i_0_3333,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_2107]),
    [final] ).

cnf(i_0_3334,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_2108]),
    [final] ).

cnf(i_0_3335,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Osgn__class_Osgn(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2109]),
    [final] ).

cnf(i_0_3336,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_2110]),
    [final] ).

cnf(i_0_3337,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_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_2111]),
    [final] ).

cnf(i_0_3338,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_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_2112]),
    [final] ).

cnf(i_0_3339,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3340,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_2113]),
    [final] ).

cnf(i_0_3341,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_2114]),
    [final] ).

cnf(i_0_3342,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_2115]),
    [final] ).

cnf(i_0_3343,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_2116]),
    [final] ).

cnf(i_0_3344,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_2117]),
    [final] ).

cnf(i_0_3345,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk9_1(X1)),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1666]),
    [final] ).

cnf(i_0_3346,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk8_1(X1)),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1545]),
    [final] ).

cnf(i_0_3347,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(rw,[status(thm)],[i_0_2118,c_0_1480]),
    [final] ).

cnf(i_0_3348,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3349,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3350,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_2056]),
    [final] ).

cnf(i_0_3351,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_2057]),
    [final] ).

cnf(i_0_3352,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_2119]),
    [final] ).

cnf(i_0_3353,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_2120]),
    [final] ).

cnf(i_0_3354,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_2058]),
    [final] ).

cnf(i_0_3355,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_2121]),
    [final] ).

cnf(i_0_3356,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1))),
    inference(split_conjunct,[status(thm)],[i_0_2122]),
    [final] ).

cnf(i_0_3357,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3358,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
    | ~ c_SEQ_Osubseq(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3359,plain,
    ( X2 = X3
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
    | c_Groups_Otimes__class_Otimes(X1,X2,X2) != c_Groups_Otimes__class_Otimes(X1,X3,X3)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2123]),
    [final] ).

cnf(i_0_3360,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_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1967]),
    [final] ).

cnf(i_0_3361,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_2124]),
    [final] ).

cnf(i_0_3362,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_2125]),
    [final] ).

cnf(i_0_3363,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_2126]),
    [final] ).

cnf(i_0_3364,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_2127]),
    [final] ).

cnf(i_0_3365,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_2128]),
    [final] ).

cnf(i_0_3366,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_1909]),
    [final] ).

cnf(i_0_3367,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_2129]),
    [final] ).

cnf(i_0_3368,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk20_1(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk19_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk18_0) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_3369,plain,
    ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk3_1(X1))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk2_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_3370,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_2103]),
    [final] ).

cnf(i_0_3371,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_2104]),
    [final] ).

cnf(i_0_3372,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_2130]),
    [final] ).

cnf(i_0_3373,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_2108]),
    [final] ).

cnf(i_0_3374,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_2109]),
    [final] ).

cnf(i_0_3375,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_2110]),
    [final] ).

cnf(i_0_3376,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_2131]),
    [final] ).

cnf(i_0_3377,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_2105]),
    [final] ).

cnf(i_0_3378,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_2106]),
    [final] ).

cnf(i_0_3379,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_2107]),
    [final] ).

cnf(i_0_3380,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_2111]),
    [final] ).

cnf(i_0_3381,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_2112]),
    [final] ).

cnf(i_0_3382,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1944]),
    [final] ).

cnf(i_0_3383,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_1946]),
    [final] ).

cnf(i_0_3384,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2132]),
    [final] ).

cnf(i_0_3385,plain,
    ( X3 = X4
    | X1 != X2
    | c_Groups_Ominus__class_Ominus(X5,X1,X2) != c_Groups_Ominus__class_Ominus(X5,X3,X4)
    | ~ class_Groups_Oab__group__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_3386,plain,
    ( X3 = X4
    | X1 != X2
    | c_Groups_Ominus__class_Ominus(X5,X3,X4) != c_Groups_Ominus__class_Ominus(X5,X1,X2)
    | ~ class_Groups_Oab__group__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_2133]),
    [final] ).

cnf(i_0_3387,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_2125]),
    [final] ).

cnf(i_0_3388,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_2126]),
    [final] ).

cnf(i_0_3389,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_2127]),
    [final] ).

cnf(i_0_3390,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_2128]),
    [final] ).

cnf(i_0_3391,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(rw,[status(thm)],[i_0_2134,c_0_1480]),
    [final] ).

cnf(i_0_3392,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[i_0_2135,c_0_1480]),
    [final] ).

cnf(i_0_3393,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_2136]),
    [final] ).

cnf(i_0_3394,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_2089]),
    [final] ).

cnf(i_0_3395,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2090]),
    [final] ).

cnf(i_0_3396,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_2091]),
    [final] ).

cnf(i_0_3397,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_1977]),
    [final] ).

cnf(i_0_3398,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2092]),
    [final] ).

cnf(i_0_3399,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_2116]),
    [final] ).

cnf(i_0_3400,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_2117]),
    [final] ).

cnf(i_0_3401,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_2114]),
    [final] ).

cnf(i_0_3402,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_2115]),
    [final] ).

cnf(i_0_3403,plain,
    ( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,X3,X2)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2137]),
    [final] ).

cnf(i_0_3404,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_2138]),
    [final] ).

cnf(i_0_3405,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_2139]),
    [final] ).

cnf(i_0_3406,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_2140]),
    [final] ).

cnf(i_0_3407,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_2141]),
    [final] ).

cnf(i_0_3408,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2142]),
    [final] ).

cnf(i_0_3409,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_2143]),
    [final] ).

cnf(i_0_3410,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_2144]),
    [final] ).

cnf(i_0_3411,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_2145]),
    [final] ).

cnf(i_0_3412,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_2146]),
    [final] ).

cnf(i_0_3413,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_2147]),
    [final] ).

cnf(i_0_3414,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_2148]),
    [final] ).

cnf(i_0_3415,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_1977]),
    [final] ).

cnf(i_0_3416,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_2149]),
    [final] ).

cnf(i_0_3417,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_2150]),
    [final] ).

cnf(i_0_3418,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_2151]),
    [final] ).

cnf(i_0_3419,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_2152]),
    [final] ).

cnf(i_0_3420,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_2153]),
    [final] ).

cnf(i_0_3421,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_2154]),
    [final] ).

cnf(i_0_3422,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_2155]),
    [final] ).

cnf(i_0_3423,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_2156]),
    [final] ).

cnf(i_0_3424,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_2157]),
    [final] ).

cnf(i_0_3425,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_2113]),
    [final] ).

cnf(i_0_3426,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_2158]),
    [final] ).

cnf(i_0_3427,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2159]),
    [final] ).

cnf(i_0_3428,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2160,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3429,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2161,c_0_1480]),c_0_1480]),
    [final] ).

cnf(i_0_3430,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
    | c_Polynomial_Oorder(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2162]),
    [final] ).

cnf(i_0_3431,plain,
    ( X1 = X2
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_2163]),
    [final] ).

cnf(i_0_3432,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(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_2164]),
    [final] ).

cnf(i_0_3433,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,esk40_1(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_1760]),
    [final] ).

cnf(i_0_3434,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_2165]),
    [final] ).

cnf(i_0_3435,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_2166,c_0_1480]),
    [final] ).

cnf(i_0_3436,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2167]),
    [final] ).

cnf(i_0_3437,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_3438,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_2169]),
    [final] ).

cnf(i_0_3439,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1967]),
    [final] ).

cnf(i_0_3440,plain,
    ( X1 = X3
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2170]),
    [final] ).

cnf(i_0_3441,plain,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2171]),
    [final] ).

cnf(i_0_3442,plain,
    ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_3443,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_2173]),
    [final] ).

cnf(i_0_3444,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_2174]),
    [final] ).

cnf(i_0_3445,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_2175]),
    [final] ).

cnf(i_0_3446,plain,
    c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1,
    inference(rw,[status(thm)],[i_0_2176,c_0_1480]),
    [final] ).

cnf(i_0_3447,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2177]),
    [final] ).

cnf(i_0_3448,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2178]),
    [final] ).

cnf(i_0_3449,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(rw,[status(thm)],[i_0_2179,c_0_1480]),
    [final] ).

cnf(i_0_3450,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_2180,c_0_1479]),c_0_1479]),
    [final] ).

cnf(i_0_3451,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_2181]),
    [final] ).

cnf(i_0_3452,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_2182]),
    [final] ).

cnf(i_0_3453,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk20_1(X1)),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk18_0) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_3454,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk3_1(X1)),v_r)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_3455,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Otimes__class_Otimes(X1,X2,X3)
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2183]),
    [final] ).

cnf(i_0_3456,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_2184]),
    [final] ).

cnf(i_0_3457,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = 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_2185]),
    [final] ).

cnf(i_0_3458,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2142]),
    [final] ).

cnf(i_0_3459,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(rw,[status(thm)],[i_0_2186,c_0_1480]),
    [final] ).

cnf(i_0_3460,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_1919]),
    [final] ).

cnf(i_0_3461,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != X2 ),
    inference(rw,[status(thm)],[i_0_2187,c_0_1480]),
    [final] ).

cnf(i_0_3462,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_2188,c_0_1480]),
    [final] ).

cnf(i_0_3463,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk41_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2189]),
    [final] ).

cnf(i_0_3464,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk6_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2190]),
    [final] ).

cnf(i_0_3465,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(rw,[status(thm)],[i_0_2191,c_0_1480]),
    [final] ).

cnf(i_0_3466,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_2165]),
    [final] ).

cnf(i_0_3467,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_2192]),
    [final] ).

cnf(i_0_3468,plain,
    ( c_Rings_Oinverse__class_Odivide(X2,X3,X4) = X1
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | X3 != c_Groups_Otimes__class_Otimes(X2,X1,X4)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_3469,plain,
    ( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X1,X3) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3470,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    inference(split_conjunct,[status(thm)],[i_0_2195]),
    [final] ).

cnf(i_0_3471,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2196]),
    [final] ).

cnf(i_0_3472,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2197]),
    [final] ).

cnf(i_0_3473,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
    inference(split_conjunct,[status(thm)],[i_0_2198]),
    [final] ).

cnf(i_0_3474,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_2199]),
    [final] ).

cnf(i_0_3475,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_2200]),
    [final] ).

cnf(i_0_3476,plain,
    ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)
    | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_3477,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) = X4
    | X3 != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3478,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Rings_Oinverse__class_Odivide(X2,X3,X1) = X4
    | X3 != c_Groups_Otimes__class_Otimes(X2,X4,X1)
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_3479,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,X3,X2) = X4
    | ~ class_Rings_Odivision__ring(X1)
    | X3 != c_Groups_Otimes__class_Otimes(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2201]),
    [final] ).

cnf(i_0_3480,plain,
    ( c_Rings_Oinverse__class_Odivide(X2,X1,X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Otimes__class_Otimes(X2,X3,X4)
    | ~ class_Rings_Odivision__ring(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2202]),
    [final] ).

cnf(i_0_3481,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Otimes__class_Otimes(X2,X4,X1)
    | c_Rings_Oinverse__class_Odivide(X2,X3,X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2193]),
    [final] ).

cnf(i_0_3482,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != X4
    | ~ class_Fields_Ofield__inverse__zero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2194]),
    [final] ).

cnf(i_0_3483,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,X4,X2)
    | ~ class_Rings_Odivision__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_2203]),
    [final] ).

cnf(i_0_3484,plain,
    ( X2 = c_Groups_Otimes__class_Otimes(X1,X4,X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,X2,X3) != X4
    | ~ class_Rings_Odivision__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2202]),
    [final] ).

cnf(i_0_3485,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | c_Groups_Oabs__class_Oabs(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = 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_2055]),
    [final] ).

cnf(i_0_3486,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_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2204]),
    [final] ).

cnf(i_0_3487,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_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_2205]),
    [final] ).

cnf(i_0_3488,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2206]),
    [final] ).

cnf(i_0_3489,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk25_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(rw,[status(thm)],[i_0_2207,c_0_1480]),
    [final] ).

cnf(i_0_3490,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_2208]),
    [final] ).

cnf(i_0_3491,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_2209]),
    [final] ).

cnf(i_0_3492,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(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_2204]),
    [final] ).

cnf(i_0_3493,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ 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_2205]),
    [final] ).

cnf(i_0_3494,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_2210]),
    [final] ).

cnf(i_0_3495,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_2211]),
    [final] ).

cnf(i_0_3496,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_2212]),
    [final] ).

cnf(i_0_3497,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_2213]),
    [final] ).

cnf(i_0_3498,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_2214]),
    [final] ).

cnf(i_0_3499,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_2215]),
    [final] ).

cnf(i_0_3500,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_2136]),
    [final] ).

cnf(i_0_3501,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_2216]),
    [final] ).

cnf(i_0_3502,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_2217]),
    [final] ).

cnf(i_0_3503,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2218]),
    [final] ).

cnf(i_0_3504,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2219]),
    [final] ).

cnf(i_0_3505,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2220]),
    [final] ).

cnf(i_0_3506,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_2214]),
    [final] ).

cnf(i_0_3507,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_2215]),
    [final] ).

cnf(i_0_3508,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_2221]),
    [final] ).

cnf(i_0_3509,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_2113]),
    [final] ).

cnf(i_0_3510,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[i_0_2222,c_0_1480]),
    [final] ).

cnf(i_0_3511,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_2223]),
    [final] ).

cnf(i_0_3512,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_2224]),
    [final] ).

cnf(i_0_3513,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_2224]),
    [final] ).

cnf(i_0_3514,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_3515,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2226]),
    [final] ).

cnf(i_0_3516,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2227]),
    [final] ).

cnf(i_0_3517,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Oplus__class_Oplus(X1,X2,X3)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2228]),
    [final] ).

cnf(i_0_3518,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2229]),
    [final] ).

cnf(i_0_3519,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2230]),
    [final] ).

cnf(i_0_3520,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2231]),
    [final] ).

cnf(i_0_3521,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2232]),
    [final] ).

cnf(i_0_3522,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk19_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk18_0) ),
    inference(split_conjunct,[status(thm)],[i_0_1773]),
    [final] ).

cnf(i_0_3523,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,esk2_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,v_s____) ),
    inference(split_conjunct,[status(thm)],[i_0_1774]),
    [final] ).

cnf(i_0_3524,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_2233]),
    [final] ).

cnf(i_0_3525,plain,
    ( c_Groups_Otimes__class_Otimes(X2,X1,X1) = 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_2123]),
    [final] ).

cnf(i_0_3526,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_2234]),
    [final] ).

cnf(i_0_3527,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_2235]),
    [final] ).

cnf(i_0_3528,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_2236]),
    [final] ).

cnf(i_0_3529,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_2237]),
    [final] ).

cnf(i_0_3530,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_2238]),
    [final] ).

cnf(i_0_3531,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_2239]),
    [final] ).

cnf(i_0_3532,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2240]),
    [final] ).

cnf(i_0_3533,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2241]),
    [final] ).

cnf(i_0_3534,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2233]),
    [final] ).

cnf(i_0_3535,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_2242]),
    [final] ).

cnf(i_0_3536,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_2189]),
    [final] ).

cnf(i_0_3537,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_2190]),
    [final] ).

cnf(i_0_3538,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_2243]),
    [final] ).

cnf(i_0_3539,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_2244]),
    [final] ).

cnf(i_0_3540,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_2234]),
    [final] ).

cnf(i_0_3541,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_2245]),
    [final] ).

cnf(i_0_3542,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_2246]),
    [final] ).

cnf(i_0_3543,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_2247]),
    [final] ).

cnf(i_0_3544,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_2236]),
    [final] ).

cnf(i_0_3545,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_2237]),
    [final] ).

cnf(i_0_3546,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_2238]),
    [final] ).

cnf(i_0_3547,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_2239]),
    [final] ).

cnf(i_0_3548,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2248]),
    [final] ).

cnf(i_0_3549,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_2249]),
    [final] ).

cnf(i_0_3550,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_2250]),
    [final] ).

cnf(i_0_3551,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_2251]),
    [final] ).

cnf(i_0_3552,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(rw,[status(thm)],[i_0_2252,c_0_1480]),
    [final] ).

cnf(i_0_3553,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_2253]),
    [final] ).

cnf(i_0_3554,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2254]),
    [final] ).

cnf(i_0_3555,plain,
    c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2255]),
    [final] ).

cnf(i_0_3556,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2256]),
    [final] ).

cnf(i_0_3557,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
    inference(split_conjunct,[status(thm)],[i_0_2257]),
    [final] ).

cnf(i_0_3558,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_2258]),
    [final] ).

cnf(i_0_3559,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2259]),
    [final] ).

cnf(i_0_3560,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_2260]),
    [final] ).

cnf(i_0_3561,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk42_2(X1,X2),esk43_2(X1,X2))
    | c_SEQ_Odecseq(X2,X1)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_1828]),
    [final] ).

cnf(i_0_3562,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_2261]),
    [final] ).

cnf(i_0_3563,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_2262]),
    [final] ).

cnf(i_0_3564,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[i_0_2263]),
    [final] ).

cnf(i_0_3565,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_2244]),
    [final] ).

cnf(i_0_3566,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_2264]),
    [final] ).

cnf(i_0_3567,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_2265]),
    [final] ).

cnf(i_0_3568,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_2216]),
    [final] ).

cnf(i_0_3569,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk39_0,X1)),v_r),
    inference(split_conjunct,[status(thm)],[i_0_1286]),
    [final] ).

cnf(i_0_3570,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(esk37_0,X1)),v_r),
    inference(split_conjunct,[status(thm)],[i_0_1287]),
    [final] ).

cnf(i_0_3571,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_2266]),
    [final] ).

cnf(i_0_3572,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_2267]),
    [final] ).

cnf(i_0_3573,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_2150]),
    [final] ).

cnf(i_0_3574,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_2268]),
    [final] ).

cnf(i_0_3575,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_2269]),
    [final] ).

cnf(i_0_3576,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_2270]),
    [final] ).

cnf(i_0_3577,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_2271]),
    [final] ).

cnf(i_0_3578,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2272]),
    [final] ).

cnf(i_0_3579,plain,
    ( c_Groups_Oabs__class_Oabs(X1,X2) = X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2273]),
    [final] ).

cnf(i_0_3580,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_2274]),
    [final] ).

cnf(i_0_3581,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_2275]),
    [final] ).

cnf(i_0_3582,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_2153]),
    [final] ).

cnf(i_0_3583,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_2276]),
    [final] ).

cnf(i_0_3584,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_2152]),
    [final] ).

cnf(i_0_3585,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_2277]),
    [final] ).

cnf(i_0_3586,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_2278]),
    [final] ).

cnf(i_0_3587,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_2279]),
    [final] ).

cnf(i_0_3588,plain,
    ( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
    | ~ class_Rings_Odivision__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2280]),
    [final] ).

cnf(i_0_3589,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_2281]),
    [final] ).

cnf(i_0_3590,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_2282]),
    [final] ).

cnf(i_0_3591,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_2283]),
    [final] ).

cnf(i_0_3592,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2284]),
    [final] ).

cnf(i_0_3593,plain,
    ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_3594,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2286]),
    [final] ).

cnf(i_0_3595,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[i_0_2287]),
    [final] ).

cnf(i_0_3596,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_2288]),
    [final] ).

cnf(i_0_3597,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_2289]),
    [final] ).

cnf(i_0_3598,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(rw,[status(thm)],[i_0_2290,c_0_1480]),
    [final] ).

cnf(i_0_3599,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2291]),
    [final] ).

cnf(i_0_3600,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2292]),
    [final] ).

cnf(i_0_3601,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_3602,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_2294]),
    [final] ).

cnf(i_0_3603,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_2295]),
    [final] ).

cnf(i_0_3604,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_2296]),
    [final] ).

cnf(i_0_3605,plain,
    ( c_Polynomial_Oorder(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2162]),
    [final] ).

cnf(i_0_3606,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_2193]),
    [final] ).

cnf(i_0_3607,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_3608,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_2261]),
    [final] ).

cnf(i_0_3609,plain,
    ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
    | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X1),X2) = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2172]),
    [final] ).

cnf(i_0_3610,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_2297]),
    [final] ).

cnf(i_0_3611,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_2298]),
    [final] ).

cnf(i_0_3612,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_2299]),
    [final] ).

cnf(i_0_3613,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_2300]),
    [final] ).

cnf(i_0_3614,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_2301]),
    [final] ).

cnf(i_0_3615,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_2302]),
    [final] ).

cnf(i_0_3616,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_2303]),
    [final] ).

cnf(i_0_3617,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2304]),
    [final] ).

cnf(i_0_3618,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_2305]),
    [final] ).

cnf(i_0_3619,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_2306]),
    [final] ).

cnf(i_0_3620,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_2307]),
    [final] ).

cnf(i_0_3621,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_2308]),
    [final] ).

cnf(i_0_3622,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_2309]),
    [final] ).

cnf(i_0_3623,plain,
    ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2220]),
    [final] ).

cnf(i_0_3624,plain,
    ( X2 = X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2310]),
    [final] ).

cnf(i_0_3625,plain,
    ( X2 = X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_3626,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_2312]),
    [final] ).

cnf(i_0_3627,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_2313]),
    [final] ).

cnf(i_0_3628,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1))
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2206]),
    [final] ).

cnf(i_0_3629,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2314]),
    [final] ).

cnf(i_0_3630,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2232]),
    [final] ).

cnf(i_0_3631,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | 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_2315]),
    [final] ).

cnf(i_0_3632,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | 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_2316]),
    [final] ).

cnf(i_0_3633,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | 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_2317]),
    [final] ).

cnf(i_0_3634,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2215]),
    [final] ).

cnf(i_0_3635,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2150]),
    [final] ).

cnf(i_0_3636,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2318]),
    [final] ).

cnf(i_0_3637,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2319]),
    [final] ).

cnf(i_0_3638,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2320]),
    [final] ).

cnf(i_0_3639,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X2 != X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [final] ).

cnf(i_0_3640,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X3 != X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2266]),
    [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_Oone__class_Oone(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2265]),
    [final] ).

cnf(i_0_3642,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_2321]),
    [final] ).

cnf(i_0_3643,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_2322]),
    [final] ).

cnf(i_0_3644,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_2323]),
    [final] ).

cnf(i_0_3645,plain,
    ( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ 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_2324]),
    [final] ).

cnf(i_0_3646,plain,
    ( c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ 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_2325]),
    [final] ).

cnf(i_0_3647,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2225]),
    [final] ).

cnf(i_0_3648,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_2326]),
    [final] ).

cnf(i_0_3649,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2327]),
    [final] ).

cnf(i_0_3650,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2328]),
    [final] ).

cnf(i_0_3651,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_2329]),
    [final] ).

cnf(i_0_3652,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Oabs__class_Oabs(X1,X2))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2330]),
    [final] ).

cnf(i_0_3653,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_2331]),
    [final] ).

cnf(i_0_3654,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rw,[status(thm)],[i_0_2332,c_0_1480]),
    [final] ).

cnf(i_0_3655,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rw,[status(thm)],[i_0_2333,c_0_1480]),
    [final] ).

cnf(i_0_3656,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(rw,[status(thm)],[i_0_2334,c_0_1480]),
    [final] ).

cnf(i_0_3657,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_2335,c_0_1480]),
    [final] ).

cnf(i_0_3658,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_2336,c_0_1480]),
    [final] ).

cnf(i_0_3659,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_2337,c_0_1480]),
    [final] ).

cnf(i_0_3660,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_2338]),
    [final] ).

cnf(i_0_3661,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_2339]),
    [final] ).

cnf(i_0_3662,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_2340]),
    [final] ).

cnf(i_0_3663,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_2341]),
    [final] ).

cnf(i_0_3664,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_2341]),
    [final] ).

cnf(i_0_3665,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2))
    | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2342]),
    [final] ).

cnf(i_0_3666,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_2343]),
    [final] ).

cnf(i_0_3667,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
    inference(rw,[status(thm)],[i_0_2344,c_0_1480]),
    [final] ).

cnf(i_0_3668,plain,
    X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_2345,c_0_1480]),
    [final] ).

cnf(i_0_3669,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2346]),
    [final] ).

cnf(i_0_3670,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_2282]),
    [final] ).

cnf(i_0_3671,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_2283]),
    [final] ).

cnf(i_0_3672,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2347]),
    [final] ).

cnf(i_0_3673,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_2348]),
    [final] ).

cnf(i_0_3674,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_2349]),
    [final] ).

cnf(i_0_3675,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_2350]),
    [final] ).

cnf(i_0_3676,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_2351]),
    [final] ).

cnf(i_0_3677,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_2297]),
    [final] ).

cnf(i_0_3678,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_2298]),
    [final] ).

cnf(i_0_3679,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_2299]),
    [final] ).

cnf(i_0_3680,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_2352]),
    [final] ).

cnf(i_0_3681,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
    inference(split_conjunct,[status(thm)],[i_0_2353]),
    [final] ).

cnf(i_0_3682,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2354]),
    [final] ).

cnf(i_0_3683,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2355]),
    [final] ).

cnf(i_0_3684,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2356]),
    [final] ).

cnf(i_0_3685,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2234]),
    [final] ).

cnf(i_0_3686,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2295]),
    [final] ).

cnf(i_0_3687,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2295]),
    [final] ).

cnf(i_0_3688,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2357]),
    [final] ).

cnf(i_0_3689,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2358]),
    [final] ).

cnf(i_0_3690,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2237]),
    [final] ).

cnf(i_0_3691,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2239]),
    [final] ).

cnf(i_0_3692,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_2359]),
    [final] ).

cnf(i_0_3693,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_2360]),
    [final] ).

cnf(i_0_3694,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2361]),
    [final] ).

cnf(i_0_3695,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2362]),
    [final] ).

cnf(i_0_3696,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2363]),
    [final] ).

cnf(i_0_3697,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk38_1(X1)),v_r),
    inference(split_conjunct,[status(thm)],[i_0_1288]),
    [final] ).

cnf(i_0_3698,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk36_1(X1)),v_r),
    inference(split_conjunct,[status(thm)],[i_0_1289]),
    [final] ).

cnf(i_0_3699,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X1)),v_r),
    inference(split_conjunct,[status(thm)],[i_0_2364]),
    [final] ).

cnf(i_0_3700,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,hAPP(X1,X2))
    | ~ c_SEQ_Osubseq(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2365]),
    [final] ).

cnf(i_0_3701,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_2366]),
    [final] ).

cnf(i_0_3702,plain,
    c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),esk22_0)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,esk21_0),
    inference(split_conjunct,[status(thm)],[i_0_2367]),
    [final] ).

cnf(i_0_3703,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_2368]),
    [final] ).

cnf(i_0_3704,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_2369]),
    [final] ).

cnf(i_0_3705,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) ),
    inference(rw,[status(thm)],[i_0_2370,c_0_1479]),
    [final] ).

cnf(i_0_3706,plain,
    ( X1 = c_Int_OPls
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_2371,c_0_1479]),
    [final] ).

cnf(i_0_3707,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2258]),
    [final] ).

cnf(i_0_3708,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_2259]),
    [final] ).

cnf(i_0_3709,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_2372]),
    [final] ).

cnf(i_0_3710,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_2373]),
    [final] ).

cnf(i_0_3711,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2374]),
    [final] ).

cnf(i_0_3712,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2375]),
    [final] ).

cnf(i_0_3713,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_2249]),
    [final] ).

cnf(i_0_3714,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | 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_2376]),
    [final] ).

cnf(i_0_3715,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_2262]),
    [final] ).

cnf(i_0_3716,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ouminus__class_Ouminus(X1,X2)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2377]),
    [final] ).

cnf(i_0_3717,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_2378]),
    [final] ).

cnf(i_0_3718,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_2379]),
    [final] ).

cnf(i_0_3719,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r),
    inference(split_conjunct,[status(thm)],[fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096]),
    [final] ).

cnf(i_0_3720,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_2193]),
    [final] ).

cnf(i_0_3721,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_3722,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),
    inference(split_conjunct,[status(thm)],[i_0_2380]),
    [final] ).

cnf(i_0_3723,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[i_0_2381]),
    [final] ).

cnf(i_0_3724,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_2382]),
    [final] ).

cnf(i_0_3725,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_2312]),
    [final] ).

cnf(i_0_3726,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_2321]),
    [final] ).

cnf(i_0_3727,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_2322]),
    [final] ).

cnf(i_0_3728,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_2300]),
    [final] ).

cnf(i_0_3729,plain,
    ( c_Groups_Otimes__class_Otimes(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_3730,plain,
    ( c_Groups_Otimes__class_Otimes(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2293]),
    [final] ).

cnf(i_0_3731,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_2383]),
    [final] ).

cnf(i_0_3732,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_2307]),
    [final] ).

cnf(i_0_3733,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_2308]),
    [final] ).

cnf(i_0_3734,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_2384]),
    [final] ).

cnf(i_0_3735,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_2385]),
    [final] ).

cnf(i_0_3736,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2386]),
    [final] ).

cnf(i_0_3737,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2387]),
    [final] ).

cnf(i_0_3738,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2388]),
    [final] ).

cnf(i_0_3739,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2389]),
    [final] ).

cnf(i_0_3740,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2390]),
    [final] ).

cnf(i_0_3741,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_2391]),
    [final] ).

cnf(i_0_3742,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_2392]),
    [final] ).

cnf(i_0_3743,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2393]),
    [final] ).

cnf(i_0_3744,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2394]),
    [final] ).

cnf(i_0_3745,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2395]),
    [final] ).

cnf(i_0_3746,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2396]),
    [final] ).

cnf(i_0_3747,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2397]),
    [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_2398]),
    [final] ).

cnf(i_0_3749,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,esk22_0),v_r),
    inference(split_conjunct,[status(thm)],[i_0_2367]),
    [final] ).

cnf(i_0_3750,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
    inference(split_conjunct,[status(thm)],[fact_wr]),
    [final] ).

cnf(i_0_3751,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_2313]),
    [final] ).

cnf(i_0_3752,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_2383]),
    [final] ).

cnf(i_0_3753,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2399]),
    [final] ).

cnf(i_0_3754,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_2400]),
    [final] ).

cnf(i_0_3755,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_2401]),
    [final] ).

cnf(i_0_3756,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_1(X1),esk17_1(X1))
    | c_SEQ_Osubseq(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2102]),
    [final] ).

cnf(i_0_3757,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2285]),
    [final] ).

cnf(i_0_3758,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2286]),
    [final] ).

cnf(i_0_3759,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = X1 ),
    inference(split_conjunct,[status(thm)],[i_0_2287]),
    [final] ).

cnf(i_0_3760,plain,
    ( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
    | X1 != X2
    | ~ class_Groups_Ogroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2310]),
    [final] ).

cnf(i_0_3761,plain,
    ( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
    | X1 != X2
    | ~ class_Groups_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2311]),
    [final] ).

cnf(i_0_3762,plain,
    ( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2162]),
    [final] ).

cnf(i_0_3763,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2402]),
    [final] ).

cnf(i_0_3764,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2403]),
    [final] ).

cnf(i_0_3765,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2404]),
    [final] ).

cnf(i_0_3766,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_2405]),
    [final] ).

cnf(i_0_3767,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_2406]),
    [final] ).

cnf(i_0_3768,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_2407]),
    [final] ).

cnf(i_0_3769,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2408]),
    [final] ).

cnf(i_0_3770,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2409]),
    [final] ).

cnf(i_0_3771,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2410]),
    [final] ).

cnf(i_0_3772,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2411]),
    [final] ).

cnf(i_0_3773,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_2412]),
    [final] ).

cnf(i_0_3774,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2413]),
    [final] ).

cnf(i_0_3775,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_2414]),
    [final] ).

cnf(i_0_3776,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_2415]),
    [final] ).

cnf(i_0_3777,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_2416]),
    [final] ).

cnf(i_0_3778,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_2341]),
    [final] ).

cnf(i_0_3779,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2417]),
    [final] ).

cnf(i_0_3780,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | X2 != X3
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2141]),
    [final] ).

cnf(i_0_3781,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | X3 != X2
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2141]),
    [final] ).

cnf(i_0_3782,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_2418]),
    [final] ).

cnf(i_0_3783,plain,
    ( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
    | X1 != X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_2214]),
    [final] ).

cnf(i_0_3784,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_2419]),
    [final] ).

cnf(i_0_3785,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),
    inference(split_conjunct,[status(thm)],[i_0_2420]),
    [final] ).

cnf(i_0_3786,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X1)),
    inference(split_conjunct,[status(thm)],[i_0_2421]),
    [final] ).

cnf(i_0_3787,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_2331]),
    [final] ).

cnf(i_0_3788,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2422]),
    [final] ).

cnf(i_0_3789,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[i_0_2423,c_0_1480]),
    [final] ).

cnf(i_0_3790,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2059]),
    [final] ).

cnf(i_0_3791,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_2424]),
    [final] ).

cnf(i_0_3792,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2425]),
    [final] ).

cnf(i_0_3793,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2426]),
    [final] ).

cnf(i_0_3794,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2427]),
    [final] ).

cnf(i_0_3795,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_2428]),
    [final] ).

cnf(i_0_3796,plain,
    ( X2 = X3
    | c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2429]),
    [final] ).

cnf(i_0_3797,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_2326]),
    [final] ).

cnf(i_0_3798,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_2430]),
    [final] ).

cnf(i_0_3799,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_1350]),
    [final] ).

cnf(i_0_3800,plain,
    ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2431]),
    [final] ).

cnf(i_0_3801,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_2432]),
    [final] ).

cnf(i_0_3802,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_3803,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(split_conjunct,[status(thm)],[fact_th000_I2_J]),
    [final] ).

cnf(i_0_3804,plain,
    c_Orderings_Oord__class_Oless__eq(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_th000_I1_J]),
    [final] ).

cnf(i_0_3805,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[i_0_2433]),
    [final] ).

cnf(i_0_3806,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_2434]),
    [final] ).

cnf(i_0_3807,plain,
    ( c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2435]),
    [final] ).

cnf(i_0_3808,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2436]),
    [final] ).

cnf(i_0_3809,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_2437]),
    [final] ).

cnf(i_0_3810,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_2438]),
    [final] ).

cnf(i_0_3811,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2439]),
    [final] ).

cnf(i_0_3812,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_2440]),
    [final] ).

cnf(i_0_3813,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_2441]),
    [final] ).

cnf(i_0_3814,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2246]),
    [final] ).

cnf(i_0_3815,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2236]),
    [final] ).

cnf(i_0_3816,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2442]),
    [final] ).

cnf(i_0_3817,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_2238]),
    [final] ).

cnf(i_0_3818,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_2443]),
    [final] ).

cnf(i_0_3819,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_2444]),
    [final] ).

cnf(i_0_3820,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2445]),
    [final] ).

cnf(i_0_3821,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(rw,[status(thm)],[i_0_2446,c_0_1479]),
    [final] ).

cnf(i_0_3822,plain,
    ( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)
    | c_Int_OPls != X1 ),
    inference(rw,[status(thm)],[i_0_2447,c_0_1479]),
    [final] ).

cnf(i_0_3823,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2168]),
    [final] ).

cnf(i_0_3824,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_2448]),
    [final] ).

cnf(i_0_3825,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_RealVector_Onorm__class_Onorm(X2,c_Groups_Osgn__class_Osgn(X2,X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2435]),
    [final] ).

cnf(i_0_3826,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk45_0),
    inference(split_conjunct,[status(thm)],[i_0_1264]),
    [final] ).

cnf(i_0_3827,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_3828,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
    inference(split_conjunct,[status(thm)],[fact_rp]),
    [final] ).

cnf(i_0_3829,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_2449]),
    [final] ).

cnf(i_0_3830,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_2450]),
    [final] ).

cnf(i_0_3831,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_2451]),
    [final] ).

cnf(i_0_3832,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2452]),
    [final] ).

cnf(i_0_3833,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2453]),
    [final] ).

cnf(i_0_3834,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[i_0_2454]),
    [final] ).

cnf(i_0_3835,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2455]),
    [final] ).

cnf(i_0_3836,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2456]),
    [final] ).

cnf(i_0_3837,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2457]),
    [final] ).

cnf(i_0_3838,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_3839,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
    inference(rw,[status(thm)],[i_0_2458,c_0_1479]),
    [final] ).

cnf(i_0_3840,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_2459]),
    [final] ).

cnf(i_0_3841,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_2460]),
    [final] ).

cnf(i_0_3842,plain,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)) = c_RealDef_Oreal(tc_Nat_Onat,X1),
    inference(split_conjunct,[status(thm)],[i_0_2461]),
    [final] ).

cnf(i_0_3843,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_2462]),
    [final] ).

cnf(i_0_3844,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_2462]),
    [final] ).

cnf(i_0_3845,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_2463]),
    [final] ).

cnf(i_0_3846,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_2463]),
    [final] ).

cnf(i_0_3847,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Groups_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2464]),
    [final] ).

cnf(i_0_3848,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | ~ class_Groups_Ozero(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2464]),
    [final] ).

cnf(i_0_3849,plain,
    ( X1 = X2
    | c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2465]),
    [final] ).

cnf(i_0_3850,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_2466]),
    [final] ).

cnf(i_0_3851,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_2467]),
    [final] ).

cnf(i_0_3852,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_2468]),
    [final] ).

cnf(i_0_3853,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_2469]),
    [final] ).

cnf(i_0_3854,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_2470]),
    [final] ).

cnf(i_0_3855,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_2471]),
    [final] ).

cnf(i_0_3856,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_2472]),
    [final] ).

cnf(i_0_3857,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_2473]),
    [final] ).

cnf(i_0_3858,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2474]),
    [final] ).

cnf(i_0_3859,plain,
    c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),
    inference(split_conjunct,[status(thm)],[i_0_2475]),
    [final] ).

cnf(i_0_3860,plain,
    c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),
    inference(split_conjunct,[status(thm)],[i_0_2476]),
    [final] ).

cnf(i_0_3861,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2477]),
    [final] ).

cnf(i_0_3862,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2478]),
    [final] ).

cnf(i_0_3863,plain,
    ( class_Groups_Ominus(tc_fun(X2,X1))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2479]),
    [final] ).

cnf(i_0_3864,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2480]),
    [final] ).

cnf(i_0_3865,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2481]),
    [final] ).

cnf(i_0_3866,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2482]),
    [final] ).

cnf(i_0_3867,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2483]),
    [final] ).

cnf(i_0_3868,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_2484]),
    [final] ).

cnf(i_0_3869,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_2485]),
    [final] ).

cnf(i_0_3870,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_2486]),
    [final] ).

cnf(i_0_3871,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_2467]),
    [final] ).

cnf(i_0_3872,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_2470]),
    [final] ).

cnf(i_0_3873,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_2261]),
    [final] ).

cnf(i_0_3874,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_2471]),
    [final] ).

cnf(i_0_3875,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_2472]),
    [final] ).

cnf(i_0_3876,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_2473]),
    [final] ).

cnf(i_0_3877,plain,
    ( c_Groups_Oabs__class_Oabs(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2474]),
    [final] ).

cnf(i_0_3878,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_2466]),
    [final] ).

cnf(i_0_3879,plain,
    ( c_RealVector_Onorm__class_Onorm(X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_2477]),
    [final] ).

cnf(i_0_3880,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_2487]),
    [final] ).

cnf(i_0_3881,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_2488]),
    [final] ).

cnf(i_0_3882,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_2489]),
    [final] ).

cnf(i_0_3883,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_2490]),
    [final] ).

cnf(i_0_3884,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_2491]),
    [final] ).

cnf(i_0_3885,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_2492]),
    [final] ).

cnf(i_0_3886,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_2493]),
    [final] ).

cnf(i_0_3887,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_2494]),
    [final] ).

cnf(i_0_3888,plain,
    ( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2495]),
    [final] ).

cnf(i_0_3889,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_2485]),
    [final] ).

cnf(i_0_3890,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_2486]),
    [final] ).

cnf(i_0_3891,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2496]),
    [final] ).

cnf(i_0_3892,plain,
    ( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2497]),
    [final] ).

cnf(i_0_3893,plain,
    c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2498]),
    [final] ).

cnf(i_0_3894,plain,
    c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2499]),
    [final] ).

cnf(i_0_3895,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_RealDef_Oreal(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_3896,plain,
    c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[i_0_2501]),
    [final] ).

cnf(i_0_3897,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_2502]),
    [final] ).

cnf(i_0_3898,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_2503]),
    [final] ).

cnf(i_0_3899,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_2297]),
    [final] ).

cnf(i_0_3900,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_2298]),
    [final] ).

cnf(i_0_3901,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_2299]),
    [final] ).

cnf(i_0_3902,plain,
    ( c_RealDef_Oreal(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_2500]),
    [final] ).

cnf(i_0_3903,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_2504]),
    [final] ).

cnf(i_0_3904,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_2505]),
    [final] ).

cnf(i_0_3905,plain,
    c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X1),
    inference(split_conjunct,[status(thm)],[i_0_2506]),
    [final] ).

cnf(i_0_3906,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_3907,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__of__nat__1]),
    [final] ).

cnf(i_0_3908,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]),
    [final] ).

cnf(i_0_3909,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_3910,plain,
    ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2507]),
    [final] ).

cnf(i_0_3911,plain,
    ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2508]),
    [final] ).

cnf(i_0_3912,plain,
    ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2509]),
    [final] ).

cnf(i_0_3913,plain,
    ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2510]),
    [final] ).

cnf(i_0_3914,plain,
    ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2511]),
    [final] ).

cnf(i_0_3915,plain,
    ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2512]),
    [final] ).

cnf(i_0_3916,plain,
    ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2513]),
    [final] ).

cnf(i_0_3917,plain,
    ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2514]),
    [final] ).

cnf(i_0_3918,plain,
    ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2515]),
    [final] ).

cnf(i_0_3919,plain,
    ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2516]),
    [final] ).

cnf(i_0_3920,plain,
    ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2517]),
    [final] ).

cnf(i_0_3921,plain,
    ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2518]),
    [final] ).

cnf(i_0_3922,plain,
    ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2519]),
    [final] ).

cnf(i_0_3923,plain,
    ( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2520]),
    [final] ).

cnf(i_0_3924,plain,
    ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2521]),
    [final] ).

cnf(i_0_3925,plain,
    ( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2522]),
    [final] ).

cnf(i_0_3926,plain,
    ( class_Rings_Oring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2523]),
    [final] ).

cnf(i_0_3927,plain,
    ( class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2524]),
    [final] ).

cnf(i_0_3928,plain,
    ( class_Int_Onumber(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2525]),
    [final] ).

cnf(i_0_3929,plain,
    ( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2526]),
    [final] ).

cnf(i_0_3930,plain,
    ( class_Groups_Ouminus(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2527]),
    [final] ).

cnf(i_0_3931,plain,
    ( class_Groups_Ominus(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2528]),
    [final] ).

cnf(i_0_3932,plain,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2529]),
    [final] ).

cnf(i_0_3933,plain,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2530]),
    [final] ).

cnf(i_0_3934,plain,
    ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2531]),
    [final] ).

cnf(i_0_3935,plain,
    ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2532]),
    [final] ).

cnf(i_0_3936,plain,
    ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2533]),
    [final] ).

cnf(i_0_3937,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2534]),
    [final] ).

cnf(i_0_3938,plain,
    ( class_Groups_Oone(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2535]),
    [final] ).

cnf(i_0_3939,plain,
    ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2536]),
    [final] ).

cnf(i_0_3940,plain,
    ( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2537]),
    [final] ).

cnf(i_0_3941,plain,
    ( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2538]),
    [final] ).

cnf(i_0_3942,plain,
    ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2539]),
    [final] ).

cnf(i_0_3943,plain,
    ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2540]),
    [final] ).

cnf(i_0_3944,plain,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2541]),
    [final] ).

cnf(i_0_3945,plain,
    ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2542]),
    [final] ).

cnf(i_0_3946,plain,
    ( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2543]),
    [final] ).

cnf(i_0_3947,plain,
    ( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2544]),
    [final] ).

cnf(i_0_3948,plain,
    ( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2545]),
    [final] ).

cnf(i_0_3949,plain,
    ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2546]),
    [final] ).

cnf(i_0_3950,plain,
    ( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2547]),
    [final] ).

cnf(i_0_3951,plain,
    ( class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2548]),
    [final] ).

cnf(i_0_3952,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2549]),
    [final] ).

cnf(i_0_3953,plain,
    ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2550]),
    [final] ).

cnf(i_0_3954,plain,
    ( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2551]),
    [final] ).

cnf(i_0_3955,plain,
    ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2552]),
    [final] ).

cnf(i_0_3956,plain,
    ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2553]),
    [final] ).

cnf(i_0_3957,plain,
    ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2554]),
    [final] ).

cnf(i_0_3958,plain,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2555]),
    [final] ).

cnf(i_0_3959,plain,
    ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2556]),
    [final] ).

cnf(i_0_3960,plain,
    ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2557]),
    [final] ).

cnf(i_0_3961,plain,
    ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2558]),
    [final] ).

cnf(i_0_3962,plain,
    ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
    | ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2559]),
    [final] ).

cnf(i_0_3963,plain,
    ( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_2560]),
    [final] ).

cnf(i_0_3964,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_3965,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_3966,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_3967,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_2561]),
    [final] ).

cnf(i_0_3968,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_3969,plain,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_natfloor__one]),
    [final] ).

cnf(i_0_3970,plain,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_natfloor__zero]),
    [final] ).

cnf(i_0_3971,plain,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_natceiling__one]),
    [final] ).

cnf(i_0_3972,plain,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_natceiling__zero]),
    [final] ).

cnf(i_0_3973,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_3974,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_3975,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[fact_complex__i__not__one]),
    [final] ).

cnf(i_0_3976,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[fact_complex__i__not__zero]),
    [final] ).

cnf(i_0_3977,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]),
    [final] ).

cnf(i_0_3978,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]),
    [final] ).

cnf(i_0_3979,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]),
    [final] ).

cnf(i_0_3980,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]),
    [final] ).

cnf(i_0_3981,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_3982,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_3983,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_3984,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_3985,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_3986,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_3987,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_3988,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_3989,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_3990,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_3991,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_3992,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_3993,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_3994,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_3995,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_3996,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_3997,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_3998,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_3999,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_4000,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_4001,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_4002,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_4003,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_4004,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_4005,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_4006,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4007,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4008,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4009,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_4010,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_4011,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_4012,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_4013,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_4014,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_4015,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_4016,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_4017,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4018,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4019,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4020,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
    [final] ).

cnf(i_0_4021,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4022,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4023,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4024,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_4025,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
    [final] ).

cnf(i_0_4026,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
    [final] ).

cnf(i_0_4027,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
    [final] ).

cnf(i_0_4028,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
    [final] ).

cnf(i_0_4029,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_4030,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
    [final] ).

cnf(i_0_4031,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
    [final] ).

cnf(i_0_4032,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_4033,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_4034,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_4035,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_4036,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_4037,plain,
    class_Groups_Osgn__if(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]),
    [final] ).

cnf(i_0_4038,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_4039,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_4040,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]),
    [final] ).

cnf(i_0_4041,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]),
    [final] ).

cnf(i_0_4042,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_4043,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]),
    [final] ).

cnf(i_0_4044,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]),
    [final] ).

cnf(i_0_4045,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_4046,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_4047,plain,
    class_Groups_Ouminus(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
    [final] ).

cnf(i_0_4048,plain,
    class_Groups_Ouminus(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
    [final] ).

cnf(i_0_4049,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
    [final] ).

cnf(i_0_4050,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
    [final] ).

cnf(i_0_4051,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
    [final] ).

cnf(i_0_4052,plain,
    class_Groups_Ominus(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]),
    [final] ).

cnf(i_0_4053,plain,
    class_Groups_Ominus(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]),
    [final] ).

cnf(i_0_4054,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
    [final] ).

cnf(i_0_4055,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
    [final] ).

cnf(i_0_4056,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_4057,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_4058,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_4059,plain,
    class_Fields_Olinordered__field(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
    [final] ).

cnf(i_0_4060,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_4061,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_4062,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_4063,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_4064,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_4065,plain,
    class_Rings_Odivision__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
    [final] ).

cnf(i_0_4066,plain,
    class_Rings_Odivision__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
    [final] ).

cnf(i_0_4067,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_4068,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_4069,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_4070,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_4071,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_4072,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_4073,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_4074,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_4075,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_4076,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4077,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4078,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_4079,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_4080,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_4081,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_4082,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_4083,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_4084,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_4085,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_4086,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_4087,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_4088,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_4089,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_4090,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_4091,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
    [final] ).

cnf(i_0_4092,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
    [final] ).

cnf(i_0_4093,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_4094,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_4095,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_4096,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
    [final] ).

cnf(i_0_4097,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
    [final] ).

cnf(i_0_4098,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_4099,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_4100,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_4101,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_4102,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_4103,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_4104,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_4105,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4106,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4107,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4108,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_4109,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_4110,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_4111,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_4112,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_4113,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_4114,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_4115,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_4116,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_4117,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_4118,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
    [final] ).

cnf(i_0_4119,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_4120,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_4121,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_4122,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
    [final] ).

cnf(i_0_4123,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4124,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4125,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
    [final] ).

cnf(i_0_4126,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_4127,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_4128,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_4129,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_4130,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
    [final] ).

cnf(i_0_4131,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
    [final] ).

cnf(i_0_4132,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_4133,plain,
    class_Groups_Oabs__if(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]),
    [final] ).

cnf(i_0_4134,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]),
    [final] ).

cnf(i_0_4135,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]),
    [final] ).

cnf(i_0_4136,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]),
    [final] ).

cnf(i_0_4137,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]),
    [final] ).

cnf(i_0_4138,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
    [final] ).

cnf(i_0_4139,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
    [final] ).

cnf(i_0_4140,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
    [final] ).

cnf(i_0_4141,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4142,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4143,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4144,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
    [final] ).

cnf(i_0_4145,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_4146,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_4147,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_4148,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_4149,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_4150,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_4151,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_4152,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_4153,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_4154,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_4155,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_4156,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_4157,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_4158,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_4159,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_4160,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_4161,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_4162,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_4163,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_4164,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_4165,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_4166,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_4167,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_4168,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_4169,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_4170,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_4171,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_4172,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_4173,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_4174,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_4175,plain,
    c_SEQ_Osubseq(v_f____),
    inference(split_conjunct,[status(thm)],[fact_fz_I1_J]),
    [final] ).

cnf(i_0_4176,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_4177,axiom,
    X1 = X1 ).

cnf(i_0_4178,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4179,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4180,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).

cnf(i_0_4181,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).

cnf(i_0_4182,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_4183,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_4184,axiom,
    ( X1 != X2
    | c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).

cnf(i_0_4185,axiom,
    ( X1 != X2
    | c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).

cnf(i_0_4186,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_4187,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_4188,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_4189,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_4190,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_4191,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_4192,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).

cnf(i_0_4193,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).

cnf(i_0_4194,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).

cnf(i_0_4195,axiom,
    ( X1 != X2
    | c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).

cnf(i_0_4196,axiom,
    ( X1 != X2
    | c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).

cnf(i_0_4197,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_4198,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_4199,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_4200,axiom,
    ( X1 != X2
    | c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).

cnf(i_0_4201,axiom,
    ( X1 != X2
    | c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).

cnf(i_0_4202,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_4203,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_4204,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_4205,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).

cnf(i_0_4206,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).

cnf(i_0_4207,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).

cnf(i_0_4208,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).

cnf(i_0_4209,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).

cnf(i_0_4210,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).

cnf(i_0_4211,axiom,
    ( X1 != X2
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).

cnf(i_0_4212,axiom,
    ( X1 != X2
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).

cnf(i_0_4213,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_4214,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_4215,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).

cnf(i_0_4216,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).

cnf(i_0_4217,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_4218,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_4219,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_4220,axiom,
    ( X1 != X2
    | c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).

cnf(i_0_4221,axiom,
    ( X1 != X2
    | c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).

cnf(i_0_4222,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_4223,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
    | c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_4224,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
    | c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_4225,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_4226,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_4227,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_4228,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_4229,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_4230,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_4231,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_4232,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4233,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_4234,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_4235,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).

cnf(i_0_4236,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
    | c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).

cnf(i_0_4237,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).

cnf(i_0_4238,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_4239,axiom,
    ( X1 != X2
    | ~ c_SEQ_Osubseq(X1)
    | c_SEQ_Osubseq(X2) ) ).

cnf(i_0_4240,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_4241,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_4242,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_4243,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__0(X1)
    | class_Rings_Ocomm__semiring__0(X2) ) ).

cnf(i_0_4244,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_4245,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_4246,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_4247,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_4248,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_4249,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_4250,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4251,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_4252,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_4253,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__div__algebra(X1)
    | class_RealVector_Oreal__normed__div__algebra(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_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_4256,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_4257,axiom,
    ( X1 != X2
    | ~ c_SEQ_Odecseq(X1,X3)
    | c_SEQ_Odecseq(X2,X3) ) ).

cnf(i_0_4258,axiom,
    ( X1 != X2
    | ~ c_SEQ_Odecseq(X3,X1)
    | c_SEQ_Odecseq(X3,X2) ) ).

cnf(i_0_4259,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_4260,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_4261,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_4262,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_4263,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_4264,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_4265,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_4266,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_4267,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_4268,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_4269,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_4270,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_4271,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | class_RealVector_Oreal__normed__vector(X2) ) ).

cnf(i_0_4272,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_4273,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_4274,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_4275,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4276,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_4277,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_4278,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_4279,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_4280,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_4281,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_4282,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_4283,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_4284,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra__1(X1)
    | class_RealVector_Oreal__normed__algebra__1(X2) ) ).

cnf(i_0_4285,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_4286,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_4287,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_4288,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_4289,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(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_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_4292,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_4293,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | class_RealVector_Oreal__normed__algebra(X2) ) ).

cnf(i_0_4294,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__comm__monoid__add(X1)
    | class_Groups_Ocancel__comm__monoid__add(X2) ) ).

cnf(i_0_4295,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_4296,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_4297,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__field(X1)
    | class_RealVector_Oreal__normed__field(X2) ) ).

cnf(i_0_4177_001,axiom,
    X1 = X1 ).

cnf(i_0_4178_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_4179_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_4180_004,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).

cnf(i_0_4181_005,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).

cnf(i_0_4182_006,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_4183_007,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_4184_008,axiom,
    ( X1 != X2
    | c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).

cnf(i_0_4185_009,axiom,
    ( X1 != X2
    | c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).

cnf(i_0_4186_010,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_4187_011,axiom,
    ( X1 != X2
    | c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_4188_012,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_4189_013,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_4190_014,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_4191_015,axiom,
    ( X1 != X2
    | c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_4192_016,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).

cnf(i_0_4193_017,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).

cnf(i_0_4194_018,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).

cnf(i_0_4195_019,axiom,
    ( X1 != X2
    | c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).

cnf(i_0_4196_020,axiom,
    ( X1 != X2
    | c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).

cnf(i_0_4197_021,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_4198_022,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_4199_023,axiom,
    ( X1 != X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_4200_024,axiom,
    ( X1 != X2
    | c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).

cnf(i_0_4201_025,axiom,
    ( X1 != X2
    | c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).

cnf(i_0_4202_026,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_4203_027,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_4204_028,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_4205_029,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).

cnf(i_0_4206_030,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).

cnf(i_0_4207_031,axiom,
    ( X1 != X2
    | c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).

cnf(i_0_4208_032,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).

cnf(i_0_4209_033,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).

cnf(i_0_4210_034,axiom,
    ( X1 != X2
    | c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).

cnf(i_0_4211_035,axiom,
    ( X1 != X2
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).

cnf(i_0_4212_036,axiom,
    ( X1 != X2
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).

cnf(i_0_4213_037,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_4214_038,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_4215_039,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).

cnf(i_0_4216_040,axiom,
    ( X1 != X2
    | c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).

cnf(i_0_4217_041,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_4218_042,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_4219_043,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_4220_044,axiom,
    ( X1 != X2
    | c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).

cnf(i_0_4221_045,axiom,
    ( X1 != X2
    | c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).

cnf(i_0_4222_046,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_4223_047,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
    | c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_4224_048,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
    | c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_4225_049,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_4226_050,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_4227_051,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_4228_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_4229_053,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_4230_054,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_4231_055,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_4232_056,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_4233_057,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_4234_058,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_4235_059,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).

cnf(i_0_4236_060,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
    | c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).

cnf(i_0_4237_061,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).

cnf(i_0_4238_062,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_4239_063,axiom,
    ( X1 != X2
    | ~ c_SEQ_Osubseq(X1)
    | c_SEQ_Osubseq(X2) ) ).

cnf(i_0_4240_064,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_4241_065,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_4242_066,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_4243_067,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__0(X1)
    | class_Rings_Ocomm__semiring__0(X2) ) ).

cnf(i_0_4244_068,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_4245_069,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_4246_070,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_4247_071,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_4248_072,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_4249_073,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_4250_074,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4251_075,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_4252_076,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_4253_077,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__div__algebra(X1)
    | class_RealVector_Oreal__normed__div__algebra(X2) ) ).

cnf(i_0_4254_078,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_4255_079,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_4256_080,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_4257_081,axiom,
    ( X1 != X2
    | ~ c_SEQ_Odecseq(X1,X3)
    | c_SEQ_Odecseq(X2,X3) ) ).

cnf(i_0_4258_082,axiom,
    ( X1 != X2
    | ~ c_SEQ_Odecseq(X3,X1)
    | c_SEQ_Odecseq(X3,X2) ) ).

cnf(i_0_4259_083,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_4260_084,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_4261_085,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_4262_086,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_4263_087,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_4264_088,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_4265_089,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_4266_090,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_4267_091,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_4268_092,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_4269_093,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_4270_094,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_4271_095,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__vector(X1)
    | class_RealVector_Oreal__normed__vector(X2) ) ).

cnf(i_0_4272_096,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_4273_097,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_4274_098,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_4275_099,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_4276_100,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_4277_101,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_4278_102,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_4279_103,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_4280_104,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_4281_105,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_4282_106,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_4283_107,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_4284_108,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra__1(X1)
    | class_RealVector_Oreal__normed__algebra__1(X2) ) ).

cnf(i_0_4285_109,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_4286_110,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_4287_111,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_4288_112,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_4289_113,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_4290_114,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_4291_115,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_4292_116,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_4293_117,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__algebra(X1)
    | class_RealVector_Oreal__normed__algebra(X2) ) ).

cnf(i_0_4294_118,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__comm__monoid__add(X1)
    | class_Groups_Ocancel__comm__monoid__add(X2) ) ).

cnf(i_0_4295_119,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_4296_120,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_4297_121,axiom,
    ( X1 != X2
    | ~ class_RealVector_Oreal__normed__field(X1)
    | class_RealVector_Oreal__normed__field(X2) ) ).

cnf(i_0_4298,plain,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4)) ),
    inference(equality_inference,[],[2649]) ).

cnf(i_0_4299,plain,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5) ),
    inference(equality_inference,[],[2650]) ).

cnf(i_0_4300,plain,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X2),X3),X4) = X4 ),
    inference(equality_inference,[],[2651]) ).

cnf(i_0_4301,plain,
    ( ~ class_Rings_Oring(X1)
    | X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X3),X4),X2) ),
    inference(equality_inference,[],[2652]) ).

cnf(i_0_4302,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[2656]) ).

cnf(i_0_4303,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(equality_inference,[],[2743]) ).

cnf(i_0_4304,plain,
    X1 = X1,
    inference(equality_inference,[],[2766]) ).

cnf(i_0_4305,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X3))) ),
    inference(equality_inference,[],[2784]) ).

cnf(i_0_4306,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(equality_inference,[],[3041]) ).

cnf(i_0_4307,plain,
    ( X1 = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(equality_inference,[],[3042]) ).

cnf(i_0_4308,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_inference,[],[3113]) ).

cnf(i_0_4309,plain,
    ( ~ class_Fields_Ofield(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) = c_Groups_Otimes__class_Otimes(X1,X3,X2) ),
    inference(equality_inference,[],[3132]) ).

cnf(i_0_4310,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,[],[3133]) ).

cnf(i_0_4311,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3134]) ).

cnf(i_0_4312,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3135]) ).

cnf(i_0_4313,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3232]) ).

cnf(i_0_4314,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3233]) ).

cnf(i_0_4315,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3234]) ).

cnf(i_0_4316,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(equality_inference,[],[3235]) ).

cnf(i_0_4317,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1) = X2 ),
    inference(equality_inference,[],[3275]) ).

cnf(i_0_4318,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) ),
    inference(equality_inference,[],[3276]) ).

cnf(i_0_4319,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
    inference(equality_inference,[],[3359]) ).

cnf(i_0_4320,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[3391]) ).

cnf(i_0_4321,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[3392]) ).

cnf(i_0_4322,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[3411]) ).

cnf(i_0_4323,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[3412]) ).

cnf(i_0_4324,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[3414]) ).

cnf(i_0_4325,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3440]) ).

cnf(i_0_4326,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3441]) ).

cnf(i_0_4327,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_inference,[],[3449]) ).

cnf(i_0_4328,plain,
    X1 = X1,
    inference(equality_inference,[],[3450]) ).

cnf(i_0_4329,plain,
    X1 = X1,
    inference(equality_inference,[],[3451]) ).

cnf(i_0_4330,plain,
    X1 = X1,
    inference(equality_inference,[],[3452]) ).

cnf(i_0_4331,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,[],[3460]) ).

cnf(i_0_4332,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_inference,[],[3461]) ).

cnf(i_0_4333,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) = X3 ),
    inference(equality_inference,[],[3477]) ).

cnf(i_0_4334,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) = X3 ),
    inference(equality_inference,[],[3478]) ).

cnf(i_0_4335,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) = X3 ),
    inference(equality_inference,[],[3480]) ).

cnf(i_0_4336,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) ),
    inference(equality_inference,[],[3481]) ).

cnf(i_0_4337,plain,
    ( ~ class_Fields_Ofield__inverse__zero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(equality_inference,[],[3482]) ).

cnf(i_0_4338,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(equality_inference,[],[3483]) ).

cnf(i_0_4339,plain,
    ( ~ class_Rings_Odivision__ring(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) ),
    inference(equality_inference,[],[3484]) ).

cnf(i_0_4340,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(equality_inference,[],[3488]) ).

cnf(i_0_4341,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
    inference(equality_inference,[],[3510]) ).

cnf(i_0_4342,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(equality_inference,[],[3514]) ).

cnf(i_0_4343,plain,
    ( ~ class_Rings_Oidom(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(X1,X2)) = c_Groups_Otimes__class_Otimes(X1,X2,X2) ),
    inference(equality_inference,[],[3525]) ).

cnf(i_0_4344,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(equality_inference,[],[3537]) ).

cnf(i_0_4345,plain,
    X1 = X1,
    inference(equality_inference,[],[3560]) ).

cnf(i_0_4346,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,[],[3568]) ).

cnf(i_0_4347,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[3623]) ).

cnf(i_0_4348,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(equality_inference,[],[3630]) ).

cnf(i_0_4349,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3637]) ).

cnf(i_0_4350,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3638]) ).

cnf(i_0_4351,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3639]) ).

cnf(i_0_4352,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
    inference(equality_inference,[],[3640]) ).

cnf(i_0_4353,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(equality_inference,[],[3666]) ).

cnf(i_0_4354,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,[],[3670]) ).

cnf(i_0_4355,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,[],[3671]) ).

cnf(i_0_4356,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
    inference(equality_inference,[],[3685]) ).

cnf(i_0_4357,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3688]) ).

cnf(i_0_4358,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3690]) ).

cnf(i_0_4359,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
    inference(equality_inference,[],[3691]) ).

cnf(i_0_4360,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(equality_inference,[],[3707]) ).

cnf(i_0_4361,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(equality_inference,[],[3708]) ).

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,[],[3715]) ).

cnf(i_0_4363,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,[],[3725]) ).

cnf(i_0_4364,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,[],[3728]) ).

cnf(i_0_4365,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3729]) ).

cnf(i_0_4366,plain,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3730]) ).

cnf(i_0_4367,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,[],[3731]) ).

cnf(i_0_4368,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,[],[3732]) ).

cnf(i_0_4369,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,[],[3733]) ).

cnf(i_0_4370,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,[],[3751]) ).

cnf(i_0_4371,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3760]) ).

cnf(i_0_4372,plain,
    ( ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3761]) ).

cnf(i_0_4373,plain,
    ( ~ class_Rings_Oidom(X1)
    | hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3762]) ).

cnf(i_0_4374,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3781]) ).

cnf(i_0_4375,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3782]) ).

cnf(i_0_4376,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
    inference(equality_inference,[],[3783]) ).

cnf(i_0_4377,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,[],[3784]) ).

cnf(i_0_4378,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(equality_inference,[],[3790]) ).

cnf(i_0_4379,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3795]) ).

cnf(i_0_4380,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | ~ class_Rings_Oidom(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3796]) ).

cnf(i_0_4381,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
    inference(equality_inference,[],[3799]) ).

cnf(i_0_4382,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | c_RealVector_Onorm__class_Onorm(X1,c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3807]) ).

cnf(i_0_4383,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(equality_inference,[],[3816]) ).

cnf(i_0_4384,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(equality_inference,[],[3817]) ).

cnf(i_0_4385,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
    inference(equality_inference,[],[3821]) ).

cnf(i_0_4386,plain,
    c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(equality_inference,[],[3822]) ).

cnf(i_0_4387,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
    inference(equality_inference,[],[3823]) ).

cnf(i_0_4388,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3829]) ).

cnf(i_0_4389,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[3830]) ).

cnf(i_0_4390,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
    inference(equality_inference,[],[3844]) ).

cnf(i_0_4391,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
    inference(equality_inference,[],[3846]) ).

cnf(i_0_4392,plain,
    ( ~ class_Groups_Ozero(X1)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[3848]) ).

cnf(i_0_4393,plain,
    X1 = X1,
    inference(equality_inference,[],[3849]) ).

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,[],[3871]) ).

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,[],[3872]) ).

cnf(i_0_4396,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,[],[3873]) ).

cnf(i_0_4397,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,[],[3874]) ).

cnf(i_0_4398,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,[],[3875]) ).

cnf(i_0_4399,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,[],[3876]) ).

cnf(i_0_4400,plain,
    ( ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[3877]) ).

cnf(i_0_4401,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,[],[3878]) ).

cnf(i_0_4402,plain,
    ( ~ class_RealVector_Oreal__normed__vector(X1)
    | c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(equality_inference,[],[3879]) ).

cnf(i_0_4403,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,[],[3889]) ).

cnf(i_0_4404,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,[],[3890]) ).

cnf(i_0_4405,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,[],[3899]) ).

cnf(i_0_4406,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,[],[3901]) ).

cnf(i_0_4407,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(equality_inference,[],[3902]) ).

cnf(i_0_4408,plain,
    $false,
    inference(scs_inference,[],[i_0_2563,i_0_4173,i_0_2673]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW229+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 : n020.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 06:28:19 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 5.95/5.80  % Version  : CSE_E---1.7
% 5.95/5.80  % Problem  : theBenchmark.p
% 5.95/5.80  % SZS status Theorem for theBenchmark.p
% 5.95/5.80  % SZS output start CNFRefutation
% See solution above
% 6.16/5.94  % Total time : 5.451s
%------------------------------------------------------------------------------