%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW262+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 : n007.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 05:30:50 PM UTC 2026
% Result : Theorem 0.84s 5.79s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 2392)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096_B_Bthesis_O_A_I_B_Bt_O_A_091_124_A0_A_060_At_059_At_A_060_A1_059_At_A_060_Ainverse_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X39] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X39)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bt_O_A_091_124_A0_A_060_At_059_At_A_060_A1_059_At_A_060_Ainverse_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X5)),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_nat__diff__split__asm,axiom,
! [X19,X16,X51] :
( hBOOL(hAPP(X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X19)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X19)
& ~ hBOOL(hAPP(X51,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X63] :
( X16 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X63)
& ~ hBOOL(hAPP(X51,X63)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_add__leE,axiom,
! [X9,X44,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44),X9)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X8,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X8,X67),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_less_Ohyps,axiom,
! [X73] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X73),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
=> ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X73))
=> ? [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X73),X59) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Ohyps) ).
fof(fact_not__square__less__zero,axiom,
! [X10,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X10),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_not__add__less1,axiom,
! [X45,X22] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X22,X45] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X22),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X18] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X18))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_add__diff__inverse,axiom,
! [X9,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X17,X18,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X10,X23,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X10)
=> ~ c_Orderings_Oord__class_Oless(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_linorder__not__le,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> c_Orderings_Oord__class_Oless(X8,X17,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X7,X5,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless(X8,X17,X18)
| X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__not__sym,axiom,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__asym_H,axiom,
! [X23,X10,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ~ c_Orderings_Oord__class_Oless(X8,X23,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__asym,axiom,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_sgn__poly__def,axiom,
! [X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_abs__poly__def,axiom,
! [X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X7) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X8),X7) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).
fof(fact_tsub__def,axiom,
! [X7,X5] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X7)
=> c_Nat__Transfer_Otsub(X7,X5) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X5) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X7)
=> c_Nat__Transfer_Otsub(X7,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_abs__not__less__zero,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_norm__not__less__zero,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),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,
! [X10,X8] :
( class_Groups_Oabs__if(X8)
=> ( ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = c_Groups_Ouminus__class_Ouminus(X8,X10) )
& ( ~ c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).
fof(fact_sgn__if,axiom,
! [X7,X8] :
( class_Groups_Osgn__if(X8)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Ozero__class_Ozero(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Oone__class_Oone(X8) )
& ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),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__antisym__conv3,axiom,
! [X18,X17,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X17,X18)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__cases,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ( X7 != X5
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__le__cases,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_leI,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [X7,X5,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> c_Orderings_Oord__class_Oless(X8,X7,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_zabs__def,axiom,
! [X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X22) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X22) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(fact_abs__real__def,axiom,
! [X10] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).
fof(fact_real__abs__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_real__abs__def) ).
fof(fact_not__one__le__zero,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X5,X7] :
( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X7,X8] :
( class_Orderings_Opreorder(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_not__less0,axiom,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,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,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,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,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_not__pos__poly__0,axiom,
! [X8] :
( class_Rings_Olinordered__idom(X8)
=> ~ c_Polynomial_Opos__poly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_lemmaCauchy,axiom,
! [X80,X81,X8,X67] :
( ( class_RealVector_Oreal__normed__vector(X67)
& class_Orderings_Oord(X8) )
=> ( ! [X49] :
( c_Orderings_Oord__class_Oless__eq(X8,X81,X49)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X67,c_Groups_Ominus__class_Ominus(X67,hAPP(X80,X81),hAPP(X80,X49))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X49] :
( c_Orderings_Oord__class_Oless__eq(X8,X81,X49)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X67,hAPP(X80,X49)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X67,hAPP(X80,X81)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_mrmq__eq,axiom,
! [X32] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X32)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X32)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mrmq__eq) ).
fof(fact_decr__lemma,axiom,
! [X20,X7,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X20)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25)),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [X7,X20,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X20)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).
fof(fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096,axiom,
? [X50,X77] :
( X77 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X74] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X74),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& ! [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X59) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X59),X50)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X77,X74)),X59))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
fof(fact_kas_I4_J,axiom,
! [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X59) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X59),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X59))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I4_J) ).
fof(fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> ? [X58] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X58)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096) ).
fof(fact_qr,axiom,
! [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X59) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X59)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qr) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X8,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X23,X10,X5,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X10)),c_Groups_Ominus__class_Ominus(X8,X5,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X10)),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ominus__class_Ominus(X8,X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [X11,X46,X5,X7] : 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,X7,X5),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X46),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X46))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).
fof(fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096,axiom,
~ ! [X3,X68] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096) ).
fof(fact_synthetic__div__correct_H,axiom,
! [X13,X26,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X26),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Osynthetic__div(X8,X13,X26)),c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X13),X26),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_le__add__iff1,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X16,X19)),X60),X36),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X16,X19)),X60),X36),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35))
<=> c_Orderings_Oord__class_Oless__eq(X8,X36,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X19,X16)),X60),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35))
<=> c_Orderings_Oord__class_Oless(X8,X36,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X19,X16)),X60),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_nat__le__add__iff1,axiom,
! [X14,X15,X64,X62,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X62)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X62,X61)),X64),X15),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X14,X15,X64,X62,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X62)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X62,X61)),X64),X15),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [X14,X15,X64,X61,X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X61)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X62)),X64),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X14,X15,X64,X61,X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X61)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X62)),X64),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_th01,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th01) ).
fof(fact_order__1,axiom,
! [X13,X10,X8] :
( class_Rings_Oidom(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))))),c_Polynomial_Oorder(X8,X10,X13)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X25,X26,X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Oplus__class_Oplus(X8,X26,X25))),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X10,X26)),c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X23,X25)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_reduce__poly__simple,axiom,
! [X9,X23] :
( X23 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X59] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X23),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X59),X9)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [X25,X26,X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Oplus__class_Oplus(X8,X26,X25))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X10,X26)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X23,X25)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_poly__cont,axiom,
! [X13,X20,X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ? [X63] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X63)
& ! [X58] :
( ( 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,X58,X20)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X58,X20)),X63) )
=> 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,X13),X58),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X13),X20))),X56) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).
fof(fact_Deriv_Oinverse__diff__inverse,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),c_Groups_Ominus__class_Ominus(X8,X10,X23))),c_Rings_Oinverse__class_Oinverse(X8,X23))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X9,X11,X41,X22,X45] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45,X22)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X41),X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X41),X9)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X45)),X41),X11),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X9,X11,X41,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X41),X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X41),X9)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X22)),X41),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_poly__replicate__append,axiom,
! [X7,X13,X9,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,c_Groups_Oone__class_Oone(X8),X9)),X13)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X9)),hAPP(c_Polynomial_Opoly(X8,X13),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
fof(fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096,axiom,
? [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),X59) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096) ).
fof(fact_inf__period_I4_J,axiom,
! [X86,X87,X35,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X35,X87)
=> ! [X3,X50] :
( c_Rings_Odvd__class_Odvd(X8,X35,c_Groups_Oplus__class_Oplus(X8,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X8,X35,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X50),X87)),X86)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_inf__period_I3_J,axiom,
! [X86,X87,X35,X8] :
( ( class_Rings_Ocomm__ring(X8)
& class_Rings_Odvd(X8) )
=> ( c_Rings_Odvd__class_Odvd(X8,X35,X87)
=> ! [X3,X50] :
( c_Rings_Odvd__class_Odvd(X8,X35,c_Groups_Oplus__class_Oplus(X8,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X8,X35,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X50),X87)),X86)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_rnc,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rnc) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X71,X72,X38,X6,X12,X23] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X12),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X12) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X71,X72,X38,X6,X12,X23] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X12),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X38)
=> ( 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),X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X38,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,X72) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_mult_Opos__bounded,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X76] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76)
& ! [X77,X82] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X77),X82)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X77)),c_RealVector_Onorm__class_Onorm(X8,X82))),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_inverse__add,axiom,
! [X23,X10,X8] :
( class_Fields_Ofield(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)),c_Rings_Oinverse__class_Oinverse(X8,X10))),c_Rings_Oinverse__class_Oinverse(X8,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
fof(fact_unique__quotient__lemma,axiom,
! [X6,X12,X71,X72,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X72),X71),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X12),X6))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X71)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X23)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,X12) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X6,X12,X71,X72,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X72),X71),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X12),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,X23,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X71)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,X72) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X14,X15,X64,X62,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X62)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X62,X61)),X64),X15) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X14,X15,X64,X61,X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X61)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X64),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X64),X14)
<=> X15 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X62)),X64),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35)
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X16,X19)),X60),X36) = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X35,X19,X36,X60,X16,X8] :
( class_Rings_Oring(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X60),X36) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X60),X35)
<=> X36 = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X19,X16)),X60),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_unimodular__reduce__norm,axiom,
! [X20] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X20) = 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,X20,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,X20,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,X20,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,X20,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).
fof(fact_mult__diff__mult,axiom,
! [X23,X10,X5,X7,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ominus__class_Ominus(X8,X5,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X10)),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X9)),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_combine__common__factor,axiom,
! [X26,X23,X56,X10,X8] :
( class_Rings_Osemiring(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X56),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X56),X26)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)),X56),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_division__ring__inverse__diff,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),c_Groups_Ominus__class_Ominus(X8,X23,X10))),c_Rings_Oinverse__class_Oinverse(X8,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
fof(fact_division__ring__inverse__add,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),c_Groups_Oplus__class_Oplus(X8,X10,X23))),c_Rings_Oinverse__class_Oinverse(X8,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
fof(fact_convex__bound__le,axiom,
! [X40,X41,X5,X10,X7,X8] :
( class_Rings_Olinordered__semiring__1(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X41)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X40)
=> ( c_Groups_Oplus__class_Oplus(X8,X41,X40) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X41),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X40),X5)),X10) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X40,X41,X5,X10,X7,X8] :
( class_Rings_Olinordered__semiring__1__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X10)
=> ( c_Orderings_Oord__class_Oless(X8,X5,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X41)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X40)
=> ( c_Groups_Oplus__class_Oplus(X8,X41,X40) = c_Groups_Oone__class_Oone(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X41),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X40),X5)),X10) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_unity__coeff__ex,axiom,
! [X47,X51,X8] :
( ( class_Rings_Odvd(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ? [X3] : hBOOL(hAPP(X51,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X47),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X8,X47,c_Groups_Oplus__class_Oplus(X8,X3,c_Groups_Ozero__class_Ozero(X8)))
& hBOOL(hAPP(X51,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_left__add__mult__distrib,axiom,
! [X44,X45,X41,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X41),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X41),X44)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45)),X41),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_real__mult__inverse__cancel,axiom,
! [X41,X5,X57,X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X57)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X57),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X41))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X57)),X41)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X17,X18,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X17)))
<=> ( X18 != c_Groups_Ozero__class_Ozero(X8)
| X17 != c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X27,X28,X29,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X17,X18,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X17)),c_Groups_Ozero__class_Ozero(X8))
<=> ( X18 = c_Groups_Ozero__class_Ozero(X8)
& X17 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_ath,axiom,
! [X52,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7,X52)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X52,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X52)),X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath) ).
fof(fact_mult__pCons__left,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_OpCons(X8,X10,X13)),X12) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X12),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(fact_offset__poly__pCons,axiom,
! [X85,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X8,c_Polynomial_OpCons(X8,X10,X13),X85) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X85,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X8,X13,X85)),c_Polynomial_OpCons(X8,X10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X8,X13,X85))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_real__mult__inverse__cancel2,axiom,
! [X41,X5,X57,X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X57)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X57),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X41))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X41),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X57))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).
fof(fact_realpow__minus__mult,axiom,
! [X7,X9,X8] :
( class_Groups_Omonoid__mult(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_crossproduct__noteq,axiom,
! [X35,X36,X19,X16,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( ( X16 != X19
& X36 != X35 )
<=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X35)) != c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X31,X18,X17,X32,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X32),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X31)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X32),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X17))
<=> ( X32 = X18
| X17 = X31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_abs__diff__less__iff,axiom,
! [X65,X16,X18,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X18,X16)),X65)
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ominus__class_Ominus(X8,X16,X65),X18)
& c_Orderings_Oord__class_Oless(X8,X18,c_Groups_Oplus__class_Oplus(X8,X16,X65)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_mult__pCons__right,axiom,
! [X12,X10,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),c_Polynomial_OpCons(X8,X10,X12)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_power__minus,axiom,
! [X9,X10,X8] :
( class_Rings_Oring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_q__neg__lemma,axiom,
! [X71,X72,X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71),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),X71)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X72,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X71,X72,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X72),X71))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X38)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X72) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23))),c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_norm__triangle__ineq3,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> 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(X8,X10),c_RealVector_Onorm__class_Onorm(X8,X23))),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_pcompose__pCons,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Polynomial_OpCons(X8,X10,X13),X12) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X12),c_Polynomial_Opcompose(X8,X13,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X27,X28,X29,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X27,X28,X29,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [X10,X23] : 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,X23,X10)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X20,X21] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X21,X20)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X20))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_mult__poly__add__left,axiom,
! [X6,X12,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,X12)),X6) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X12),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_nat__diff__split,axiom,
! [X19,X16,X51] :
( hBOOL(hAPP(X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X19)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X19)
=> hBOOL(hAPP(X51,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X63] :
( X16 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X63)
=> hBOOL(hAPP(X51,X63)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_abs__mult__less,axiom,
! [X25,X23,X26,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,X10),X26)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,X23),X25)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oabs__class_Oabs(X8,X10)),c_Groups_Oabs__class_Oabs(X8,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_mult__monom,axiom,
! [X9,X23,X11,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Omonom(X8,X10,X11)),c_Polynomial_Omonom(X8,X23,X9)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(fact_power__Suc__less,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_odd__less__0,axiom,
! [X31] :
( 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),X31),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X31,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X4,X5,X6,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X5),X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X7,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_poly__mult,axiom,
! [X7,X12,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Polynomial_Opoly(X8,X13),X7)),hAPP(c_Polynomial_Opoly(X8,X12),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_mult__eq__if,axiom,
! [X9,X11] :
( ( X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X11 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_le__diff__iff,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X48))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X14)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X48),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X48))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_mult__mono_H,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_norm__mult__less,axiom,
! [X4,X5,X6,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X5),X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_synthetic__div__correct,axiom,
! [X26,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,c_Polynomial_Osmult(X8,X26,c_Polynomial_Osynthetic__div(X8,X13,X26))) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X13),X26),c_Polynomial_Osynthetic__div(X8,X13,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(fact_power__mult__distrib,axiom,
! [X9,X23,X10,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X23),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X12,X5,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X5),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X7,X8] :
( class_Rings_Oring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),c_Groups_Oone__class_Oone(X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Oone__class_Oone(X8))),c_Groups_Ominus__class_Ominus(X8,X7,c_Groups_Oone__class_Oone(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_poly__pCons,axiom,
! [X7,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_OpCons(X8,X10,X13)),X7) = c_Groups_Oplus__class_Oplus(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),hAPP(c_Polynomial_Opoly(X8,X13),X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_power__less__power__Suc,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X23,X26,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X23,X10,X26,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X36)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X23,X26,X10,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X23,X26,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X23,X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X23),X9))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X23,X10,X26,X8] :
( class_Rings_Olinordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X23,X10,X26,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X36)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> c_Orderings_Oord__class_Oless(X8,X16,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X36,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> c_Orderings_Oord__class_Oless__eq(X8,X19,X16) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X36,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> c_Orderings_Oord__class_Oless(X8,X19,X16) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_power__increasing__iff,axiom,
! [X17,X18,X19,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X19),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X19),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X9,X11,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X9,X11,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X17,X18,X19,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X19)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X19),X18),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X19),X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_diff__pCons,axiom,
! [X12,X23,X13,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X10,X13),c_Polynomial_OpCons(X8,X23,X12)) = c_Polynomial_OpCons(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(fact_add__pCons,axiom,
! [X12,X23,X13,X10,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X10,X13),c_Polynomial_OpCons(X8,X23,X12)) = c_Polynomial_OpCons(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(fact_poly__power,axiom,
! [X7,X9,X13,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X8)),X13),X9)),X7) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(c_Polynomial_Opoly(X8,X13),X7)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_le__mult__natfloor,axiom,
! [X23,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X10)),c_RComplete_Onatfloor(X23)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X25,X23,X26,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23),c_Groups_Ominus__class_Ominus(X8,X26,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Oplus__class_Oplus(X8,X26,X25)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_power__decreasing,axiom,
! [X10,X24,X9,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X10,X24,X9,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X24),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__strict__mono,axiom,
! [X9,X23,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X23),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X36)
& c_Orderings_Oord__class_Oless(X8,X16,X19) )
| ( c_Orderings_Oord__class_Oless(X8,X36,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X19,X16) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X19,X36,X16,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X36))
<=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X36)
& c_Orderings_Oord__class_Oless(X8,X16,X19) )
| ( c_Orderings_Oord__class_Oless(X8,X36,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless(X8,X19,X16) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X5,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X76] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X3),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> ? [X76] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X3)),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X23,X11,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mult__left_Odiff,axiom,
! [X33,X5,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X7,X5)),X33) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_mult_Odiff__left,axiom,
! [X23,X34,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ominus__class_Ominus(X8,X10,X34)),X23) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X34),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)),X26) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)),X26) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_mult_Oadd__left,axiom,
! [X23,X34,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,X34)),X23) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X34),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_mult__left_Oadd,axiom,
! [X33,X5,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X7,X5)),X33) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X12,X13,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X13)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X12)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X9,X11,X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X28,X29,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X28)),X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23)),c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ominus__class_Ominus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23)),c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X23,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23)),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X25,X26,X23,X10,X6,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X6 != c_Groups_Ozero__class_Ozero(X8)
=> ( ( X10 = X23
& X26 != X25 )
=> c_Groups_Oplus__class_Oplus(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X26)) != c_Groups_Oplus__class_Oplus(X8,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X6),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_mult__le__cancel2,axiom,
! [X14,X48,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X48))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X17,X18,X31] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X31))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X17,X18,X31] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X9,X11,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X11),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X9))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_real__mult__less__iff1,axiom,
! [X17,X18,X31] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X31)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X31))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_natceiling__eq,axiom,
! [X7,X9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10),c_RealVector_Onorm__class_Onorm(X8,X23)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__diff__ineq,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10),c_RealVector_Onorm__class_Onorm(X8,X23)),c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10),c_RealVector_Onorm__class_Onorm(X8,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_norm__triangle__ineq,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oplus__class_Oplus(X8,X7,X5)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_RealVector_Onorm__class_Onorm(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_mult__smult__left,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Polynomial_Osmult(X8,X10,X13)),X12) = c_Polynomial_Osmult(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_poly__diff,axiom,
! [X7,X12,X13,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X13,X12)),X7) = c_Groups_Ominus__class_Ominus(X8,hAPP(c_Polynomial_Opoly(X8,X13),X7),hAPP(c_Polynomial_Opoly(X8,X12),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__add,axiom,
! [X7,X12,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,X12)),X7) = c_Groups_Oplus__class_Oplus(X8,hAPP(c_Polynomial_Opoly(X8,X13),X7),hAPP(c_Polynomial_Opoly(X8,X12),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_le__diff__conv2,axiom,
! [X62,X61,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X61)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X48))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X62,X48),X61) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X21,X54,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X55,X54)),X21) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X54),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X21,X54,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54)),X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X54),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X44,X9,X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)),X44) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X44,X9,X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)),X44) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X21,X54,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X55,X54)),X21) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_norm__power__ineq,axiom,
! [X9,X7,X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__le__cancel__right,axiom,
! [X19,X36,X16,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X16,X36),c_Groups_Oplus__class_Oplus(X8,X19,X36))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X23,X26,X10,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X26))
=> c_Orderings_Oord__class_Oless__eq(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X19,X16,X36,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X36,X16),c_Groups_Oplus__class_Oplus(X8,X36,X19))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X23,X10,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X10),c_Groups_Oplus__class_Oplus(X8,X26,X23))
=> c_Orderings_Oord__class_Oless__eq(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__cancel__right,axiom,
! [X19,X36,X16,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X16,X36),c_Groups_Oplus__class_Oplus(X8,X19,X36))
<=> c_Orderings_Oord__class_Oless(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X23,X26,X10,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X26))
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X19,X16,X36,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X36,X16),c_Groups_Oplus__class_Oplus(X8,X36,X19))
<=> c_Orderings_Oord__class_Oless(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X23,X10,X26,X8] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X10),c_Groups_Oplus__class_Oplus(X8,X26,X23))
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X9,X11,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X9)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X44),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X44)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X19,X16,X36,X8] :
( class_Rings_Oidom(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X36),X19))
<=> ( X36 = c_Groups_Ozero__class_Ozero(X8)
| c_Rings_Odvd__class_Odvd(X8,X16,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_power__gt1__lemma,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X58] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X58),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X20,X5,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X10,X13,X26,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X26,X13),c_Polynomial_OpCons(X8,X10,X13)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_self__quotient__aux2,axiom,
! [X12,X6,X10] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> ( X10 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [X12,X6,X10] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> ( X10 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),X12))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_smult__diff__right,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X13,X12)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),c_Polynomial_Osmult(X8,X10,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(fact_smult__add__right,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X10,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,X12)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),c_Polynomial_Osmult(X8,X10,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X23,X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X23),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
=> X10 = X23 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X11,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X11),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oone__class_Oone(X8))),X11) ),
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,
! [X10,X11,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oone__class_Oone(X8))),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_natfloor__eq,axiom,
! [X7,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X7) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_mult__right__le__one__le,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X7),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X5,X7,X26,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),c_RealVector_Onorm__class_Onorm(X8,X5)))
=> X7 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__right__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Oordered__comm__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Oordered__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_power__mono,axiom,
! [X9,X23,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X23),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Olinordered__comm__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__right__mono__neg,axiom,
! [X26,X10,X23,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X26,X10,X23,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X26,X10,X23,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X10)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X26,X10,X23,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X10)
=> ( c_Orderings_Oord__class_Oless(X8,X26,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X26),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X11,X9,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X11),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X26,X25)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X26,X25)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_power__increasing,axiom,
! [X10,X24,X9,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X10,X24,X9,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X24)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_abs__eq__mult,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__ring__abs(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
| c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8)) )
& ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
| c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8)) ) )
=> c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oabs__class_Oabs(X8,X10)),c_Groups_Oabs__class_Oabs(X8,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_diff__monom,axiom,
! [X23,X9,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X10,X9),c_Polynomial_Omonom(X8,X23,X9)) = c_Polynomial_Omonom(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(fact_add__monom,axiom,
! [X23,X9,X10,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X10,X9),c_Polynomial_Omonom(X8,X23,X9)) = c_Polynomial_Omonom(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(fact_smult__diff__left,axiom,
! [X13,X23,X10,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23),X13) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),c_Polynomial_Osmult(X8,X23,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(fact_smult__add__left,axiom,
! [X13,X23,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X13) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),c_Polynomial_Osmult(X8,X23,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(fact_mult__dvd__mono,axiom,
! [X25,X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X10,X23)
=> ( c_Rings_Odvd__class_Odvd(X8,X26,X25)
=> c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_realpow__num__eq__if,axiom,
! [X11,X9,X8] :
( class_Power_Opower(X8)
=> ( ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X9) = c_Groups_Oone__class_Oone(X8) )
& ( X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X11),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_smult__pCons,axiom,
! [X13,X23,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X10,c_Polynomial_OpCons(X8,X23,X13)) = c_Polynomial_OpCons(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Polynomial_Osmult(X8,X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(fact_add__le__mono,axiom,
! [X46,X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X46)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X20,X69,X21,X70] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X69,X20)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X69),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X26,X23,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X26),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X46,X9,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X46)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X46,X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X46,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X46,X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X46)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X17,X18,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X17)) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X18 = c_Groups_Ozero__class_Ozero(X8)
& X17 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [X5,X7,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5)))
=> X7 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_mult__right_Odiff,axiom,
! [X5,X7,X37,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),c_Groups_Ominus__class_Ominus(X8,X7,X5)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Odiff__right,axiom,
! [X38,X23,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ominus__class_Ominus(X8,X23,X38)) = c_Groups_Ominus__class_Ominus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X20,X5,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Oplus__class_Oplus(X8,X5,X20)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult_Oadd__right,axiom,
! [X38,X23,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Oplus__class_Oplus(X8,X23,X38)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_mult__right_Oadd,axiom,
! [X5,X7,X37,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),c_Groups_Oplus__class_Oplus(X8,X7,X5)) = c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult__less__cancel1,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X14,X48,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X48))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X10,X23,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X10))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oab__semigroup__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X28,X29,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X29)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X29),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_power__commutes,axiom,
! [X9,X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X27,X28,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X28)),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_nat__less__real__le,axiom,
! [X15,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X15)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X15,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X15),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_poly__monom,axiom,
! [X7,X9,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Omonom(X8,X10,X9)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_synthetic__div__unique,axiom,
! [X6,X12,X26,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,c_Polynomial_Osmult(X8,X26,X12)) = c_Polynomial_OpCons(X8,X6,X12)
=> ( X6 = hAPP(c_Polynomial_Opoly(X8,X13),X26)
& X12 = c_Polynomial_Osynthetic__div(X8,X13,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_reals__Archimedean6,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ? [X49] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X49,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_synthetic__div__pCons,axiom,
! [X26,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Polynomial_OpCons(X8,X10,X13),X26) = c_Polynomial_OpCons(X8,hAPP(c_Polynomial_Opoly(X8,X13),X26),c_Polynomial_Osynthetic__div(X8,X13,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_power__mult,axiom,
! [X9,X11,X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X11)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X12,X13,X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X13)),X12) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X45)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X44)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X44),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X44)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X44)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X45)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X5,X7,X20] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X20)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_power__eq__if,axiom,
! [X13,X11] :
( ( X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),X11) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X11 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_le__diff__conv,axiom,
! [X62,X48,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X48),X62)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X62,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X48,X61,X62] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X62,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X48))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X62,X48),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X46,X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X46)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_add__diff__assoc2,axiom,
! [X22,X45,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X45)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X44),X22) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X22),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X22,X45,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X45)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X22),X44) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X44),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X22,X45,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X45)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45),X44) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X22,X45,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X45)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X44)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X44),X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X22,X45,X44] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X45)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X44)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_mult__smult__right,axiom,
! [X12,X10,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),c_Polynomial_Osmult(X8,X10,X12)) = c_Polynomial_Osmult(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_poly__smult,axiom,
! [X7,X13,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Osmult(X8,X10,X13)),X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(c_Polynomial_Opoly(X8,X13),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_mult__le__0__iff,axiom,
! [X19,X16,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X19),c_Groups_Ozero__class_Ozero(X8))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16)
& c_Orderings_Oord__class_Oless__eq(X8,X19,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X19) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X19,X16,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X19))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X19) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X19,c_Groups_Ozero__class_Ozero(X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X18)),X14))
<=> ( X18 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X54,X55,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X55,X54)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X54,X55,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X9,X11,X44] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X9,X11,X44] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_poly__pcompose,axiom,
! [X7,X12,X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Polynomial_Opcompose(X8,X13,X12)),X7) = hAPP(c_Polynomial_Opoly(X8,X13),hAPP(c_Polynomial_Opoly(X8,X12),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X11,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X11,X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_Bseq__inverse__lemma,axiom,
! [X7,X6,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealVector_Onorm__class_Onorm(X8,X7))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X7)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X17,X18] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X17)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X17 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_cq0,axiom,
! [X58] : 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_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X58))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cq0) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__pos__nonneg,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X10,X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__gr__0,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_zmult__assoc,axiom,
! [X53,X54,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),X54)),X53) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X54),X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X44,X9,X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9)),X44) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X53,X54,X55] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),X54)),X53) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X55),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X54),X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_zpower__zpower,axiom,
! [X20,X5,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X5)),X20) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
& c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8)) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X10),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__neg__pos,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X10),c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_split__mult__pos__le,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__ring(X8)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23) )
| ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
& c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8)) ) )
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__cancel__semiring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__pos__pos,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__semiring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_less__1__mult,axiom,
! [X9,X11,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X11)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X9)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X11),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X23,X10,X8] :
( class_Rings_Oordered__ring(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__neg__neg,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_add__right__mono,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X26,X10),c_Groups_Oplus__class_Oplus(X8,X26,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),c_Groups_Oplus__class_Oplus(X8,X23,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X26,X10),c_Groups_Oplus__class_Oplus(X8,X26,X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X66] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X66)
=> ~ ! [X59] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X59),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> 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_s____),X59)),X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096,axiom,
? [X66] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X66)
& ! [X59] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X59),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> 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_s____),X59)),X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096) ).
fof(fact_m_I2_J,axiom,
! [X59] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X59),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
=> 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_s____),X59)),v_m____) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I2_J) ).
fof(fact_c,axiom,
! [X58] : 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_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X58))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_c) ).
fof(fact_one__less__power,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_decseq__def,axiom,
! [X80,X8] :
( class_Orderings_Oorder(X8)
=> ( c_SEQ_Odecseq(X8,X80)
<=> ! [X66,X49] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X49)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(X80,X49),hAPP(X80,X66)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X9,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X9)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X20,c_RealDef_Oreal(tc_Nat_Onat,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_add__increasing,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X26)
=> c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Oplus__class_Oplus(X8,X10,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X10,X23,X26,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X26)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X10)
=> c_Orderings_Oord__class_Oless__eq(X8,X23,c_Groups_Oplus__class_Oplus(X8,X10,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X26)
=> c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Oplus__class_Oplus(X8,X10,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X26)
=> c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Oplus__class_Oplus(X8,X10,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X26)
=> c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Oplus__class_Oplus(X8,X10,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_real__minus__mult__self__le,axiom,
! [X7,X41] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X41),X41)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_zadd__left__mono,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X44,X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X44,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X46,X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X46),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X46,X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X46,X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X46,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X20,X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X20,X7),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X20,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X45)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X44),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X45,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_abs__power__minus,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),X9)) = c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).
fof(fact_dvd__diff,axiom,
! [X20,X5,X7,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X5)
=> ( c_Rings_Odvd__class_Odvd(X8,X7,X20)
=> c_Rings_Odvd__class_Odvd(X8,X7,c_Groups_Ominus__class_Ominus(X8,X5,X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_of__real_Obounded,axiom,
! [X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> ? [X76] :
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X76)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Obounded) ).
fof(fact_of__real_Ononneg__bounded,axiom,
! [X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> ? [X76] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ononneg__bounded) ).
fof(fact_of__real_Opos__bounded,axiom,
! [X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> ? [X76] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X76)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Opos__bounded) ).
fof(fact_abs__add__abs,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Oplus__class_Oplus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23))) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Oabs__class_Oabs(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_smult__dvd__iff,axiom,
! [X75,X73,X16,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X16,X73),X75)
<=> ( ( X16 = c_Groups_Ozero__class_Ozero(X8)
=> X75 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) )
& ( X16 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X73,X75) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(fact_dvd__smult__cancel,axiom,
! [X12,X10,X13,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,c_Polynomial_Osmult(X8,X10,X12))
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
fof(fact_dvd__smult__iff,axiom,
! [X75,X73,X16,X8] :
( class_Fields_Ofield(X8)
=> ( X16 != c_Groups_Ozero__class_Ozero(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X73,c_Polynomial_Osmult(X8,X16,X75))
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X73,X75) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
fof(fact_eq__diff__iff,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X14)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X48) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X48)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__less,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_natfloor__subtract,axiom,
! [X7,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X10),X7)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X10))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_natceiling__subtract,axiom,
! [X7,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X10),X7)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X10))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_smult__dvd__cancel,axiom,
! [X12,X13,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),X12)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X16,X16))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,X16,X16))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oplus__class_Oplus(X8,X16,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X16,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,X16,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X26) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Oab__semigroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X26) = c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oplus__class_Oplus(X8,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X26) = c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oplus__class_Oplus(X8,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X25,X26,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oplus__class_Oplus(X8,X26,X25)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X26),X25) ),
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,
! [X25,X26,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oplus__class_Oplus(X8,X26,X25)) = c_Groups_Oplus__class_Oplus(X8,X26,c_Groups_Oplus__class_Oplus(X8,X10,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_real__0__le__add__iff,axiom,
! [X17,X18] :
( 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,X18,X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__0__less__add__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_inverse__le__imp__le,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
fof(fact_inverse__less__imp__less,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23))
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
fof(fact_inverse__le__imp__le__neg,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23))
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
fof(fact_inverse__less__imp__less__neg,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Rings_Oinverse__class_Oinverse(X8,X23))
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X16,X19)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ominus__class_Ominus(X8,X16,X19),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X16,X19)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ominus__class_Ominus(X8,X16,X19),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_smult__monom,axiom,
! [X9,X23,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X10,c_Polynomial_Omonom(X8,X23,X9)) = c_Polynomial_Omonom(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(fact_smult__smult,axiom,
! [X13,X23,X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X10,c_Polynomial_Osmult(X8,X23,X13)) = c_Polynomial_Osmult(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X5,X7] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_real__mult__order,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_abs__mult__pos,axiom,
! [X5,X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oabs__class_Oabs(X8,X5)),X7) = c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_le__cube,axiom,
! [X11] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X11))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X35,X36,X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X16,X19) = c_Groups_Ominus__class_Ominus(X8,X36,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X16,X19)
<=> c_Orderings_Oord__class_Oless__eq(X8,X36,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X35,X36,X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X16,X19) = c_Groups_Ominus__class_Ominus(X8,X36,X35)
=> ( c_Orderings_Oord__class_Oless(X8,X16,X19)
<=> c_Orderings_Oord__class_Oless(X8,X36,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_mult__le__mono1,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X27,X28,X30,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),X27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X28),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X9,X11,X44] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X9)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X9,X44,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X44)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X44,X45,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X45),X44) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X44),X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X44,X45,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X45),X44) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X53,X54,X55] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54),X53) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X44,X9,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9),X44) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X20,X5,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,X20)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X20,X5,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X31,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X31)
| X32 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X32,c_Groups_Oone__class_Oone(tc_Int_Oint)),X31)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X31,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X31,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_dvd__mult__left,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),X26)
=> c_Rings_Odvd__class_Odvd(X8,X10,X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23),X26)
=> c_Rings_Odvd__class_Odvd(X8,X23,X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_real__le__eq__diff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X17),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_less__bin__lemma,axiom,
! [X47,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X48,X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zero__less__diff,axiom,
! [X15,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X14,X15))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X9,X11,X46,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X46)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X46) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X9)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_natfloor__add,axiom,
! [X10,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X10))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_natceiling__add,axiom,
! [X10,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X10))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_abs__leI,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X10),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__le__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X16),X19)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X16,X19)
& c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__less__iff,axiom,
! [X19,X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,X16),X19)
<=> ( c_Orderings_Oord__class_Oless(X8,X16,X19)
& c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_add__leD1,axiom,
! [X9,X44,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X9,X44,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44),X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45),X44)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_real__of__nat__diff,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_RealDef_Oreal(tc_Nat_Onat,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X17,X18,X8] :
( class_Groups_Oordered__comm__monoid__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X17)
=> ( c_Groups_Oplus__class_Oplus(X8,X18,X17) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X18 = c_Groups_Ozero__class_Ozero(X8)
& X17 = c_Groups_Ozero__class_Ozero(X8) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_le__imp__inverse__le,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X23),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
fof(fact_less__imp__inverse__less,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X23),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
fof(fact_le__imp__inverse__le__neg,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X23),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
fof(fact_less__imp__inverse__less__neg,axiom,
! [X23,X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ( c_Orderings_Oord__class_Oless(X8,X23,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X23),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X14))
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X14,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X18),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_minus__apply,axiom,
! [X18,X83,X84,X67,X8] :
( class_Groups_Ominus(X8)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X67,X8),X84,X83),X18) = c_Groups_Ominus__class_Ominus(X8,hAPP(X84,X18),hAPP(X83,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_one__le__inverse__iff,axiom,
! [X18,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X18))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X18)
& c_Orderings_Oord__class_Oless__eq(X8,X18,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
fof(fact_one__le__inverse,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).
fof(fact_one__less__inverse__iff,axiom,
! [X18,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X18))
<=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X18)
& c_Orderings_Oord__class_Oless(X8,X18,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
fof(fact_one__less__inverse,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Oone__class_Oone(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
fof(fact_abs__le__interval__iff,axiom,
! [X65,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),X65)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X65),X18)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X65) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_less__eq__poly__def,axiom,
! [X17,X18,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X8),X18,X17)
<=> ( X18 = X17
| c_Polynomial_Opos__poly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X17,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_less__poly__def,axiom,
! [X17,X18,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),X18,X17)
<=> c_Polynomial_Opos__poly(X8,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X17,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(fact_smult__dvd,axiom,
! [X10,X12,X13,X8] :
( class_Fields_Ofield(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,X12)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13),X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
fof(fact_zero__le__power__abs,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oabs__class_Oabs(X8,X10)),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_pos__poly__pCons,axiom,
! [X73,X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,c_Polynomial_OpCons(X8,X16,X73))
<=> ( c_Polynomial_Opos__poly(X8,X73)
| ( X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
& c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_dvd__smult,axiom,
! [X10,X12,X13,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,X12)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X8),X13,c_Polynomial_Osmult(X8,X10,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(fact_power__inject__exp,axiom,
! [X14,X15,X16,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X16)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X16),X15) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X16),X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_natceiling__le__eq,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X18),X16)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_less__natfloor,axiom,
! [X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X9))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X7),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_le__natfloor__eq,axiom,
! [X16,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_RComplete_Onatfloor(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X16),X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_zero__le__power,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_one__le__power,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X10)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__less__power,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_inverse__le__1__iff,axiom,
! [X18,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X18),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
fof(fact_inverse__less__1__iff,axiom,
! [X18,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X18),c_Groups_Oone__class_Oone(X8))
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,c_Groups_Ozero__class_Ozero(X8))
| c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
fof(fact_natfloor__add__one,axiom,
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X7),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,
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_nonzero__inverse__mult__distrib,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X23)),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
fof(fact_odd__nonzero,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X20),X20) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X7,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X16,X78,X79,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X79,X78),X16),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X79,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_le__imp__0__less,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> 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),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_sgn__times,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Osgn__class_Osgn(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Osgn__class_Osgn(X8,X10)),c_Groups_Osgn__class_Osgn(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).
fof(fact_sgn__mult,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_Groups_Osgn__class_Osgn(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Osgn__class_Osgn(X8,X7)),c_Groups_Osgn__class_Osgn(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).
fof(fact_abs__mult,axiom,
! [X23,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oabs__class_Oabs(X8,X10)),c_Groups_Oabs__class_Oabs(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_inverse__mult__distrib,axiom,
! [X23,X10,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),c_Rings_Oinverse__class_Oinverse(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [X13,X10,X67] :
( class_Groups_Oab__group__add(X67)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X67),c_Polynomial_OpCons(X67,X10,X13)) = c_Polynomial_OpCons(X67,c_Groups_Ouminus__class_Ouminus(X67,X10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X67),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_minus__pCons,axiom,
! [X13,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_OpCons(X8,X10,X13)) = c_Polynomial_OpCons(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(fact_dvd__mult2,axiom,
! [X26,X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X10,X23)
=> c_Rings_Odvd__class_Odvd(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X23,X26,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X10,X26)
=> c_Rings_Odvd__class_Odvd(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_abs__minus__commute,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)) = c_Groups_Oabs__class_Oabs(X8,c_Groups_Ominus__class_Ominus(X8,X23,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_norm__minus__commute,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)) = c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ominus__class_Ominus(X8,X23,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_norm__mult,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),c_RealVector_Onorm__class_Onorm(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X20,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),X9) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X9,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X9)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X22)) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_of__real__mult,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X7),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_RealVector_Oof__real(X8,X7)),c_RealVector_Oof__real(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__mult) ).
fof(fact_le__funE,axiom,
! [X18,X1,X2,X8,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X18),hAPP(X1,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X18,X1,X2,X8,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X18),hAPP(X1,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_less__imp__diff__less,axiom,
! [X9,X44,X45] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X45,X44)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X45,X9),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X20,X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X11,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X5,X20,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X11,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X20,X5,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X11,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X5,X20,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X11,X45,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X45)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_of__real_Odiff,axiom,
! [X5,X7,X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> c_RealVector_Oof__real(X8,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X5)) = c_Groups_Ominus__class_Ominus(X8,c_RealVector_Oof__real(X8,X7),c_RealVector_Oof__real(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Odiff) ).
fof(fact_of__real_Oadd,axiom,
! [X5,X7,X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> c_RealVector_Oof__real(X8,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,X5)) = c_Groups_Oplus__class_Oplus(X8,c_RealVector_Oof__real(X8,X7),c_RealVector_Oof__real(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Oadd) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X7)),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X14,X15,X48] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X48)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_order__trans,axiom,
! [X20,X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X20)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X20,X7,X5,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X20,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X20,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_order__less__le__trans,axiom,
! [X20,X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X20)
=> c_Orderings_Oord__class_Oless(X8,X7,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X20,X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless(X8,X5,X20)
=> c_Orderings_Oord__class_Oless(X8,X7,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__trans,axiom,
! [X20,X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless(X8,X5,X20)
=> c_Orderings_Oord__class_Oless(X8,X7,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [X20,X7,X5,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X5,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X20,X5)
=> c_Orderings_Oord__class_Oless(X8,X20,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I8_J,axiom,
! [X20,X7,X5,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X20,X5)
=> c_Orderings_Oord__class_Oless(X8,X20,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I10_J,axiom,
! [X20,X7,X5,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X5,X7)
=> ( c_Orderings_Oord__class_Oless(X8,X20,X5)
=> c_Orderings_Oord__class_Oless(X8,X20,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X23,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Groups_Ouminus__class_Ouminus(X8,X23)) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_minus__add__distrib,axiom,
! [X23,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Groups_Ouminus__class_Ouminus(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23)) = c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X23),c_Groups_Ouminus__class_Ouminus(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X7] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X7,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_nonzero__power__inverse,axiom,
! [X9,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
fof(fact_of__real__diff,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X5)) = c_Groups_Ominus__class_Ominus(X8,c_RealVector_Oof__real(X8,X7),c_RealVector_Oof__real(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__diff) ).
fof(fact_of__real__add,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,X5)) = c_Groups_Oplus__class_Oplus(X8,c_RealVector_Oof__real(X8,X7),c_RealVector_Oof__real(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__add) ).
fof(fact_compl__le__compl__iff,axiom,
! [X17,X18,X8] :
( class_Lattices_Oboolean__algebra(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X18),c_Groups_Ouminus__class_Ouminus(X8,X17))
<=> c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X16,X19,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X19),c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_neg__less__iff__less,axiom,
! [X16,X19,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X19),c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless(X8,X16,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_mult__left_Ominus,axiom,
! [X5,X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X7)),X5) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),X23) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_power__abs,axiom,
! [X9,X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Oabs__class_Oabs(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oabs__class_Oabs(X8,X10)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_minus__mult__left,axiom,
! [X23,X10,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_power__inverse,axiom,
! [X9,X10,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
fof(fact_smult__minus__right,axiom,
! [X13,X10,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,X10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X13)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X48,X61,X62] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62,X61)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X61,X62) = X48
<=> X61 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X62) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_norm__power,axiom,
! [X9,X7,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> c_RealVector_Onorm__class_Onorm(X8,hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_add__minus__cancel,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_zle__trans,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X45)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X45,X44)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X45)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45,X44)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_real__le__trans,axiom,
! [X44,X45,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X45)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X45,X44)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_pos__poly__mult,axiom,
! [X12,X13,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X13)
=> ( c_Polynomial_Opos__poly(X8,X12)
=> c_Polynomial_Opos__poly(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_real__of__nat__mult,axiom,
! [X9,X11] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X11)),c_RealDef_Oreal(tc_Nat_Onat,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_of__real__power,axiom,
! [X9,X7,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_RealVector_Oof__real(X8,X7)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__power) ).
fof(fact_poly__minus,axiom,
! [X7,X13,X8] :
( class_Rings_Ocomm__ring(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X13)),X7) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(c_Polynomial_Opoly(X8,X13),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_abs__le__D2,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X10),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).
fof(fact_minus__le__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X19)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X19),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_minus__less__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X19)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X19),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_le__minus__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ouminus__class_Ouminus(X8,X19))
<=> c_Orderings_Oord__class_Oless__eq(X8,X19,c_Groups_Ouminus__class_Ouminus(X8,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ouminus__class_Ouminus(X8,X19))
<=> c_Orderings_Oord__class_Oless(X8,X19,c_Groups_Ouminus__class_Ouminus(X8,X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_real__of__nat__add,axiom,
! [X9,X11] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),c_RealDef_Oreal(tc_Nat_Onat,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X21,X20] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X21)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_minus__monom,axiom,
! [X9,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Omonom(X8,X10,X9)) = c_Polynomial_Omonom(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(fact_smult__minus__left,axiom,
! [X13,X10,X8] :
( class_Rings_Ocomm__ring(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X13) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Polynomial_Osmult(X8,X10,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(fact_mult__left__idem,axiom,
! [X23,X10,X8] :
( class_Lattices_Oab__semigroup__idem__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X7] : 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,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_inverse__positive__imp__positive,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X10))
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
fof(fact_inverse__negative__imp__negative,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Groups_Ozero__class_Ozero(X8))
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X15,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_RealDef_Oreal(tc_Nat_Onat,X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X15,X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_RealDef_Oreal(tc_Nat_Onat,X15))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
! [X16,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X16))
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
fof(fact_sgn__greater,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Osgn__class_Osgn(X8,X16))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X16,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X16))
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
! [X16,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Rings_Oinverse__class_Oinverse(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
fof(fact_sgn__less,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Osgn__class_Osgn(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).
fof(fact_inverse__negative__iff__negative,axiom,
! [X16,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_mult__right_Ominus,axiom,
! [X7,X37,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X37),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [X23,X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ouminus__class_Ouminus(X8,X23)) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_minus__mult__right,axiom,
! [X23,X10,X8] :
( class_Rings_Oring(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ouminus__class_Ouminus(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_compl__mono,axiom,
! [X5,X7,X8] :
( class_Lattices_Oboolean__algebra(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X5),c_Groups_Ouminus__class_Ouminus(X8,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X23),c_Groups_Ouminus__class_Ouminus(X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_zero__less__two,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oplus__class_Oplus(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Oone__class_Oone(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X7] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_minus__add__cancel,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Groups_Oplus__class_Oplus(X8,X10,X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_minus__le__self__iff,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X16)
<=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__less__nonneg,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ouminus__class_Ouminus(X8,X16),X16)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_le__minus__self__iff,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless__eq(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ouminus__class_Ouminus(X8,X16))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_zmult__zminus,axiom,
! [X21,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)),X21) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_complex__of__real__power,axiom,
! [X9,X7] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X7)),X9) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(fact_power__real__of__nat,axiom,
! [X9,X11] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X11)),X9) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__power,axiom,
! [X9,X11] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X11)),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_nat__less__cases,axiom,
! [X51,X14,X15] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
=> hBOOL(hAPP(hAPP(X51,X14),X15)) )
=> ( ( X15 = X14
=> hBOOL(hAPP(hAPP(X51,X14),X15)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X15)
=> hBOOL(hAPP(hAPP(X51,X14),X15)) )
=> hBOOL(hAPP(hAPP(X51,X14),X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_negative__imp__inverse__negative,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Orderings_Oord__class_Oless(X8,c_Rings_Oinverse__class_Oinverse(X8,X10),c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X10,X13,X26,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Polynomial_Osmult(X8,X26,X13) = c_Polynomial_OpCons(X8,X10,X13)
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(fact_abs__mult__self,axiom,
! [X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oabs__class_Oabs(X8,X10)),c_Groups_Oabs__class_Oabs(X8,X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_minus__mult__minus,axiom,
! [X23,X10,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),c_Groups_Ouminus__class_Ouminus(X8,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X23,X10,X8] :
( class_Rings_Oring(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,X10)),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ouminus__class_Ouminus(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__dvd__iff,axiom,
! [X17,X18,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,c_Groups_Ouminus__class_Ouminus(X8,X18),X17)
<=> c_Rings_Odvd__class_Odvd(X8,X18,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_abs__le__D1,axiom,
! [X23,X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X10),X23)
=> c_Orderings_Oord__class_Oless__eq(X8,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_dvd__minus__iff,axiom,
! [X17,X18,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> ( c_Rings_Odvd__class_Odvd(X8,X18,c_Groups_Ouminus__class_Ouminus(X8,X17))
<=> c_Rings_Odvd__class_Odvd(X8,X18,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_square__eq__iff,axiom,
! [X19,X16,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X19),X19)
<=> ( X16 = X19
| X16 = c_Groups_Ouminus__class_Ouminus(X8,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_pos__poly__add,axiom,
! [X12,X13,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Polynomial_Opos__poly(X8,X13)
=> ( c_Polynomial_Opos__poly(X8,X12)
=> c_Polynomial_Opos__poly(X8,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X35,X36,X19,X16,X8] :
( class_Groups_Oab__group__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X16,X19) = c_Groups_Ominus__class_Ominus(X8,X36,X35)
=> ( X16 = X19
<=> X36 = X35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_natfloor__power,axiom,
! [X9,X7] :
( X7 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X7),X9)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_minus__diff__eq,axiom,
! [X23,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23)) = c_Groups_Ominus__class_Ominus(X8,X23,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_xt1_I5_J,axiom,
! [X7,X5,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> X7 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X5,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> X7 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X18,X17,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X17,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X17,X18,X8] :
( class_Orderings_Oorder(X8)
=> ( X18 = X17
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
& c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_less__add__one,axiom,
! [X10,X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Oone__class_Oone(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_pCons__eq__iff,axiom,
! [X75,X19,X73,X16,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X16,X73) = c_Polynomial_OpCons(X8,X19,X75)
<=> ( X16 = X19
& X73 = X75 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_monom__eq__iff,axiom,
! [X19,X14,X16,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X16,X14) = c_Polynomial_Omonom(X8,X19,X14)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_add__right__cancel,axiom,
! [X36,X16,X19,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X19,X16) = c_Groups_Oplus__class_Oplus(X8,X36,X16)
<=> X19 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X26,X10,X23,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X23,X10) = c_Groups_Oplus__class_Oplus(X8,X26,X10)
=> X23 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Ocancel__ab__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X23) = c_Groups_Oplus__class_Oplus(X8,X10,X26)
=> X23 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X36,X19,X16,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X16,X19) = c_Groups_Oplus__class_Oplus(X8,X16,X36)
<=> X19 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X26,X23,X10,X8] :
( class_Groups_Ocancel__semigroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X23) = c_Groups_Oplus__class_Oplus(X8,X10,X26)
=> X23 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X9,X11] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X9)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X11) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_natceiling__le,axiom,
! [X10,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,X10))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X10,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_RComplete_Onatfloor(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_order__root,axiom,
! [X16,X73,X8] :
( class_Rings_Oidom(X8)
=> ( hAPP(c_Polynomial_Opoly(X8,X73),X16) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| c_Polynomial_Oorder(X8,X16,X73) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diffs0__imp__equal,axiom,
! [X9,X11] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X11 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_real__natfloor__le,axiom,
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_zero__le__square,axiom,
! [X10,X8] :
( class_Rings_Olinordered__ring(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_zle__antisym,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X20)
=> X20 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> X11 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20)
=> X20 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Oplus__class_Oplus(X8,X10,X23),X23) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ominus__class_Ominus(X8,X10,X23),X23) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X15)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15),X14) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X15 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X14 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [X14,X48,X15] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X48) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X48)
<=> X15 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X14,X15,X48] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X14)
<=> X15 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X74] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X74) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
=> ~ ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X74),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096,axiom,
? [X74] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X74) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X74),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).
fof(fact_q_I2_J,axiom,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I2_J) ).
fof(fact_dvd__triv__left,axiom,
! [X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_le__iff__add,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
<=> ? [X50] : X14 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X47,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48,X47)
<=> ? [X49] : X47 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_diff__add__0,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X11)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__add__inverse,axiom,
! [X11,X9] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X11),X9) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X9,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9),X9) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__le__self,axiom,
! [X9,X11] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X11,X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X11,X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X18),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,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,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oabs__class_Oabs(X8,X16))
<=> X16 != c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096,axiom,
! [X42] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X42)
=> ? [X43] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X43)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X43,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X43,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096) ).
fof(fact_mult__cancel2,axiom,
! [X14,X48,X15] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X48) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X48)
<=> ( X15 = X14
| X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__right__cancel,axiom,
! [X19,X16,X36] :
( X36 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X36)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X14,X15,X48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14)
<=> ( X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X14,X15,X48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X15) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X14)
<=> ( X15 = X14
| X48 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_real__mult__left__cancel,axiom,
! [X19,X16,X36] :
( X36 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X16) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X19)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_tsub__eq,axiom,
! [X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X7)
=> c_Nat__Transfer_Otsub(X7,X5) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_order__less__le,axiom,
! [X17,X18,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
& X18 != X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X17,X18,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless(X8,X18,X17)
| X18 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__neq__le__trans,axiom,
! [X23,X10,X8] :
( class_Orderings_Oorder(X8)
=> ( X10 != X23
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X5,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
| X7 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X23,X10,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,X23)
=> ( X10 != X23
=> c_Orderings_Oord__class_Oless(X8,X10,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X10,X23,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X10)
=> ( X10 != X23
=> c_Orderings_Oord__class_Oless(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X23,X10,X8] :
( class_Orderings_Oorder(X8)
=> ( X10 != X23
=> ( c_Orderings_Oord__class_Oless__eq(X8,X23,X10)
=> c_Orderings_Oord__class_Oless(X8,X23,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X7,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X7) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_natfloor__mono,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X7),c_RComplete_Onatfloor(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natceiling__mono,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X7),c_RComplete_Onatceiling(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_abs__le__zero__iff,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oabs__class_Oabs(X8,X16),c_Groups_Ozero__class_Ozero(X8))
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_order__less__imp__le,axiom,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_dvdI,axiom,
! [X44,X23,X10,X8] :
( class_Rings_Odvd(X8)
=> ( X10 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X44)
=> c_Rings_Odvd__class_Odvd(X8,X23,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_abs__minus__le__zero,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oabs__class_Oabs(X8,X10)),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X31] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X31)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X18,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X18))
<=> X18 != c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X7] : 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,X7)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_le__square,axiom,
! [X11] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_diff__minus__eq__add,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X10,c_Groups_Ouminus__class_Ouminus(X8,X23)) = c_Groups_Oplus__class_Oplus(X8,X10,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X5,X7,X8] :
( class_Rings_Ocomm__ring__1(X8)
=> c_Groups_Ominus__class_Ominus(X8,X7,X5) = c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ouminus__class_Ouminus(X8,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_ab__diff__minus,axiom,
! [X23,X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X10,X23) = c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ouminus__class_Ouminus(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X10,X23) = c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ouminus__class_Ouminus(X8,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_norm__le__zero__iff,axiom,
! [X18,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X18 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X14,X15] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X32,X31] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X31,X32)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X31,X32)
& X31 != X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
& X15 != X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
| X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> ( X11 != X9
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__eq__real__def,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
| X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
& X18 != X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_complex__i__mult__minus,axiom,
! [X7] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X7)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(fact_uminus__apply,axiom,
! [X18,X84,X67,X8] :
( class_Groups_Ouminus(X8)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X67,X8),X84),X18) = c_Groups_Ouminus__class_Ouminus(X8,hAPP(X84,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_mult__sgn__abs,axiom,
! [X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Osgn__class_Osgn(X8,X7)),c_Groups_Oabs__class_Oabs(X8,X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_monom__0,axiom,
! [X10,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X8,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(fact_sgn__neg,axiom,
! [X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Osgn__class_Osgn(X8,X10) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).
fof(fact_sgn__1__neg,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Groups_Osgn__class_Osgn(X8,X16) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8))
<=> c_Orderings_Oord__class_Oless(X8,X16,c_Groups_Ozero__class_Ozero(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__imp__le__nat,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X9,X11] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
| X11 = X9 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_abs__of__nonpos,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = c_Groups_Ouminus__class_Ouminus(X8,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__of__neg,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = c_Groups_Ouminus__class_Ouminus(X8,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).
fof(fact_mult__poly__0__left,axiom,
! [X12,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X21,X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X21,X20] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X20,X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_complex__diff__def,axiom,
! [X5,X7] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X7,X5) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X7,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(fact_real__diff__def,axiom,
! [X4,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X4) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(fact_minus__real__def,axiom,
! [X5,X7] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,X5) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X7,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_zabs__less__one__iff,axiom,
! [X31] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X31),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> X31 = 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,
! [X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X14 = 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_smult__eq__0__iff,axiom,
! [X73,X16,X8] :
( class_Rings_Oidom(X8)
=> ( c_Polynomial_Osmult(X8,X16,X73) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X8)
| X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [X16,X18] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X16)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X18 = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X14,X16,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Omult__zero(X8)
& class_Rings_Ono__zero__divisors(X8)
& class_Rings_Ozero__neq__one(X8) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X8),X16),X14) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X16 = c_Groups_Ozero__class_Ozero(X8)
& X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [X18,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X18),X18) = c_Groups_Oone__class_Oone(X8)
<=> ( X18 = c_Groups_Oone__class_Oone(X8)
| X18 = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_sgn__pos,axiom,
! [X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Groups_Osgn__class_Osgn(X8,X10) = c_Groups_Oone__class_Oone(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Groups_Osgn__class_Osgn(X8,X16) = c_Groups_Oone__class_Oone(X8)
<=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_field__inverse,axiom,
! [X10,X8] :
( class_Fields_Ofield(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),X10) = c_Groups_Oone__class_Oone(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
fof(fact_left__inverse,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X10)),X10) = c_Groups_Oone__class_Oone(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X73,X16,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X16,X73) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X16 = c_Groups_Ozero__class_Ozero(X8)
& X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( X18 != X17
<=> ( c_Orderings_Oord__class_Oless(X8,X18,X17)
| c_Orderings_Oord__class_Oless(X8,X17,X18) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
| X7 = X5
| c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_constant__def,axiom,
! [X2,X67,X8] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X8,X67,X2)
<=> ! [X3,X68] : hAPP(X2,X3) = hAPP(X2,X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
fof(fact_abs__of__nonneg,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Groups_Oabs__class_Oabs(X8,X10) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X10)
=> c_Groups_Oabs__class_Oabs(X8,X10) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_linorder__linear,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
| c_Orderings_Oord__class_Oless__eq(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
| c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X26,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,X26) = c_Groups_Oplus__class_Oplus(X8,X26,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_minus__unique,axiom,
! [X23,X10,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X10,X23) = c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,X10) = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X19,X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X16 = c_Groups_Ouminus__class_Ouminus(X8,X19)
<=> c_Groups_Oplus__class_Oplus(X8,X16,X19) = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X17,X18,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X18,X17) = c_Groups_Ozero__class_Ozero(X8)
<=> X17 = c_Groups_Ouminus__class_Ouminus(X8,X18) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_monom__eq__0__iff,axiom,
! [X14,X16,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_Omonom(X8,X16,X14) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),c_Groups_Oabs__class_Oabs(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
fof(fact_qnc,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qnc) ).
fof(fact_less_Oprems,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Oprems) ).
fof(fact_assms,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_mult__poly__0__right,axiom,
! [X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X8)),X13),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X23,X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_inverse__unique,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) = c_Groups_Oone__class_Oone(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X10) = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
fof(fact_zless__linear,axiom,
! [X5,X7] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X5)
| X7 = X5
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X14,X15] :
( X15 != X14
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_zle__linear,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X20,X21)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_real__le__linear,axiom,
! [X21,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X20,X21)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_mult__eq__0__iff,axiom,
! [X19,X16,X8] :
( class_Rings_Oring__no__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X16),X19) = c_Groups_Ozero__class_Ozero(X8)
<=> ( X16 = c_Groups_Ozero__class_Ozero(X8)
| X19 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_divisors__zero,axiom,
! [X23,X10,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) = c_Groups_Ozero__class_Ozero(X8)
=> ( X10 = c_Groups_Ozero__class_Ozero(X8)
| X23 = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X23,X10,X8] :
( class_Rings_Ono__zero__divisors(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X23) != c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [X12,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_zadd__commute,axiom,
! [X21,X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X9,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Oplus__class_Oplus(X8,X16,X16) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Oplus__class_Oplus(X8,X16,X16)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X19,X16,X8] :
( class_Groups_Oab__group__add(X8)
=> ( X16 = X19
<=> c_Groups_Ominus__class_Ominus(X8,X16,X19) = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X19,X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ominus__class_Ominus(X8,X16,X19) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_field__power__not__zero,axiom,
! [X9,X10,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),X9) != c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X17,X18] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X17 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [X16,X19,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( X19 = c_Groups_Oplus__class_Oplus(X8,X19,X16)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_abs__sgn,axiom,
! [X44,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Oabs__class_Oabs(X8,X44) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X44),c_Groups_Osgn__class_Osgn(X8,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).
fof(fact_poly__zero,axiom,
! [X73,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X73) = c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
<=> X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_real__mult__inverse__left,axiom,
! [X7] :
( X7 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)),X7) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
fof(fact_less__imp__neq,axiom,
! [X5,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> X7 != X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X5,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> X7 != X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X5,X7,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> X5 != X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_pCons__0__0,axiom,
! [X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_OpCons(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_one__poly__def,axiom,
! [X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8)) = c_Polynomial_OpCons(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(fact_natfloor__neg,axiom,
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [X7] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_right__inverse,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Rings_Oinverse__class_Oinverse(X8,X10)) = c_Groups_Oone__class_Oone(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
fof(fact_neq0__conv,axiom,
! [X14] :
( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_abs__ge__zero,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oabs__class_Oabs(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_norm__inverse,axiom,
! [X10,X8] :
( ( class_RealVector_Oreal__normed__div__algebra(X8)
& class_Rings_Odivision__ring__inverse__zero(X8) )
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__inverse) ).
fof(fact_nonzero__abs__inverse,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oabs__class_Oabs(X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__inverse) ).
fof(fact_nonzero__inverse__minus__eq,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X10)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
fof(fact_le__0__eq,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X21,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X9,X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X21,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X21),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_ab__left__minus,axiom,
! [X10,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X10) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10),X10) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_right__minus,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ouminus__class_Ouminus(X8,X10)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_of__real_Ominus,axiom,
! [X7,X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> c_RealVector_Oof__real(X8,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_RealVector_Oof__real(X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ominus) ).
fof(fact_of__real__inverse,axiom,
! [X7,X8] :
( ( class_RealVector_Oreal__div__algebra(X8)
& class_Rings_Odivision__ring__inverse__zero(X8) )
=> c_RealVector_Oof__real(X8,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)) = c_Rings_Oinverse__class_Oinverse(X8,c_RealVector_Oof__real(X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__inverse) ).
fof(fact_add__is__0,axiom,
! [X14,X15] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X14 = 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,
! [X10,X8] :
( class_RealVector_Oreal__normed__div__algebra(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).
fof(fact_pcompose__0,axiom,
! [X12,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Opcompose(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(fact_synthetic__div__0,axiom,
! [X26,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osynthetic__div(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X26) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_smult__0__right,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ? [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X59) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096) ).
fof(fact_gr__implies__not0,axiom,
! [X9,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
=> X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__ge__zero,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X9,X8] :
( ( class_Power_Opower(X8)
& class_Rings_Osemiring__0(X8) )
=> ( ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X9) = c_Groups_Oone__class_Oone(X8) )
& ( X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Ozero__class_Ozero(X8)),X9) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X9,X11] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X9) = X11
=> X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_real__natceiling__ge,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_nonzero__of__real__inverse,axiom,
! [X7,X8] :
( class_RealVector_Oreal__div__algebra(X8)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_RealVector_Oof__real(X8,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X7)) = c_Rings_Oinverse__class_Oinverse(X8,c_RealVector_Oof__real(X8,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__of__real__inverse) ).
fof(fact_poly__0,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))),X7) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_poly__1,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(c_Polynomial_Opoly(X8,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8))),X7) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_abs__ge__self,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X10,c_Groups_Oabs__class_Oabs(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_less__not__refl2,axiom,
! [X11,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X11)
=> X11 != X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X52,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X52)
=> X4 != X52 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_sgn__minus,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Osgn__class_Osgn(X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).
fof(fact_abs__inverse,axiom,
! [X10,X8] :
( class_Fields_Olinordered__field__inverse__zero(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oabs__class_Oabs(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__inverse) ).
fof(fact_inverse__minus__eq,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ouminus__class_Ouminus(X8,X10)) = c_Groups_Ouminus__class_Ouminus(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X12,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X12) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [X13,X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X8),X13,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X13,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X8),X13,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_pos__poly__total,axiom,
! [X13,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
| c_Polynomial_Opos__poly(X8,X13)
| c_Polynomial_Opos__poly(X8,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(fact_mult__is__0,axiom,
! [X14,X15] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_of__real__minus,axiom,
! [X7,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X7)) = c_Groups_Ouminus__class_Ouminus(X8,c_RealVector_Oof__real(X8,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__minus) ).
fof(fact_sgn__of__real,axiom,
! [X6,X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_RealVector_Oof__real(X8,X6)) = c_RealVector_Oof__real(X8,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__of__real) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X9,X11] :
( X11 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X9)
=> ( X9 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X11 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_diff__0,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,c_Groups_Ozero__class_Ozero(X8),X10) = c_Groups_Ouminus__class_Ouminus(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X14,X15] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X14) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X15 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X14,X15] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X14)
<=> ( X15 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_monom__eq__0,axiom,
! [X9,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Omonom(X8,c_Groups_Ozero__class_Ozero(X8),X9) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(fact_smult__0__left,axiom,
! [X13,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Ozero__class_Ozero(X8),X13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_power__power__power,axiom,
! [X8] :
( class_Power_Opower(X8)
=> c_Power_Opower__class_Opower(X8) = c_Power_Opower_Opower(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Otimes__class_Otimes(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_mult__zero__left,axiom,
! [X10,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X10) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X10) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult_Ozero__left,axiom,
! [X23,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X23) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X5,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Ozero__class_Ozero(X8)),X5) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_power__one,axiom,
! [X9,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),c_Groups_Oone__class_Oone(X8)),X9) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_zero__le__one,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),c_Groups_Oone__class_Oone(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_mult__1,axiom,
! [X10,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__1__left,axiom,
! [X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_mult__zero__right,axiom,
! [X10,X8] :
( class_Rings_Omult__zero(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult_Ozero__right,axiom,
! [X10,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__algebra(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_smult__1__left,axiom,
! [X13,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Polynomial_Osmult(X8,c_Groups_Oone__class_Oone(X8),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(fact_add__0__left,axiom,
! [X10,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X10,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_diff__0__right,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X10,c_Groups_Ozero__class_Ozero(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_add__0__right,axiom,
! [X10,X8] :
( class_Groups_Omonoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ozero__class_Ozero(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X10,X8] :
( class_Groups_Ocomm__monoid__add(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ozero__class_Ozero(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Groups_Oplus__class_Oplus(X8,X10,c_Groups_Ozero__class_Ozero(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_dvd__0__right,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> c_Rings_Odvd__class_Odvd(X8,X10,c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_power__0,axiom,
! [X10,X8] :
( class_Power_Opower(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X10,X8] :
( class_Groups_Ocomm__monoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Oone__class_Oone(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X10,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Oone__class_Oone(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_mult__1__right,axiom,
! [X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),c_Groups_Oone__class_Oone(X8)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_diff__self,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ominus__class_Ominus(X8,X10,X10) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_order__eq__refl,axiom,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( X7 = X5
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_nonzero__inverse__eq__imp__eq,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X10) = c_Rings_Oinverse__class_Oinverse(X8,X23)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> ( X23 != c_Groups_Ozero__class_Ozero(X8)
=> X10 = X23 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X7,X8] :
( class_Rings_Ocomm__semiring__1(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_power__one__right,axiom,
! [X10,X8] :
( class_Groups_Omonoid__mult(X8)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X8),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__natfloor,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_zero__le__natceiling,axiom,
! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_order__refl,axiom,
! [X7,X8] :
( class_Orderings_Opreorder(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X7,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_sgn__sgn,axiom,
! [X10,X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_Groups_Osgn__class_Osgn(X8,X10)) = c_Groups_Osgn__class_Osgn(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(fact_abs__idempotent,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Oabs__class_Oabs(X8,X10)) = c_Groups_Oabs__class_Oabs(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__minus__cancel,axiom,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Ouminus__class_Ouminus(X8,X10)) = c_Groups_Oabs__class_Oabs(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_norm__minus__cancel,axiom,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = c_RealVector_Onorm__class_Onorm(X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_poly__eq__iff,axiom,
! [X75,X73,X8] :
( ( class_Int_Oring__char__0(X8)
& class_Rings_Oidom(X8) )
=> ( c_Polynomial_Opoly(X8,X73) = c_Polynomial_Opoly(X8,X75)
<=> X73 = X75 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_mult__idem,axiom,
! [X7,X8] :
( class_Lattices_Oab__semigroup__idem__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [X10,X8] :
( class_Lattices_Oab__semigroup__idem__mult(X8)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_gr0I,axiom,
! [X9] :
( X9 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_abs__norm__cancel,axiom,
! [X10,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X10)) = c_RealVector_Onorm__class_Onorm(X8,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_norm__of__real,axiom,
! [X6,X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_RealVector_Oof__real(X8,X6)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(fact_diff__0__eq__0,axiom,
! [X9] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9) = 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,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Osgn__class_Osgn(X8,X7)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Osgn__class_Osgn(X8,X7)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).
fof(fact_zadd__0,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X9,X11] :
( X11 = X9
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X8] :
( class_Groups_Oab__group__add(X8)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_diff__self__eq__0,axiom,
! [X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_mult__0,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_of__real__eq__iff,axiom,
! [X17,X18,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> ( c_RealVector_Oof__real(X8,X18) = c_RealVector_Oof__real(X8,X17)
<=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X17,X18,X8] :
( class_Lattices_Oboolean__algebra(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X18) = c_Groups_Ouminus__class_Ouminus(X8,X17)
<=> X18 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X19,X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X16) = c_Groups_Ouminus__class_Ouminus(X8,X19)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_inverse__eq__iff__eq,axiom,
! [X19,X16,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X16) = c_Rings_Oinverse__class_Oinverse(X8,X19)
<=> X16 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
fof(fact_inverse__eq__imp__eq,axiom,
! [X23,X10,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X10) = c_Rings_Oinverse__class_Oinverse(X8,X23)
=> X10 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
fof(fact_nonzero__inverse__inverse__eq,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(fact_zmult__1,axiom,
! [X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__1,axiom,
! [X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zle__refl,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_real__le__refl,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_mult__0__right,axiom,
! [X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X9] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_double__compl,axiom,
! [X7,X8] :
( class_Lattices_Oboolean__algebra(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X10,X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ouminus__class_Ouminus(X8,X10)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_inverse__inverse__eq,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Rings_Oinverse__class_Oinverse(X8,X10)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X7] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X7)) = c_RealDef_Oreal(tc_Nat_Onat,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_minus__equation__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X16) = X19
<=> c_Groups_Ouminus__class_Ouminus(X8,X19) = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X19,X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( X16 = c_Groups_Ouminus__class_Ouminus(X8,X19)
<=> X19 = c_Groups_Ouminus__class_Ouminus(X8,X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_psize__eq__0__iff,axiom,
! [X73,X8] :
( class_Groups_Ozero(X8)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X8,X73) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_real__of__nat__inject,axiom,
! [X15,X14] :
( c_RealDef_Oreal(tc_Nat_Onat,X14) = c_RealDef_Oreal(tc_Nat_Onat,X15)
<=> X14 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Ouminus__class_Ouminus(X8,X16)
<=> c_Groups_Ozero__class_Ozero(X8) = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_sgn__0__0,axiom,
! [X16,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Groups_Osgn__class_Osgn(X8,X16) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn__zero__iff,axiom,
! [X18,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_Groups_Osgn__class_Osgn(X8,X18) = c_Groups_Ozero__class_Ozero(X8)
<=> X18 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_abs__eq__0,axiom,
! [X16,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Groups_Oabs__class_Oabs(X8,X16) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X16,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X16) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_nonzero__imp__inverse__nonzero,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( X10 != c_Groups_Ozero__class_Ozero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,X10) != c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(fact_inverse__zero__imp__zero,axiom,
! [X10,X8] :
( class_Rings_Odivision__ring(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X10) = c_Groups_Ozero__class_Ozero(X8)
=> X10 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X16,X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X16) = c_Groups_Ozero__class_Ozero(X8)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(fact_inverse__eq__1__iff,axiom,
! [X18,X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> ( c_Rings_Oinverse__class_Oinverse(X8,X18) = c_Groups_Oone__class_Oone(X8)
<=> X18 = c_Groups_Oone__class_Oone(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X18,X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> ( c_RealVector_Oof__real(X8,X18) = c_Groups_Ozero__class_Ozero(X8)
<=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
fof(fact_norm__eq__zero,axiom,
! [X18,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ( c_RealVector_Onorm__class_Onorm(X8,X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X18 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X89,X88] :
( class_Groups_Ouminus(X88)
=> class_Groups_Ouminus(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X89,X88] :
( class_Groups_Ominus(X88)
=> class_Groups_Ominus(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X89,X88] :
( class_Lattices_Oboolean__algebra(X88)
=> class_Lattices_Oboolean__algebra(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X89,X88] :
( class_Orderings_Oorder(X88)
=> class_Orderings_Oorder(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X89,X88] :
( class_Orderings_Oord(X88)
=> class_Orderings_Oord(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X89,X88] :
( class_Orderings_Opreorder(X88)
=> class_Orderings_Opreorder(tc_fun(X89,X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_zminus__zminus,axiom,
! [X20] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_neg__equal__zero,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ouminus__class_Ouminus(X8,X16) = X16
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X16,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( X16 = c_Groups_Ouminus__class_Ouminus(X8,X16)
<=> X16 = c_Groups_Ozero__class_Ozero(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_of__real_Ozero,axiom,
! [X8] :
( ( class_RealVector_Oreal__algebra__1(X8)
& class_RealVector_Oreal__normed__vector(X8) )
=> c_RealVector_Oof__real(X8,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ozero) ).
fof(fact_sgn0,axiom,
! [X8] :
( class_Groups_Osgn__if(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).
fof(fact_sgn__zero,axiom,
! [X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).
fof(fact_sgn__one,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_Groups_Osgn__class_Osgn(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).
fof(fact_abs__zero,axiom,
! [X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__one,axiom,
! [X8] :
( class_Rings_Olinordered__idom(X8)
=> c_Groups_Oabs__class_Oabs(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_minus__zero,axiom,
! [X8] :
( class_Groups_Ogroup__add(X8)
=> c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(fact_field__inverse__zero,axiom,
! [X8] :
( class_Fields_Ofield__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
fof(fact_inverse__zero,axiom,
! [X8] :
( class_Rings_Odivision__ring__inverse__zero(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
fof(fact_inverse__1,axiom,
! [X8] :
( class_Rings_Odivision__ring(X8)
=> c_Rings_Oinverse__class_Oinverse(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
fof(fact_norm__zero,axiom,
! [X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Ozero__class_Ozero(X8)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_norm__one,axiom,
! [X8] :
( class_RealVector_Oreal__normed__algebra__1(X8)
=> c_RealVector_Onorm__class_Onorm(X8,c_Groups_Oone__class_Oone(X8)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_of__real__0,axiom,
! [X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__0) ).
fof(fact_of__real__1,axiom,
! [X8] :
( class_RealVector_Oreal__algebra__1(X8)
=> c_RealVector_Oof__real(X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X9] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X9] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X14] :
( c_RealDef_Oreal(tc_Nat_Onat,X14) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X14 = 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,
! [X6] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X6) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_zero__neq__one,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Ozero__class_Ozero(X8) != c_Groups_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X8] :
( class_Rings_Ozero__neq__one(X8)
=> c_Groups_Oone__class_Oone(X8) != c_Groups_Ozero__class_Ozero(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X88] :
( class_Rings_Ocomm__ring(X88)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X88] :
( class_Rings_Ocomm__ring__1(X88)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X88] :
( class_Rings_Ocomm__ring(X88)
=> class_Rings_Oring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X88] :
( class_Rings_Ocomm__ring__1(X88)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X88] :
( class_Groups_Oab__group__add(X88)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
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,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Oone(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocomm__monoid__add(X88)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X88] :
( class_Groups_Ocancel__comm__monoid__add(X88)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X88] :
( class_Groups_Ozero(X88)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X88] :
( class_Rings_Oidom(X88)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Power_Opower(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__1(X88)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X88] :
( class_Rings_Olinordered__idom(X88)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096) ).
fof(fact_th11,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th11) ).
fof(fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096) ).
fof(fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096) ).
fof(fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096) ).
fof(fact_inv0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv0) ).
fof(fact_t_I3_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I3_J) ).
fof(fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096) ).
fof(fact_r01,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r01) ).
fof(fact_th02,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th02) ).
fof(fact_kas_I3_J,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I3_J) ).
fof(fact_w,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w) ).
fof(fact_lgqr,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lgqr) ).
fof(fact_tw,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tw) ).
fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).
fof(fact_wm1,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wm1) ).
fof(fact_k1n,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_k1n) ).
fof(fact__0960_A_060_At_A_094_Ak_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_At_A_094_Ak_096) ).
fof(fact_kn,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kn) ).
fof(fact_pqc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pqc0) ).
fof(fact_a00,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_a00) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_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_i__mult__eq2,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__mult__eq2) ).
fof(fact_complex__of__real__minus__one,axiom,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__minus__one) ).
fof(fact_pc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pc0) ).
fof(fact_m_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).
fof(fact_t_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I1_J) ).
fof(fact_t_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I2_J) ).
fof(fact_q_I1_J,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I1_J) ).
fof(fact_inverse__i,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__i) ).
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_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_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(fact_INVERSE__ZERO,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
fof(fact_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_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_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_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_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__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(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_kas_I1_J,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I1_J) ).
fof(fact_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).
fof(fact_kas_I2_J,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
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_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
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_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_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_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_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_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__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_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__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__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_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__div__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__div__algebra) ).
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__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_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__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_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
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_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__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__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_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_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_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_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__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_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
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_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_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_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
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_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__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__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_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_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_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_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_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_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_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
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__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
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_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_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_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__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Complex__Ocomplex__Rings_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_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_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_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(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_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__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_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(i_0_1278,plain,
~ ! [X39] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X39)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X39,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ) ),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bt_O_A_091_124_A0_A_060_At_059_At_A_060_A1_059_At_A_060_Ainverse_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_1279,plain,
! [X5,X7,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oplus__class_Oplus(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X7),X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X5),X5)),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1280,plain,
! [X19,X16,X51] :
( hBOOL(hAPP(X51,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X19)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X19)
& ~ hBOOL(hAPP(X51,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X63] :
( X16 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X63)
& ~ hBOOL(hAPP(X51,X63)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1281,plain,
! [X7] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X7),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(i_0_1282,plain,
! [X9,X44,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X44),X9)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X9)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1283,plain,
! [X1,X2,X8,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X8,X67),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X67),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1284,plain,
! [X73] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X73),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
=> ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X73))
=> ? [X59] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X73),X59) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_simplification,[status(thm)],[fact_less_Ohyps]) ).
fof(i_0_1285,plain,
! [X10,X8] :
( class_Rings_Olinordered__ring(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X10),X10),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1286,plain,
! [X45,X22] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X45),X22),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1287,plain,
! [X22,X45] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,X22),X22),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1288,plain,
! [X18] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X18))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1289,plain,
! [X9,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X9)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9)) = X11 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1290,plain,
! [X17,X18,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1291,plain,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> X18 = X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1292,plain,
! [X10,X23,X8] :
( class_Orderings_Oorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X23,X10)
=> ~ c_Orderings_Oord__class_Oless(X8,X10,X23) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1293,plain,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> c_Orderings_Oord__class_Oless(X8,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1294,plain,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(X8,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1295,plain,
! [X7,X5,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1296,plain,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> ( c_Orderings_Oord__class_Oless(X8,X17,X18)
| X18 = X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1297,plain,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1298,plain,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1299,plain,
! [X23,X10,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X10,X23)
=> ~ c_Orderings_Oord__class_Oless(X8,X23,X10) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1300,plain,
! [X5,X7,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ~ c_Orderings_Oord__class_Oless(X8,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1301,plain,
! [X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)),X7)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X8))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__poly__def]) ).
fof(i_0_1302,plain,
! [X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X8),X7) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X8),X7) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X8),X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X8),X7) = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__poly__def]) ).
fof(i_0_1303,plain,
! [X7,X5] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X7)
=> c_Nat__Transfer_Otsub(X7,X5) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X5) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X7)
=> c_Nat__Transfer_Otsub(X7,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_1304,plain,
! [X17,X18,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X8,X18,X17)
<=> X18 = X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1305,plain,
! [X10,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oabs__class_Oabs(X8,X10),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_1306,plain,
! [X7,X8] :
( class_RealVector_Oreal__normed__vector(X8)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X8,X7),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1307,plain,
! [X10,X8] :
( class_Groups_Oabs__if(X8)
=> ( ( c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = c_Groups_Ouminus__class_Ouminus(X8,X10) )
& ( ~ c_Orderings_Oord__class_Oless(X8,X10,c_Groups_Ozero__class_Ozero(X8))
=> c_Groups_Oabs__class_Oabs(X8,X10) = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__if]) ).
fof(i_0_1308,plain,
! [X7,X8] :
( class_Groups_Osgn__if(X8)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(X8)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Ozero__class_Ozero(X8) )
& ( X7 != c_Groups_Ozero__class_Ozero(X8)
=> ( ( c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Oone__class_Oone(X8) )
& ( ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Ozero__class_Ozero(X8),X7)
=> c_Groups_Osgn__class_Osgn(X8,X7) = c_Groups_Ouminus__class_Ouminus(X8,c_Groups_Oone__class_Oone(X8)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).
fof(i_0_1309,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(i_0_1310,plain,
! [X18,X17,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X17,X18)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X18,X17)
<=> X18 = X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1311,plain,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1312,plain,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> ( X7 != X5
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1313,plain,
! [X5,X7,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless(X8,X5,X7) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1314,plain,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1315,plain,
! [X5,X7,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X7,X5)
=> c_Orderings_Oord__class_Oless__eq(X8,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1316,plain,
! [X7,X5,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X8,X5,X7)
=> c_Orderings_Oord__class_Oless(X8,X7,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1317,plain,
! [X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X22) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X22) = X22 ) ),
inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).
fof(i_0_1318,plain,
! [X10] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10) = X10 ) ),
inference(fof_simplification,[status(thm)],[fact_abs__real__def]) ).
fof(i_0_1319,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_real__abs__def]) ).
fof(i_0_1320,plain,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless__eq(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1321,plain,
! [X8] :
( class_Rings_Olinordered__semidom(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Ozero__class_Ozero(X8)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1322,plain,
! [X5,X7] :
( X7 != X5
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1323,plain,
! [X7,X8] :
( class_Orderings_Opreorder(X8)
=> ~ c_Orderings_Oord__class_Oless(X8,X7,X7) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1324,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1325,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1326,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1327,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X9),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1328,plain,
! [X9] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X9),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1329,plain,
! [X8] :
( class_Rings_Olinordered__idom(X8)
=> ~ c_Polynomial_Opos__poly(X8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))) ),
inference(fof_simplification,[status(thm)],[fact_not__pos__poly__0]) ).
fof(i_0_1330,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_1331,plain,
! [X5145,X5146,X5147,X5148,X5150] :
( ( c_Orderings_Oord__class_Oless__eq(X5147,X5146,esk27_4(X5145,X5146,X5147,X5148))
| ~ c_Orderings_Oord__class_Oless__eq(X5147,X5146,X5150)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5148,hAPP(X5145,X5150)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5148,hAPP(X5145,X5146))))
| ~ class_RealVector_Oreal__normed__vector(X5148)
| ~ class_Orderings_Oord(X5147) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5148,c_Groups_Ominus__class_Ominus(X5148,hAPP(X5145,X5146),hAPP(X5145,esk27_4(X5145,X5146,X5147,X5148)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X5147,X5146,X5150)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5148,hAPP(X5145,X5150)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5148,hAPP(X5145,X5146))))
| ~ class_RealVector_Oreal__normed__vector(X5148)
| ~ class_Orderings_Oord(X5147) ) ),
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])])])])]) ).
fof(i_0_1332,plain,
! [X4702] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4702)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4702)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4702)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4702)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mrmq__eq])]) ).
fof(i_0_1333,plain,
! [X4641,X4642,X4643] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4643)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4642,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4642,X4641)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4643)),X4641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_1334,plain,
! [X4638,X4639,X4640] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4640)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4639,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4638,X4639)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4640))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_1335,plain,
! [X4930] :
( esk23_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& esk22_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk24_0),esk22_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4930) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X4930),esk22_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk23_0,esk24_0)),X4930))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096])])]) ).
fof(i_0_1336,plain,
! [X4704] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4704) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X4704),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X4704))),
inference(variable_rename,[status(thm)],[fact_kas_I4_J]) ).
fof(i_0_1337,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk17_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096])])]) ).
fof(i_0_1338,plain,
! [X4703] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X4703)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(variable_rename,[status(thm)],[fact_qr]) ).
fof(i_0_1339,plain,
! [X4931,X4932,X4933,X4934,X4935] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4933,X4934),X4932,X4931)
| c_Orderings_Oord__class_Oless__eq(X4934,hAPP(X4932,X4935),hAPP(X4931,X4935))
| ~ class_Orderings_Oord(X4934) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4934,hAPP(X4932,esk25_4(X4931,X4932,X4933,X4934)),hAPP(X4931,esk25_4(X4931,X4932,X4933,X4934)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4933,X4934),X4932,X4931)
| ~ class_Orderings_Oord(X4934) ) ),
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])])])])]) ).
fof(i_0_1340,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1278])])]) ).
fof(i_0_1341,plain,
! [X4121,X4122,X4123,X4124,X4125] :
( ~ class_RealVector_Oreal__normed__algebra(X4125)
| c_Groups_Ominus__class_Ominus(X4125,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4125),X4124),X4123),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4125),X4122),X4121)) = c_Groups_Oplus__class_Oplus(X4125,c_Groups_Oplus__class_Oplus(X4125,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4125),c_Groups_Ominus__class_Ominus(X4125,X4124,X4122)),c_Groups_Ominus__class_Ominus(X4125,X4123,X4121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4125),c_Groups_Ominus__class_Ominus(X4125,X4124,X4122)),X4121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4125),X4122),c_Groups_Ominus__class_Ominus(X4125,X4123,X4121))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1342,plain,
! [X4556,X4557,X4558,X4559] : 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,X4559,X4558),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4557),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4556)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4559,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4557))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4558,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4556))))),
inference(variable_rename,[status(thm)],[fact_abs__sum__triangle__ineq]) ).
fof(i_0_1343,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk18_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk19_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096])])]) ).
fof(i_0_1344,plain,
! [X4892,X4893,X4894] :
( ~ class_Rings_Ocomm__ring__1(X4894)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4894)),c_Polynomial_OpCons(X4894,c_Groups_Ouminus__class_Ouminus(X4894,X4893),c_Polynomial_OpCons(X4894,c_Groups_Oone__class_Oone(X4894),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4894))))),c_Polynomial_Osynthetic__div(X4894,X4892,X4893)),c_Polynomial_OpCons(X4894,hAPP(c_Polynomial_Opoly(X4894,X4892),X4893),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4894)))) = X4892 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H])]) ).
fof(i_0_1345,plain,
! [X4155,X4156,X4157,X4158,X4159,X4160] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4160,c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),X4159),X4158),X4157),c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),X4156),X4158),X4155))
| c_Orderings_Oord__class_Oless__eq(X4160,c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),c_Groups_Ominus__class_Ominus(X4160,X4159,X4156)),X4158),X4157),X4155)
| ~ class_Rings_Oordered__ring(X4160) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4160,c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),c_Groups_Ominus__class_Ominus(X4160,X4159,X4156)),X4158),X4157),X4155)
| c_Orderings_Oord__class_Oless__eq(X4160,c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),X4159),X4158),X4157),c_Groups_Oplus__class_Oplus(X4160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),X4156),X4158),X4155))
| ~ class_Rings_Oordered__ring(X4160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1346,plain,
! [X4167,X4168,X4169,X4170,X4171,X4172] :
( ( ~ c_Orderings_Oord__class_Oless(X4172,c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),X4171),X4170),X4169),c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),X4168),X4170),X4167))
| c_Orderings_Oord__class_Oless(X4172,c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),c_Groups_Ominus__class_Ominus(X4172,X4171,X4168)),X4170),X4169),X4167)
| ~ class_Rings_Oordered__ring(X4172) )
& ( ~ c_Orderings_Oord__class_Oless(X4172,c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),c_Groups_Ominus__class_Ominus(X4172,X4171,X4168)),X4170),X4169),X4167)
| c_Orderings_Oord__class_Oless(X4172,c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),X4171),X4170),X4169),c_Groups_Oplus__class_Oplus(X4172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4172),X4168),X4170),X4167))
| ~ class_Rings_Oordered__ring(X4172) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1347,plain,
! [X4149,X4150,X4151,X4152,X4153,X4154] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4154,c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),X4153),X4152),X4151),c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),X4150),X4152),X4149))
| c_Orderings_Oord__class_Oless__eq(X4154,X4151,c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),c_Groups_Ominus__class_Ominus(X4154,X4150,X4153)),X4152),X4149))
| ~ class_Rings_Oordered__ring(X4154) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4154,X4151,c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),c_Groups_Ominus__class_Ominus(X4154,X4150,X4153)),X4152),X4149))
| c_Orderings_Oord__class_Oless__eq(X4154,c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),X4153),X4152),X4151),c_Groups_Oplus__class_Oplus(X4154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),X4150),X4152),X4149))
| ~ class_Rings_Oordered__ring(X4154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1348,plain,
! [X4161,X4162,X4163,X4164,X4165,X4166] :
( ( ~ c_Orderings_Oord__class_Oless(X4166,c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4164),X4163),c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4162),X4164),X4161))
| c_Orderings_Oord__class_Oless(X4166,X4163,c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),c_Groups_Ominus__class_Ominus(X4166,X4162,X4165)),X4164),X4161))
| ~ class_Rings_Oordered__ring(X4166) )
& ( ~ c_Orderings_Oord__class_Oless(X4166,X4163,c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),c_Groups_Ominus__class_Ominus(X4166,X4162,X4165)),X4164),X4161))
| c_Orderings_Oord__class_Oless(X4166,c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4165),X4164),X4163),c_Groups_Oplus__class_Oplus(X4166,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4166),X4162),X4164),X4161))
| ~ class_Rings_Oordered__ring(X4166) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1349,plain,
! [X4344,X4345,X4346,X4347,X4348] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4347),X4346),X4345),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4348),X4346),X4344))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4347,X4348)),X4346),X4345),X4344)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4348,X4347) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4347,X4348)),X4346),X4345),X4344)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4347),X4346),X4345),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4348),X4346),X4344))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4348,X4347) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1350,plain,
! [X4385,X4386,X4387,X4388,X4389] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4388),X4387),X4386),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4389),X4387),X4385))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4388,X4389)),X4387),X4386),X4385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4389,X4388) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4388,X4389)),X4387),X4386),X4385)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4388),X4387),X4386),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4389),X4387),X4385))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4389,X4388) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_1351,plain,
! [X4359,X4360,X4361,X4362,X4363] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4363),X4361),X4360),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4362),X4361),X4359))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4360,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4362,X4363)),X4361),X4359))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4363,X4362) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4360,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4362,X4363)),X4361),X4359))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4363),X4361),X4360),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4362),X4361),X4359))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4363,X4362) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1352,plain,
! [X4380,X4381,X4382,X4383,X4384] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4384),X4382),X4381),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4383),X4382),X4380))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4383,X4384)),X4382),X4380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4384,X4383) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4381,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4383,X4384)),X4382),X4380))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4384),X4382),X4381),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4383),X4382),X4380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4384,X4383) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_1353,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(fof_simplification,[status(thm)],[fact_th01]) ).
fof(i_0_1354,plain,
! [X5358,X5359,X5360] :
( ~ class_Rings_Oidom(X5360)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5360),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5360)),c_Polynomial_OpCons(X5360,c_Groups_Ouminus__class_Ouminus(X5360,X5359),c_Polynomial_OpCons(X5360,c_Groups_Oone__class_Oone(X5360),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5360))))),c_Polynomial_Oorder(X5360,X5359,X5358)),X5358) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__1])]) ).
fof(i_0_1355,plain,
! [X4545,X4546,X4547,X4548,X4549] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4549)
| c_Orderings_Oord__class_Oless__eq(X4549,c_Groups_Oabs__class_Oabs(X4549,c_Groups_Ominus__class_Ominus(X4549,c_Groups_Oplus__class_Oplus(X4549,X4548,X4547),c_Groups_Oplus__class_Oplus(X4549,X4546,X4545))),c_Groups_Oplus__class_Oplus(X4549,c_Groups_Oabs__class_Oabs(X4549,c_Groups_Ominus__class_Ominus(X4549,X4548,X4546)),c_Groups_Oabs__class_Oabs(X4549,c_Groups_Ominus__class_Ominus(X4549,X4547,X4545)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_1356,plain,
! [X3891,X3892] :
( X3892 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X3891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3892),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk7_2(X3891,X3892)),X3891)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduce__poly__simple])])]) ).
fof(i_0_1357,plain,
! [X4186,X4187,X4188,X4189,X4190] :
( ~ class_RealVector_Oreal__normed__vector(X4190)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4190,c_Groups_Ominus__class_Ominus(X4190,c_Groups_Oplus__class_Oplus(X4190,X4189,X4188),c_Groups_Oplus__class_Oplus(X4190,X4187,X4186))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4190,c_Groups_Ominus__class_Ominus(X4190,X4189,X4187)),c_RealVector_Onorm__class_Onorm(X4190,c_Groups_Ominus__class_Ominus(X4190,X4188,X4186)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).
fof(i_0_1358,plain,
! [X5276,X5277,X5278,X5280] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_3(X5276,X5277,X5278))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5278) )
& ( ~ 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,X5280,X5277)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5280,X5277)),esk33_3(X5276,X5277,X5278))
| 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,X5276),X5280),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5276),X5277))),X5278)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5278) ) ),
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])])])])]) ).
fof(i_0_1359,plain,
! [X4191,X4192,X4193] :
( ~ class_Rings_Odivision__ring(X4193)
| X4192 = c_Groups_Ozero__class_Ozero(X4193)
| X4191 = c_Groups_Ozero__class_Ozero(X4193)
| c_Groups_Ominus__class_Ominus(X4193,c_Rings_Oinverse__class_Oinverse(X4193,X4192),c_Rings_Oinverse__class_Oinverse(X4193,X4191)) = c_Groups_Ouminus__class_Ouminus(X4193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4193),c_Rings_Oinverse__class_Oinverse(X4193,X4192)),c_Groups_Ominus__class_Ominus(X4193,X4192,X4191))),c_Rings_Oinverse__class_Oinverse(X4193,X4191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oinverse__diff__inverse])]) ).
fof(i_0_1360,plain,
! [X4349,X4350,X4351,X4352,X4353] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4353,X4352)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4352),X4351),X4350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4353),X4351),X4349)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4352,X4353)),X4351),X4350),X4349) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1361,plain,
! [X4364,X4365,X4366,X4367,X4368] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4368,X4367)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4368),X4366),X4365),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4367),X4366),X4364)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4365,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4367,X4368)),X4366),X4364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1362,plain,
! [X4712,X4713,X4714,X4715] :
( ~ class_Rings_Ocomm__ring__1(X4715)
| hAPP(c_Polynomial_Opoly(X4715,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4715)),c_Polynomial_Omonom(X4715,c_Groups_Oone__class_Oone(X4715),X4714)),X4713)),X4712) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4715),hAPP(hAPP(c_Power_Opower__class_Opower(X4715),X4712),X4714)),hAPP(c_Polynomial_Opoly(X4715,X4713),X4712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__replicate__append])]) ).
fof(i_0_1363,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk20_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096])]) ).
fof(i_0_1364,plain,
! [X5383,X5384,X5385,X5386,X5387,X5388] :
( ( ~ c_Rings_Odvd__class_Odvd(X5386,X5385,c_Groups_Oplus__class_Oplus(X5386,X5387,X5383))
| c_Rings_Odvd__class_Odvd(X5386,X5385,c_Groups_Oplus__class_Oplus(X5386,c_Groups_Ominus__class_Ominus(X5386,X5387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5386),X5388),X5384)),X5383))
| ~ c_Rings_Odvd__class_Odvd(X5386,X5385,X5384)
| ~ class_Rings_Ocomm__ring(X5386)
| ~ class_Rings_Odvd(X5386) )
& ( ~ c_Rings_Odvd__class_Odvd(X5386,X5385,c_Groups_Oplus__class_Oplus(X5386,c_Groups_Ominus__class_Ominus(X5386,X5387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5386),X5388),X5384)),X5383))
| c_Rings_Odvd__class_Odvd(X5386,X5385,c_Groups_Oplus__class_Oplus(X5386,X5387,X5383))
| ~ c_Rings_Odvd__class_Odvd(X5386,X5385,X5384)
| ~ class_Rings_Ocomm__ring(X5386)
| ~ class_Rings_Odvd(X5386) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).
fof(i_0_1365,plain,
! [X5377,X5378,X5379,X5380,X5381,X5382] :
( ( ~ c_Rings_Odvd__class_Odvd(X5380,X5379,c_Groups_Oplus__class_Oplus(X5380,X5381,X5377))
| c_Rings_Odvd__class_Odvd(X5380,X5379,c_Groups_Oplus__class_Oplus(X5380,c_Groups_Ominus__class_Ominus(X5380,X5381,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5380),X5382),X5378)),X5377))
| ~ c_Rings_Odvd__class_Odvd(X5380,X5379,X5378)
| ~ class_Rings_Ocomm__ring(X5380)
| ~ class_Rings_Odvd(X5380) )
& ( ~ c_Rings_Odvd__class_Odvd(X5380,X5379,c_Groups_Oplus__class_Oplus(X5380,c_Groups_Ominus__class_Ominus(X5380,X5381,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5380),X5382),X5378)),X5377))
| c_Rings_Odvd__class_Odvd(X5380,X5379,c_Groups_Oplus__class_Oplus(X5380,X5381,X5377))
| ~ c_Rings_Odvd__class_Odvd(X5380,X5379,X5378)
| ~ class_Rings_Ocomm__ring(X5380)
| ~ class_Rings_Odvd(X5380) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).
fof(i_0_1366,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(fof_simplification,[status(thm)],[fact_rnc]) ).
fof(i_0_1367,plain,
! [X4678,X4679,X4680,X4681,X4682,X4683] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4683),X4682),X4681) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4680),X4679),X4678)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4680),X4679),X4678),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4681,X4683)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4678)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4680)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4680,X4683)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4679,X4682) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1368,plain,
! [X4667,X4668,X4669,X4670,X4671,X4672] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4672),X4671),X4670) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4669),X4668),X4667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4669),X4668),X4667))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4667,X4669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4670)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4669,X4672)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4671,X4668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1369,plain,
! [X5159,X5161,X5162] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk30_1(X5159))
| ~ class_RealVector_Oreal__normed__algebra(X5159) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5159),X5161),X5162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5159,X5161)),c_RealVector_Onorm__class_Onorm(X5159,X5162))),esk30_1(X5159)))
| ~ class_RealVector_Oreal__normed__algebra(X5159) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded])])])])]) ).
fof(i_0_1370,plain,
! [X3663,X3664,X3665] :
( ~ class_Fields_Ofield(X3665)
| X3664 = c_Groups_Ozero__class_Ozero(X3665)
| X3663 = c_Groups_Ozero__class_Ozero(X3665)
| c_Groups_Oplus__class_Oplus(X3665,c_Rings_Oinverse__class_Oinverse(X3665,X3664),c_Rings_Oinverse__class_Oinverse(X3665,X3663)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3665),c_Groups_Oplus__class_Oplus(X3665,X3664,X3663)),c_Rings_Oinverse__class_Oinverse(X3665,X3664))),c_Rings_Oinverse__class_Oinverse(X3665,X3663)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).
fof(i_0_1371,plain,
! [X4662,X4663,X4664,X4665,X4666] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4666),X4665),X4664),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4666),X4663),X4662))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4664)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4664,X4666)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4662,X4666)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4665,X4663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1372,plain,
! [X4673,X4674,X4675,X4676,X4677] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4677),X4676),X4675),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4677),X4674),X4673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4673,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4677,X4673)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4677,X4675)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4674,X4676) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
fof(i_0_1373,plain,
! [X4354,X4355,X4356,X4357,X4358] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4357),X4356),X4355) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4358),X4356),X4354)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4357,X4358)),X4356),X4355) = X4354
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4358,X4357) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4357,X4358)),X4356),X4355) != X4354
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4357),X4356),X4355) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4358),X4356),X4354)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4358,X4357) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1374,plain,
! [X4369,X4370,X4371,X4372,X4373] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4373),X4371),X4370) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4372),X4371),X4369)
| X4370 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4372,X4373)),X4371),X4369)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4373,X4372) )
& ( X4370 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4372,X4373)),X4371),X4369)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4373),X4371),X4370) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4372),X4371),X4369)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4373,X4372) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1375,plain,
! [X4115,X4116,X4117,X4118,X4119,X4120] :
( ( c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),X4119),X4118),X4117) != c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),X4116),X4118),X4115)
| c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),c_Groups_Ominus__class_Ominus(X4120,X4119,X4116)),X4118),X4117) = X4115
| ~ class_Rings_Oring(X4120) )
& ( c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),c_Groups_Ominus__class_Ominus(X4120,X4119,X4116)),X4118),X4117) != X4115
| c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),X4119),X4118),X4117) = c_Groups_Oplus__class_Oplus(X4120,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4120),X4116),X4118),X4115)
| ~ class_Rings_Oring(X4120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1376,plain,
! [X4109,X4110,X4111,X4112,X4113,X4114] :
( ( c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),X4113),X4112),X4111) != c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),X4110),X4112),X4109)
| X4111 = c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),c_Groups_Ominus__class_Ominus(X4114,X4110,X4113)),X4112),X4109)
| ~ class_Rings_Oring(X4114) )
& ( X4111 != c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),c_Groups_Ominus__class_Ominus(X4114,X4110,X4113)),X4112),X4109)
| c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),X4113),X4112),X4111) = c_Groups_Oplus__class_Oplus(X4114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4114),X4110),X4112),X4109)
| ~ class_Rings_Oring(X4114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_1377,plain,
! [X4199] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4199) != 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,X4199,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,X4199,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,X4199,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,X4199,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])]) ).
fof(i_0_1378,plain,
! [X4104,X4105,X4106,X4107,X4108] :
( ~ class_Rings_Oring(X4108)
| c_Groups_Ominus__class_Ominus(X4108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4107),X4106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4105),X4104)) = c_Groups_Oplus__class_Oplus(X4108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),X4107),c_Groups_Ominus__class_Ominus(X4108,X4106,X4104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4108),c_Groups_Ominus__class_Ominus(X4108,X4107,X4105)),X4104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1379,plain,
! [X5269,X5270] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5270)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5269)),X5270),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5270,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
fof(i_0_1380,plain,
! [X3314,X3315,X3316,X3317,X3318] :
( ~ class_Rings_Osemiring(X3318)
| c_Groups_Oplus__class_Oplus(X3318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3318),X3317),X3316),c_Groups_Oplus__class_Oplus(X3318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3318),X3315),X3316),X3314)) = c_Groups_Oplus__class_Oplus(X3318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3318),c_Groups_Oplus__class_Oplus(X3318,X3317,X3315)),X3316),X3314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1381,plain,
! [X4175,X4176,X4177] :
( ~ class_Rings_Odivision__ring(X4177)
| X4176 = c_Groups_Ozero__class_Ozero(X4177)
| X4175 = c_Groups_Ozero__class_Ozero(X4177)
| c_Groups_Ominus__class_Ominus(X4177,c_Rings_Oinverse__class_Oinverse(X4177,X4176),c_Rings_Oinverse__class_Oinverse(X4177,X4175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4177),c_Rings_Oinverse__class_Oinverse(X4177,X4176)),c_Groups_Ominus__class_Ominus(X4177,X4175,X4176))),c_Rings_Oinverse__class_Oinverse(X4177,X4175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__diff])]) ).
fof(i_0_1382,plain,
! [X3660,X3661,X3662] :
( ~ class_Rings_Odivision__ring(X3662)
| X3661 = c_Groups_Ozero__class_Ozero(X3662)
| X3660 = c_Groups_Ozero__class_Ozero(X3662)
| c_Groups_Oplus__class_Oplus(X3662,c_Rings_Oinverse__class_Oinverse(X3662,X3661),c_Rings_Oinverse__class_Oinverse(X3662,X3660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3662),c_Rings_Oinverse__class_Oinverse(X3662,X3661)),c_Groups_Oplus__class_Oplus(X3662,X3661,X3660))),c_Rings_Oinverse__class_Oinverse(X3662,X3660)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).
fof(i_0_1383,plain,
! [X3126,X3127,X3128,X3129,X3130,X3131] :
( ~ class_Rings_Olinordered__semiring__1(X3131)
| ~ c_Orderings_Oord__class_Oless__eq(X3131,X3130,X3129)
| ~ c_Orderings_Oord__class_Oless__eq(X3131,X3128,X3129)
| ~ c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131),X3127)
| ~ c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131),X3126)
| c_Groups_Oplus__class_Oplus(X3131,X3127,X3126) != c_Groups_Oone__class_Oone(X3131)
| c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Oplus__class_Oplus(X3131,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3131),X3127),X3130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3131),X3126),X3128)),X3129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1384,plain,
! [X3109,X3110,X3111,X3112,X3113,X3114] :
( ~ class_Rings_Olinordered__semiring__1__strict(X3114)
| ~ c_Orderings_Oord__class_Oless(X3114,X3113,X3112)
| ~ c_Orderings_Oord__class_Oless(X3114,X3111,X3112)
| ~ c_Orderings_Oord__class_Oless__eq(X3114,c_Groups_Ozero__class_Ozero(X3114),X3110)
| ~ c_Orderings_Oord__class_Oless__eq(X3114,c_Groups_Ozero__class_Ozero(X3114),X3109)
| c_Groups_Oplus__class_Oplus(X3114,X3110,X3109) != c_Groups_Oone__class_Oone(X3114)
| c_Orderings_Oord__class_Oless(X3114,c_Groups_Oplus__class_Oplus(X3114,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3110),X3113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3114),X3109),X3111)),X3112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1385,plain,
! [X5393,X5394,X5395,X5396,X5398] :
( ( c_Rings_Odvd__class_Odvd(X5395,X5393,c_Groups_Oplus__class_Oplus(X5395,esk37_3(X5393,X5394,X5395),c_Groups_Ozero__class_Ozero(X5395)))
| ~ hBOOL(hAPP(X5394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5395),X5393),X5396)))
| ~ class_Rings_Odvd(X5395)
| ~ class_Rings_Osemiring__0(X5395) )
& ( hBOOL(hAPP(X5394,esk37_3(X5393,X5394,X5395)))
| ~ hBOOL(hAPP(X5394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5395),X5393),X5396)))
| ~ class_Rings_Odvd(X5395)
| ~ class_Rings_Osemiring__0(X5395) )
& ( ~ c_Rings_Odvd__class_Odvd(X5395,X5393,c_Groups_Oplus__class_Oplus(X5395,X5398,c_Groups_Ozero__class_Ozero(X5395)))
| ~ hBOOL(hAPP(X5394,X5398))
| hBOOL(hAPP(X5394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5395),X5393),esk38_3(X5393,X5394,X5395))))
| ~ class_Rings_Odvd(X5395)
| ~ class_Rings_Osemiring__0(X5395) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).
fof(i_0_1386,plain,
! [X3822,X3823,X3824,X3825] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3825),X3824),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3823),X3824),X3822)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3825,X3823)),X3824),X3822),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1387,plain,
! [X3686,X3687,X3688,X3689] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3689)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3688)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3688),X3687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3689),X3686))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3689)),X3687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3688)),X3686)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel])]) ).
fof(i_0_1388,plain,
! [X3696,X3697,X3698] :
( ( ~ c_Orderings_Oord__class_Oless(X3698,c_Groups_Ozero__class_Ozero(X3698),c_Groups_Oplus__class_Oplus(X3698,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3697),X3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3696),X3696)))
| X3697 != c_Groups_Ozero__class_Ozero(X3698)
| X3696 != c_Groups_Ozero__class_Ozero(X3698)
| ~ class_Rings_Olinordered__ring__strict(X3698) )
& ( X3697 = c_Groups_Ozero__class_Ozero(X3698)
| c_Orderings_Oord__class_Oless(X3698,c_Groups_Ozero__class_Ozero(X3698),c_Groups_Oplus__class_Oplus(X3698,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3697),X3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3696),X3696)))
| ~ class_Rings_Olinordered__ring__strict(X3698) )
& ( X3696 = c_Groups_Ozero__class_Ozero(X3698)
| c_Orderings_Oord__class_Oless(X3698,c_Groups_Ozero__class_Ozero(X3698),c_Groups_Oplus__class_Oplus(X3698,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3697),X3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3698),X3696),X3696)))
| ~ class_Rings_Olinordered__ring__strict(X3698) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1389,plain,
! [X2977,X2978,X2979,X2980,X2981] :
( ~ class_Rings_Ocomm__semiring__1(X2981)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),X2980),X2979)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),X2978),X2977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),X2978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2981),X2980),X2979)),X2977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1390,plain,
! [X3702,X3703,X3704] :
( ( X3703 = c_Groups_Ozero__class_Ozero(X3704)
| ~ c_Orderings_Oord__class_Oless__eq(X3704,c_Groups_Oplus__class_Oplus(X3704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3703),X3703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3702),X3702)),c_Groups_Ozero__class_Ozero(X3704))
| ~ class_Rings_Olinordered__ring__strict(X3704) )
& ( X3702 = c_Groups_Ozero__class_Ozero(X3704)
| ~ c_Orderings_Oord__class_Oless__eq(X3704,c_Groups_Oplus__class_Oplus(X3704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3703),X3703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3702),X3702)),c_Groups_Ozero__class_Ozero(X3704))
| ~ class_Rings_Olinordered__ring__strict(X3704) )
& ( X3703 != c_Groups_Ozero__class_Ozero(X3704)
| X3702 != c_Groups_Ozero__class_Ozero(X3704)
| c_Orderings_Oord__class_Oless__eq(X3704,c_Groups_Oplus__class_Oplus(X3704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3703),X3703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3702),X3702)),c_Groups_Ozero__class_Ozero(X3704))
| ~ class_Rings_Olinordered__ring__strict(X3704) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1391,plain,
! [X3693,X3694,X3695] :
( ~ class_Rings_Olinordered__ring(X3695)
| ~ c_Orderings_Oord__class_Oless(X3695,c_Groups_Oplus__class_Oplus(X3695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3695),X3694),X3694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3695),X3693),X3693)),c_Groups_Ozero__class_Ozero(X3695)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1279])]) ).
fof(i_0_1392,plain,
! [X4407,X4408] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4408)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4408,X4407)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4407,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4407)),X4408),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ath])]) ).
fof(i_0_1393,plain,
! [X4888,X4889,X4890,X4891] :
( ~ class_Rings_Ocomm__semiring__0(X4891)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4891)),c_Polynomial_OpCons(X4891,X4890,X4889)),X4888) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4891),c_Polynomial_Osmult(X4891,X4890,X4888),c_Polynomial_OpCons(X4891,c_Groups_Ozero__class_Ozero(X4891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4891)),X4889),X4888))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__left])]) ).
fof(i_0_1394,plain,
! [X5361,X5362,X5363,X5364] :
( ~ class_Rings_Ocomm__semiring__0(X5364)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5364,c_Polynomial_OpCons(X5364,X5363,X5362),X5361) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5364),c_Polynomial_Osmult(X5364,X5361,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5364,X5362,X5361)),c_Polynomial_OpCons(X5364,X5363,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5364,X5362,X5361))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(i_0_1395,plain,
! [X3682,X3683,X3684,X3685] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3685)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3684)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3684),X3683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3685),X3682))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3683),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3682),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3684))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel2])]) ).
fof(i_0_1396,plain,
! [X4397,X4398,X4399] :
( ~ class_Groups_Omonoid__mult(X4399)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4398)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4399),hAPP(hAPP(c_Power_Opower__class_Opower(X4399),X4397),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4398,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4397) = hAPP(hAPP(c_Power_Opower__class_Opower(X4399),X4397),X4398) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
fof(i_0_1397,plain,
! [X3051,X3052,X3053,X3054,X3055] :
( ( X3054 = X3053
| X3052 = X3051
| c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3051)) != c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3051),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3052))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3055) )
& ( X3054 != X3053
| c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3051)) = c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3051),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3052))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3055) )
& ( X3052 != X3051
| c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3052),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3051)) = c_Groups_Oplus__class_Oplus(X3055,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3054),X3051),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3055),X3053),X3052))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3055) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1398,plain,
! [X3030,X3031,X3032,X3033,X3034] :
( ( c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3030)) != c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3032))
| X3033 = X3031
| X3032 = X3030
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3034) )
& ( X3033 != X3031
| c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3030)) = c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3032))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3034) )
& ( X3032 != X3030
| c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3030)) = c_Groups_Oplus__class_Oplus(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3031),X3032))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3034) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
fof(i_0_1399,plain,
! [X4566,X4567,X4568,X4569] :
( ( c_Orderings_Oord__class_Oless(X4569,c_Groups_Ominus__class_Ominus(X4569,X4567,X4566),X4568)
| ~ c_Orderings_Oord__class_Oless(X4569,c_Groups_Oabs__class_Oabs(X4569,c_Groups_Ominus__class_Ominus(X4569,X4568,X4567)),X4566)
| ~ class_Rings_Olinordered__idom(X4569) )
& ( c_Orderings_Oord__class_Oless(X4569,X4568,c_Groups_Oplus__class_Oplus(X4569,X4567,X4566))
| ~ c_Orderings_Oord__class_Oless(X4569,c_Groups_Oabs__class_Oabs(X4569,c_Groups_Ominus__class_Ominus(X4569,X4568,X4567)),X4566)
| ~ class_Rings_Olinordered__idom(X4569) )
& ( ~ c_Orderings_Oord__class_Oless(X4569,c_Groups_Ominus__class_Ominus(X4569,X4567,X4566),X4568)
| ~ c_Orderings_Oord__class_Oless(X4569,X4568,c_Groups_Oplus__class_Oplus(X4569,X4567,X4566))
| c_Orderings_Oord__class_Oless(X4569,c_Groups_Oabs__class_Oabs(X4569,c_Groups_Ominus__class_Ominus(X4569,X4568,X4567)),X4566)
| ~ class_Rings_Olinordered__idom(X4569) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).
fof(i_0_1400,plain,
! [X4884,X4885,X4886,X4887] :
( ~ class_Rings_Ocomm__semiring__0(X4887)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4887)),X4886),c_Polynomial_OpCons(X4887,X4885,X4884)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4887),c_Polynomial_Osmult(X4887,X4885,X4886),c_Polynomial_OpCons(X4887,c_Groups_Ozero__class_Ozero(X4887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4887)),X4886),X4884))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
fof(i_0_1401,plain,
! [X4178,X4179,X4180] :
( ~ class_Rings_Oring__1(X4180)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4180),c_Groups_Ouminus__class_Ouminus(X4180,X4179)),X4178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4180),hAPP(hAPP(c_Power_Opower__class_Opower(X4180),c_Groups_Ouminus__class_Ouminus(X4180,c_Groups_Oone__class_Oone(X4180))),X4178)),hAPP(hAPP(c_Power_Opower__class_Opower(X4180),X4179),X4178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1402,plain,
! [X4659,X4660,X4661] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4661),X4660),X4659),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),X4659)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4661)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4660,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).
fof(i_0_1403,plain,
! [X4656,X4657,X4658] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4658),X4657),X4656))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4656,X4658)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4658)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1404,plain,
! [X4491,X4492,X4493] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4493)
| c_Orderings_Oord__class_Oless__eq(X4493,c_Groups_Oabs__class_Oabs(X4493,c_Groups_Ominus__class_Ominus(X4493,c_Groups_Oabs__class_Oabs(X4493,X4492),c_Groups_Oabs__class_Oabs(X4493,X4491))),c_Groups_Oabs__class_Oabs(X4493,c_Groups_Ominus__class_Ominus(X4493,X4492,X4491))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_1405,plain,
! [X4560,X4561,X4562] :
( ~ class_RealVector_Oreal__normed__vector(X4562)
| 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(X4562,X4561),c_RealVector_Onorm__class_Onorm(X4562,X4560))),c_RealVector_Onorm__class_Onorm(X4562,c_Groups_Ominus__class_Ominus(X4562,X4561,X4560))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).
fof(i_0_1406,plain,
! [X4895,X4896,X4897,X4898] :
( ~ class_Rings_Ocomm__semiring__0(X4898)
| c_Polynomial_Opcompose(X4898,c_Polynomial_OpCons(X4898,X4897,X4896),X4895) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4898),c_Polynomial_OpCons(X4898,X4897,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4898))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4898)),X4895),c_Polynomial_Opcompose(X4898,X4896,X4895))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__pCons])]) ).
fof(i_0_1407,plain,
! [X2972,X2973,X2974,X2975,X2976] :
( ~ class_Rings_Ocomm__semiring__1(X2976)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),X2975),X2974)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),X2973),X2972)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),X2975),X2973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2976),X2974),X2972)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1408,plain,
! [X2982,X2983,X2984,X2985,X2986] :
( ~ class_Rings_Ocomm__semiring__1(X2986)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2985),X2984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2983),X2982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2983),X2982))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_1409,plain,
! [X4315,X4316] : 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,X4316,X4315)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4316)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4315)),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(i_0_1410,plain,
! [X2842,X2843] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2843),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2843,X2842)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2842))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
fof(i_0_1411,plain,
! [X4753,X4754,X4755,X4756] :
( ~ class_Rings_Ocomm__semiring__0(X4756)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4756)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4756),X4755,X4754)),X4753) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4756)),X4755),X4753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4756)),X4754),X4753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left])]) ).
fof(i_0_1412,plain,
! [X4328,X4329,X4330,X4331,X4332,X4333,X4334] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4329,X4328)
| hBOOL(hAPP(X4330,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4330,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4329,X4328))) )
& ( X4329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4328,X4331)
| hBOOL(hAPP(X4330,X4331))
| ~ hBOOL(hAPP(X4330,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4329,X4328))) )
& ( X4333 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4332,esk9_3(X4332,X4333,X4334))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4333,X4332)
| hBOOL(hAPP(X4334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4333,X4332))) )
& ( ~ hBOOL(hAPP(X4334,esk9_3(X4332,X4333,X4334)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4333,X4332)
| hBOOL(hAPP(X4334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4333,X4332))) )
& ( X4333 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4332,esk9_3(X4332,X4333,X4334))
| ~ hBOOL(hAPP(X4334,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4333,X4332))) )
& ( ~ hBOOL(hAPP(X4334,esk9_3(X4332,X4333,X4334)))
| ~ hBOOL(hAPP(X4334,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4333,X4332))) ) ),
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_1413,plain,
! [X4320,X4321,X4322,X4323,X4324,X4325,X4326] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4321,X4320)
| hBOOL(hAPP(X4322,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4322,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4321,X4320))) )
& ( X4321 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4320,X4323)
| hBOOL(hAPP(X4322,X4323))
| ~ hBOOL(hAPP(X4322,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4321,X4320))) )
& ( X4325 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4324,esk8_3(X4324,X4325,X4326))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4325,X4324)
| hBOOL(hAPP(X4326,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4325,X4324))) )
& ( ~ hBOOL(hAPP(X4326,esk8_3(X4324,X4325,X4326)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4325,X4324)
| hBOOL(hAPP(X4326,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4325,X4324))) )
& ( X4325 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4324,esk8_3(X4324,X4325,X4326))
| ~ hBOOL(hAPP(X4326,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4326,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4325,X4324))) )
& ( ~ hBOOL(hAPP(X4326,esk8_3(X4324,X4325,X4326)))
| ~ hBOOL(hAPP(X4326,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4326,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4325,X4324))) ) ),
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_1280])])])])])]) ).
fof(i_0_1414,plain,
! [X4483,X4484,X4485,X4486,X4487] :
( ~ class_Rings_Olinordered__idom(X4487)
| ~ c_Orderings_Oord__class_Oless(X4487,c_Groups_Oabs__class_Oabs(X4487,X4486),X4485)
| ~ c_Orderings_Oord__class_Oless(X4487,c_Groups_Oabs__class_Oabs(X4487,X4484),X4483)
| c_Orderings_Oord__class_Oless(X4487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4487),c_Groups_Oabs__class_Oabs(X4487,X4486)),c_Groups_Oabs__class_Oabs(X4487,X4484)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4487),X4485),X4483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_1415,plain,
! [X4841,X4842,X4843,X4844,X4845] :
( ~ class_Rings_Ocomm__semiring__0(X4845)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4845)),c_Polynomial_Omonom(X4845,X4844,X4843)),c_Polynomial_Omonom(X4845,X4842,X4841)) = c_Polynomial_Omonom(X4845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4845),X4844),X4842),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4843,X4841)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__monom])]) ).
fof(i_0_1416,plain,
! [X2969,X2970,X2971] :
( ~ class_Rings_Olinordered__semidom(X2971)
| ~ c_Orderings_Oord__class_Oless(X2971,c_Groups_Ozero__class_Ozero(X2971),X2970)
| ~ c_Orderings_Oord__class_Oless(X2971,X2970,c_Groups_Oone__class_Oone(X2971))
| c_Orderings_Oord__class_Oless(X2971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2971),X2970),hAPP(hAPP(c_Power_Opower__class_Opower(X2971),X2970),X2969)),hAPP(hAPP(c_Power_Opower__class_Opower(X2971),X2970),X2969)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1417,plain,
! [X4606] :
( ( ~ 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),X4606),X4606),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4606,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4606,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),X4606),X4606),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).
fof(i_0_1418,plain,
! [X2818,X2819,X2820,X2821,X2822] :
( ~ class_RealVector_Oreal__normed__vector(X2822)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2822,X2821),X2820)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2822,X2819),X2818)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2822,c_Groups_Oplus__class_Oplus(X2822,X2821,X2819)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2820,X2818)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
fof(i_0_1419,plain,
! [X4761,X4762,X4763,X4764] :
( ~ class_Rings_Ocomm__semiring__0(X4764)
| hAPP(c_Polynomial_Opoly(X4764,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4764)),X4763),X4762)),X4761) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4764),hAPP(c_Polynomial_Opoly(X4764,X4763),X4761)),hAPP(c_Polynomial_Opoly(X4764,X4762),X4761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1420,plain,
! [X4390,X4391] :
( ( X4391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4391),X4390) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4391),X4390) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4390,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4391,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4390)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1421,plain,
! [X4244,X4245,X4246] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4245,X4246),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4244,X4246))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4245,X4244)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4246,X4244)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4246,X4245) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4245,X4244)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4245,X4246),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4244,X4246))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4246,X4244)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4246,X4245) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1422,plain,
! [X4274,X4275,X4276] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4275,X4276),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4274,X4276))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4275,X4274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4276,X4274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4276,X4275) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4275,X4274)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4275,X4276),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4274,X4276))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4276,X4274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4276,X4275) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1423,plain,
! [X3421,X3422,X3423,X3424,X3425] :
( ~ class_Rings_Oordered__semiring(X3425)
| ~ c_Orderings_Oord__class_Oless__eq(X3425,X3424,X3423)
| ~ c_Orderings_Oord__class_Oless__eq(X3425,X3422,X3421)
| ~ c_Orderings_Oord__class_Oless__eq(X3425,c_Groups_Ozero__class_Ozero(X3425),X3424)
| ~ c_Orderings_Oord__class_Oless__eq(X3425,c_Groups_Ozero__class_Ozero(X3425),X3422)
| c_Orderings_Oord__class_Oless__eq(X3425,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3425),X3424),X3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3425),X3423),X3421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1424,plain,
! [X3416,X3417,X3418,X3419,X3420] :
( ~ class_Rings_Oordered__semiring(X3420)
| ~ c_Orderings_Oord__class_Oless__eq(X3420,X3419,X3418)
| ~ c_Orderings_Oord__class_Oless__eq(X3420,X3417,X3416)
| ~ c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ozero__class_Ozero(X3420),X3418)
| ~ c_Orderings_Oord__class_Oless__eq(X3420,c_Groups_Ozero__class_Ozero(X3420),X3417)
| c_Orderings_Oord__class_Oless__eq(X3420,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3420),X3419),X3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3420),X3418),X3416)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1425,plain,
! [X3605,X3606,X3607,X3608,X3609] :
( ~ class_Rings_Olinordered__semiring__strict(X3609)
| ~ c_Orderings_Oord__class_Oless(X3609,X3608,X3607)
| ~ c_Orderings_Oord__class_Oless__eq(X3609,X3606,X3605)
| ~ c_Orderings_Oord__class_Oless__eq(X3609,c_Groups_Ozero__class_Ozero(X3609),X3608)
| ~ c_Orderings_Oord__class_Oless(X3609,c_Groups_Ozero__class_Ozero(X3609),X3606)
| c_Orderings_Oord__class_Oless(X3609,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3609),X3608),X3606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3609),X3607),X3605)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1426,plain,
! [X3610,X3611,X3612,X3613,X3614] :
( ~ class_Rings_Olinordered__semiring__strict(X3614)
| ~ c_Orderings_Oord__class_Oless__eq(X3614,X3613,X3612)
| ~ c_Orderings_Oord__class_Oless(X3614,X3611,X3610)
| ~ c_Orderings_Oord__class_Oless(X3614,c_Groups_Ozero__class_Ozero(X3614),X3613)
| ~ c_Orderings_Oord__class_Oless__eq(X3614,c_Groups_Ozero__class_Ozero(X3614),X3611)
| c_Orderings_Oord__class_Oless(X3614,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3614),X3613),X3611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3614),X3612),X3610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1427,plain,
! [X3600,X3601,X3602,X3603,X3604] :
( ~ class_Rings_Olinordered__semiring__strict(X3604)
| ~ c_Orderings_Oord__class_Oless(X3604,X3603,X3602)
| ~ c_Orderings_Oord__class_Oless(X3604,X3601,X3600)
| ~ c_Orderings_Oord__class_Oless__eq(X3604,c_Groups_Ozero__class_Ozero(X3604),X3603)
| ~ c_Orderings_Oord__class_Oless__eq(X3604,c_Groups_Ozero__class_Ozero(X3604),X3601)
| c_Orderings_Oord__class_Oless(X3604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3604),X3603),X3601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3604),X3602),X3600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1428,plain,
! [X3595,X3596,X3597,X3598,X3599] :
( ~ class_Rings_Olinordered__semiring__strict(X3599)
| ~ c_Orderings_Oord__class_Oless(X3599,X3598,X3597)
| ~ c_Orderings_Oord__class_Oless(X3599,X3596,X3595)
| ~ c_Orderings_Oord__class_Oless(X3599,c_Groups_Ozero__class_Ozero(X3599),X3597)
| ~ c_Orderings_Oord__class_Oless__eq(X3599,c_Groups_Ozero__class_Ozero(X3599),X3596)
| c_Orderings_Oord__class_Oless(X3599,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3599),X3598),X3596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3599),X3597),X3595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1429,plain,
! [X2800,X2801,X2802,X2803,X2804] :
( ~ class_RealVector_Oreal__normed__algebra(X2804)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2804,X2803),X2802)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2804,X2801),X2800)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2804),X2803),X2801)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2802),X2800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1430,plain,
! [X4916,X4917,X4918] :
( ~ class_Rings_Ocomm__semiring__0(X4918)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4918),X4917,c_Polynomial_Osmult(X4918,X4916,c_Polynomial_Osynthetic__div(X4918,X4917,X4916))) = c_Polynomial_OpCons(X4918,hAPP(c_Polynomial_Opoly(X4918,X4917),X4916),c_Polynomial_Osynthetic__div(X4918,X4917,X4916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct])]) ).
fof(i_0_1431,plain,
! [X3076,X3077,X3078,X3079] :
( ~ class_Groups_Ocomm__monoid__mult(X3079)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),X3078),X3077)),X3076) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),hAPP(hAPP(c_Power_Opower__class_Opower(X3079),X3078),X3076)),hAPP(hAPP(c_Power_Opower__class_Opower(X3079),X3077),X3076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1432,plain,
! [X3072,X3073,X3074,X3075] :
( ~ class_Rings_Ocomm__semiring__1(X3075)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3075),X3074),X3073)),X3072) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3075),hAPP(hAPP(c_Power_Opower__class_Opower(X3075),X3074),X3072)),hAPP(hAPP(c_Power_Opower__class_Opower(X3075),X3073),X3072)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1433,plain,
! [X3699,X3700,X3701] :
( ~ class_Rings_Olinordered__ring(X3701)
| c_Orderings_Oord__class_Oless__eq(X3701,c_Groups_Ozero__class_Ozero(X3701),c_Groups_Oplus__class_Oplus(X3701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3701),X3700),X3700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3701),X3699),X3699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_1434,plain,
! [X4173,X4174] :
( ~ class_Rings_Oring__1(X4174)
| c_Groups_Ominus__class_Ominus(X4174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),X4173),X4173),c_Groups_Oone__class_Oone(X4174)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4174),c_Groups_Oplus__class_Oplus(X4174,X4173,c_Groups_Oone__class_Oone(X4174))),c_Groups_Ominus__class_Ominus(X4174,X4173,c_Groups_Oone__class_Oone(X4174))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
fof(i_0_1435,plain,
! [X4876,X4877,X4878,X4879] :
( ~ class_Rings_Ocomm__semiring__0(X4879)
| hAPP(c_Polynomial_Opoly(X4879,c_Polynomial_OpCons(X4879,X4878,X4877)),X4876) = c_Groups_Oplus__class_Oplus(X4879,X4878,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4879),X4876),hAPP(c_Polynomial_Opoly(X4879,X4877),X4876))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(i_0_1436,plain,
! [X2808,X2809,X2810] :
( ~ class_Rings_Olinordered__semidom(X2810)
| ~ c_Orderings_Oord__class_Oless(X2810,c_Groups_Oone__class_Oone(X2810),X2809)
| c_Orderings_Oord__class_Oless(X2810,hAPP(hAPP(c_Power_Opower__class_Opower(X2810),X2809),X2808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2810),X2809),hAPP(hAPP(c_Power_Opower__class_Opower(X2810),X2809),X2808))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1437,plain,
! [X3631,X3632,X3633,X3634] :
( ~ class_Rings_Olinordered__semiring__strict(X3634)
| ~ c_Orderings_Oord__class_Oless__eq(X3634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3634),X3633),X3632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3634),X3631),X3632))
| ~ c_Orderings_Oord__class_Oless(X3634,c_Groups_Ozero__class_Ozero(X3634),X3632)
| c_Orderings_Oord__class_Oless__eq(X3634,X3633,X3631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1438,plain,
! [X3635,X3636,X3637,X3638] :
( ~ class_Rings_Olinordered__semiring__strict(X3638)
| ~ c_Orderings_Oord__class_Oless__eq(X3638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3638),X3637),X3636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3638),X3637),X3635))
| ~ c_Orderings_Oord__class_Oless(X3638,c_Groups_Ozero__class_Ozero(X3638),X3637)
| c_Orderings_Oord__class_Oless__eq(X3638,X3636,X3635) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1439,plain,
! [X3587,X3588,X3589,X3590] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3590),X3589),X3588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3590),X3589),X3587))
| c_Orderings_Oord__class_Oless__eq(X3590,X3588,X3587)
| ~ c_Orderings_Oord__class_Oless(X3590,c_Groups_Ozero__class_Ozero(X3590),X3589)
| ~ class_Rings_Olinordered__ring__strict(X3590) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3590,X3588,X3587)
| c_Orderings_Oord__class_Oless__eq(X3590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3590),X3589),X3588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3590),X3589),X3587))
| ~ c_Orderings_Oord__class_Oless(X3590,c_Groups_Ozero__class_Ozero(X3590),X3589)
| ~ class_Rings_Olinordered__ring__strict(X3590) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1440,plain,
! [X3615,X3616,X3617,X3618] :
( ~ class_Rings_Olinordered__semiring(X3618)
| ~ c_Orderings_Oord__class_Oless(X3618,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3618),X3617),X3616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3618),X3615),X3616))
| ~ c_Orderings_Oord__class_Oless__eq(X3618,c_Groups_Ozero__class_Ozero(X3618),X3616)
| c_Orderings_Oord__class_Oless(X3618,X3617,X3615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1441,plain,
! [X3619,X3620,X3621,X3622] :
( ~ class_Rings_Olinordered__semiring__strict(X3622)
| ~ c_Orderings_Oord__class_Oless(X3622,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3622),X3621),X3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3622),X3619),X3620))
| ~ c_Orderings_Oord__class_Oless__eq(X3622,c_Groups_Ozero__class_Ozero(X3622),X3620)
| c_Orderings_Oord__class_Oless(X3622,X3621,X3619) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1442,plain,
! [X2919,X2920,X2921,X2922] :
( ~ class_Rings_Olinordered__semidom(X2922)
| ~ c_Orderings_Oord__class_Oless(X2922,hAPP(hAPP(c_Power_Opower__class_Opower(X2922),X2921),X2920),hAPP(hAPP(c_Power_Opower__class_Opower(X2922),X2919),X2920))
| ~ c_Orderings_Oord__class_Oless__eq(X2922,c_Groups_Ozero__class_Ozero(X2922),X2919)
| c_Orderings_Oord__class_Oless(X2922,X2921,X2919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1443,plain,
! [X3623,X3624,X3625,X3626] :
( ~ class_Rings_Olinordered__semiring(X3626)
| ~ c_Orderings_Oord__class_Oless(X3626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3626),X3625),X3624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3626),X3625),X3623))
| ~ c_Orderings_Oord__class_Oless__eq(X3626,c_Groups_Ozero__class_Ozero(X3626),X3625)
| c_Orderings_Oord__class_Oless(X3626,X3624,X3623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1444,plain,
! [X3627,X3628,X3629,X3630] :
( ~ class_Rings_Olinordered__semiring__strict(X3630)
| ~ c_Orderings_Oord__class_Oless(X3630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3630),X3629),X3628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3630),X3629),X3627))
| ~ c_Orderings_Oord__class_Oless__eq(X3630,c_Groups_Ozero__class_Ozero(X3630),X3629)
| c_Orderings_Oord__class_Oless(X3630,X3628,X3627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1445,plain,
! [X3479,X3480,X3481,X3482] :
( ( ~ c_Orderings_Oord__class_Oless(X3482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3482),X3481),X3480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3482),X3481),X3479))
| c_Orderings_Oord__class_Oless(X3482,X3480,X3479)
| ~ c_Orderings_Oord__class_Oless(X3482,c_Groups_Ozero__class_Ozero(X3482),X3481)
| ~ class_Rings_Olinordered__ring__strict(X3482) )
& ( ~ c_Orderings_Oord__class_Oless(X3482,X3480,X3479)
| c_Orderings_Oord__class_Oless(X3482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3482),X3481),X3480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3482),X3481),X3479))
| ~ c_Orderings_Oord__class_Oless(X3482,c_Groups_Ozero__class_Ozero(X3482),X3481)
| ~ class_Rings_Olinordered__ring__strict(X3482) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1446,plain,
! [X3591,X3592,X3593,X3594] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3594),X3593),X3592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3594),X3593),X3591))
| c_Orderings_Oord__class_Oless__eq(X3594,X3591,X3592)
| ~ c_Orderings_Oord__class_Oless(X3594,X3593,c_Groups_Ozero__class_Ozero(X3594))
| ~ class_Rings_Olinordered__ring__strict(X3594) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3594,X3591,X3592)
| c_Orderings_Oord__class_Oless__eq(X3594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3594),X3593),X3592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3594),X3593),X3591))
| ~ c_Orderings_Oord__class_Oless(X3594,X3593,c_Groups_Ozero__class_Ozero(X3594))
| ~ class_Rings_Olinordered__ring__strict(X3594) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1447,plain,
! [X3498,X3499,X3500,X3501] :
( ( ~ c_Orderings_Oord__class_Oless(X3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3501),X3500),X3499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3501),X3500),X3498))
| c_Orderings_Oord__class_Oless(X3501,X3498,X3499)
| ~ c_Orderings_Oord__class_Oless(X3501,X3500,c_Groups_Ozero__class_Ozero(X3501))
| ~ class_Rings_Olinordered__ring__strict(X3501) )
& ( ~ c_Orderings_Oord__class_Oless(X3501,X3498,X3499)
| c_Orderings_Oord__class_Oless(X3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3501),X3500),X3499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3501),X3500),X3498))
| ~ c_Orderings_Oord__class_Oless(X3501,X3500,c_Groups_Ozero__class_Ozero(X3501))
| ~ class_Rings_Olinordered__ring__strict(X3501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1448,plain,
! [X2931,X2932,X2933,X2934] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2934,hAPP(hAPP(c_Power_Opower__class_Opower(X2934),X2933),X2932),hAPP(hAPP(c_Power_Opower__class_Opower(X2934),X2933),X2931))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2932,X2931)
| ~ c_Orderings_Oord__class_Oless(X2934,c_Groups_Oone__class_Oone(X2934),X2933)
| ~ class_Rings_Olinordered__semidom(X2934) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2932,X2931)
| c_Orderings_Oord__class_Oless__eq(X2934,hAPP(hAPP(c_Power_Opower__class_Opower(X2934),X2933),X2932),hAPP(hAPP(c_Power_Opower__class_Opower(X2934),X2933),X2931))
| ~ c_Orderings_Oord__class_Oless(X2934,c_Groups_Oone__class_Oone(X2934),X2933)
| ~ class_Rings_Olinordered__semidom(X2934) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1449,plain,
! [X2927,X2928,X2929,X2930] :
( ~ class_Rings_Olinordered__semidom(X2930)
| ~ c_Orderings_Oord__class_Oless(X2930,c_Groups_Oone__class_Oone(X2930),X2929)
| ~ c_Orderings_Oord__class_Oless__eq(X2930,hAPP(hAPP(c_Power_Opower__class_Opower(X2930),X2929),X2928),hAPP(hAPP(c_Power_Opower__class_Opower(X2930),X2929),X2927))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2928,X2927) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1450,plain,
! [X3101,X3102,X3103,X3104] :
( ~ class_Rings_Olinordered__semidom(X3104)
| ~ c_Orderings_Oord__class_Oless(X3104,c_Groups_Oone__class_Oone(X3104),X3103)
| ~ c_Orderings_Oord__class_Oless(X3104,hAPP(hAPP(c_Power_Opower__class_Opower(X3104),X3103),X3102),hAPP(hAPP(c_Power_Opower__class_Opower(X3104),X3103),X3101))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3102,X3101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1451,plain,
! [X2835,X2836,X2837,X2838] :
( ( ~ c_Orderings_Oord__class_Oless(X2838,hAPP(hAPP(c_Power_Opower__class_Opower(X2838),X2837),X2836),hAPP(hAPP(c_Power_Opower__class_Opower(X2838),X2837),X2835))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2836,X2835)
| ~ c_Orderings_Oord__class_Oless(X2838,c_Groups_Oone__class_Oone(X2838),X2837)
| ~ class_Rings_Olinordered__semidom(X2838) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2836,X2835)
| c_Orderings_Oord__class_Oless(X2838,hAPP(hAPP(c_Power_Opower__class_Opower(X2838),X2837),X2836),hAPP(hAPP(c_Power_Opower__class_Opower(X2838),X2837),X2835))
| ~ c_Orderings_Oord__class_Oless(X2838,c_Groups_Oone__class_Oone(X2838),X2837)
| ~ class_Rings_Olinordered__semidom(X2838) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1452,plain,
! [X4778,X4779,X4780,X4781,X4782] :
( ~ class_Groups_Oab__group__add(X4782)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4782),c_Polynomial_OpCons(X4782,X4781,X4780),c_Polynomial_OpCons(X4782,X4779,X4778)) = c_Polynomial_OpCons(X4782,c_Groups_Ominus__class_Ominus(X4782,X4781,X4779),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4782),X4780,X4778)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__pCons])]) ).
fof(i_0_1453,plain,
! [X4855,X4856,X4857,X4858,X4859] :
( ~ class_Groups_Ocomm__monoid__add(X4859)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4859),c_Polynomial_OpCons(X4859,X4858,X4857),c_Polynomial_OpCons(X4859,X4856,X4855)) = c_Polynomial_OpCons(X4859,c_Groups_Oplus__class_Oplus(X4859,X4858,X4856),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4859),X4857,X4855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pCons])]) ).
fof(i_0_1454,plain,
! [X4774,X4775,X4776,X4777] :
( ~ class_Rings_Ocomm__semiring__1(X4777)
| hAPP(c_Polynomial_Opoly(X4777,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4777)),X4776),X4775)),X4774) = hAPP(hAPP(c_Power_Opower__class_Opower(X4777),hAPP(c_Polynomial_Opoly(X4777,X4776),X4774)),X4775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1455,plain,
! [X5177,X5178] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5177)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X5178)),c_RComplete_Onatfloor(X5177)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5178),X5177))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1456,plain,
! [X4402,X4403,X4404,X4405,X4406] :
( ~ class_Groups_Oab__group__add(X4406)
| c_Groups_Ominus__class_Ominus(X4406,c_Groups_Oplus__class_Oplus(X4406,X4405,X4404),c_Groups_Oplus__class_Oplus(X4406,X4403,X4402)) = c_Groups_Oplus__class_Oplus(X4406,c_Groups_Ominus__class_Ominus(X4406,X4405,X4403),c_Groups_Ominus__class_Ominus(X4406,X4404,X4402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1457,plain,
! [X3006,X3007,X3008,X3009,X3010] :
( ~ class_Rings_Ocomm__semiring__1(X3010)
| c_Groups_Oplus__class_Oplus(X3010,c_Groups_Oplus__class_Oplus(X3010,X3009,X3008),c_Groups_Oplus__class_Oplus(X3010,X3007,X3006)) = c_Groups_Oplus__class_Oplus(X3010,c_Groups_Oplus__class_Oplus(X3010,X3009,X3007),c_Groups_Oplus__class_Oplus(X3010,X3008,X3006)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1458,plain,
! [X2874,X2875,X2876,X2877] :
( ~ class_Rings_Olinordered__semidom(X2877)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2876,X2875)
| ~ c_Orderings_Oord__class_Oless__eq(X2877,c_Groups_Ozero__class_Ozero(X2877),X2874)
| ~ c_Orderings_Oord__class_Oless__eq(X2877,X2874,c_Groups_Oone__class_Oone(X2877))
| c_Orderings_Oord__class_Oless__eq(X2877,hAPP(hAPP(c_Power_Opower__class_Opower(X2877),X2874),X2875),hAPP(hAPP(c_Power_Opower__class_Opower(X2877),X2874),X2876)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1459,plain,
! [X2956,X2957,X2958,X2959] :
( ~ class_Rings_Olinordered__semidom(X2959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2958,X2957)
| ~ c_Orderings_Oord__class_Oless(X2959,c_Groups_Ozero__class_Ozero(X2959),X2956)
| ~ c_Orderings_Oord__class_Oless(X2959,X2956,c_Groups_Oone__class_Oone(X2959))
| c_Orderings_Oord__class_Oless(X2959,hAPP(hAPP(c_Power_Opower__class_Opower(X2959),X2956),X2957),hAPP(hAPP(c_Power_Opower__class_Opower(X2959),X2956),X2958)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1460,plain,
! [X2878,X2879,X2880,X2881] :
( ~ class_Rings_Olinordered__semidom(X2881)
| ~ c_Orderings_Oord__class_Oless(X2881,X2880,X2879)
| ~ c_Orderings_Oord__class_Oless__eq(X2881,c_Groups_Ozero__class_Ozero(X2881),X2880)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2878)
| c_Orderings_Oord__class_Oless(X2881,hAPP(hAPP(c_Power_Opower__class_Opower(X2881),X2880),X2878),hAPP(hAPP(c_Power_Opower__class_Opower(X2881),X2879),X2878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1461,plain,
! [X3475,X3476,X3477,X3478] :
( ( c_Orderings_Oord__class_Oless(X3478,X3477,c_Groups_Ozero__class_Ozero(X3478))
| c_Orderings_Oord__class_Oless(X3478,c_Groups_Ozero__class_Ozero(X3478),X3477)
| ~ c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) )
& ( c_Orderings_Oord__class_Oless(X3478,X3475,X3476)
| c_Orderings_Oord__class_Oless(X3478,c_Groups_Ozero__class_Ozero(X3478),X3477)
| ~ c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) )
& ( c_Orderings_Oord__class_Oless(X3478,X3477,c_Groups_Ozero__class_Ozero(X3478))
| c_Orderings_Oord__class_Oless(X3478,X3476,X3475)
| ~ c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) )
& ( c_Orderings_Oord__class_Oless(X3478,X3475,X3476)
| c_Orderings_Oord__class_Oless(X3478,X3476,X3475)
| ~ c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) )
& ( ~ c_Orderings_Oord__class_Oless(X3478,c_Groups_Ozero__class_Ozero(X3478),X3477)
| ~ c_Orderings_Oord__class_Oless(X3478,X3476,X3475)
| c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) )
& ( ~ c_Orderings_Oord__class_Oless(X3478,X3477,c_Groups_Ozero__class_Ozero(X3478))
| ~ c_Orderings_Oord__class_Oless(X3478,X3475,X3476)
| c_Orderings_Oord__class_Oless(X3478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3478),X3477),X3475))
| ~ class_Rings_Olinordered__ring__strict(X3478) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1462,plain,
! [X3471,X3472,X3473,X3474] :
( ( c_Orderings_Oord__class_Oless(X3474,X3472,c_Groups_Ozero__class_Ozero(X3474))
| c_Orderings_Oord__class_Oless(X3474,c_Groups_Ozero__class_Ozero(X3474),X3472)
| ~ c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) )
& ( c_Orderings_Oord__class_Oless(X3474,X3471,X3473)
| c_Orderings_Oord__class_Oless(X3474,c_Groups_Ozero__class_Ozero(X3474),X3472)
| ~ c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) )
& ( c_Orderings_Oord__class_Oless(X3474,X3472,c_Groups_Ozero__class_Ozero(X3474))
| c_Orderings_Oord__class_Oless(X3474,X3473,X3471)
| ~ c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) )
& ( c_Orderings_Oord__class_Oless(X3474,X3471,X3473)
| c_Orderings_Oord__class_Oless(X3474,X3473,X3471)
| ~ c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) )
& ( ~ c_Orderings_Oord__class_Oless(X3474,c_Groups_Ozero__class_Ozero(X3474),X3472)
| ~ c_Orderings_Oord__class_Oless(X3474,X3473,X3471)
| c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) )
& ( ~ c_Orderings_Oord__class_Oless(X3474,X3472,c_Groups_Ozero__class_Ozero(X3474))
| ~ c_Orderings_Oord__class_Oless(X3474,X3471,X3473)
| c_Orderings_Oord__class_Oless(X3474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3473),X3472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3474),X3471),X3472))
| ~ class_Rings_Olinordered__ring__strict(X3474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1463,plain,
! [X5151,X5152,X5154] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X5151,X5152))
| ~ class_RealVector_Oreal__normed__algebra(X5152) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5152,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5152),X5154),X5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5152,X5154)),esk28_2(X5151,X5152)))
| ~ class_RealVector_Oreal__normed__algebra(X5152) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded])])])])]) ).
fof(i_0_1464,plain,
! [X2960,X2961,X2962] :
( ~ class_RealVector_Oreal__normed__algebra(X2962)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2962),X2961),X2960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2962,X2961)),c_RealVector_Onorm__class_Onorm(X2962,X2960))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1465,plain,
! [X5155,X5156,X5158] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X5155,X5156))
| ~ class_RealVector_Oreal__normed__algebra(X5156) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5156),X5155),X5158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5156,X5158)),esk29_2(X5155,X5156)))
| ~ class_RealVector_Oreal__normed__algebra(X5156) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Opos__bounded])])])])]) ).
fof(i_0_1466,plain,
! [X3035,X3036,X3037,X3038] :
( ~ class_Rings_Ocomm__semiring__1(X3038)
| c_Groups_Oplus__class_Oplus(X3038,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3038),X3037),X3036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3038),X3035),X3036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3038),c_Groups_Oplus__class_Oplus(X3038,X3037,X3035)),X3036) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1467,plain,
! [X4007,X4008,X4009,X4010] :
( ~ class_RealVector_Oreal__normed__algebra(X4010)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4010),c_Groups_Ominus__class_Ominus(X4010,X4009,X4008)),X4007) = c_Groups_Ominus__class_Ominus(X4010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4010),X4009),X4007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4010),X4008),X4007)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1468,plain,
! [X4003,X4004,X4005,X4006] :
( ~ class_RealVector_Oreal__normed__algebra(X4006)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4006),c_Groups_Ominus__class_Ominus(X4006,X4005,X4004)),X4003) = c_Groups_Ominus__class_Ominus(X4006,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4006),X4005),X4003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4006),X4004),X4003)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1469,plain,
! [X3310,X3311,X3312,X3313] :
( ~ class_Rings_Ocomm__semiring(X3313)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3313),c_Groups_Oplus__class_Oplus(X3313,X3312,X3311)),X3310) = c_Groups_Oplus__class_Oplus(X3313,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3313),X3312),X3310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3313),X3311),X3310)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1470,plain,
! [X3047,X3048,X3049,X3050] :
( ~ class_Rings_Ocomm__semiring__1(X3050)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3050),c_Groups_Oplus__class_Oplus(X3050,X3049,X3048)),X3047) = c_Groups_Oplus__class_Oplus(X3050,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3050),X3049),X3047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3050),X3048),X3047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1471,plain,
! [X3043,X3044,X3045,X3046] :
( ~ class_RealVector_Oreal__normed__algebra(X3046)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3046),c_Groups_Oplus__class_Oplus(X3046,X3045,X3044)),X3043) = c_Groups_Oplus__class_Oplus(X3046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3046),X3045),X3043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3046),X3044),X3043)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1472,plain,
! [X3039,X3040,X3041,X3042] :
( ~ class_RealVector_Oreal__normed__algebra(X3042)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3042),c_Groups_Oplus__class_Oplus(X3042,X3041,X3040)),X3039) = c_Groups_Oplus__class_Oplus(X3042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3042),X3041),X3039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3042),X3040),X3039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1473,plain,
! [X2827,X2828,X2829,X2830] :
( ~ class_Rings_Ocomm__semiring__1(X2830)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2830),hAPP(hAPP(c_Power_Opower__class_Opower(X2830),X2829),X2828)),hAPP(hAPP(c_Power_Opower__class_Opower(X2830),X2829),X2827)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2830),X2829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1474,plain,
! [X2823,X2824,X2825,X2826] :
( ~ class_Groups_Omonoid__mult(X2826)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2826),X2825),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2824,X2823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2826),hAPP(hAPP(c_Power_Opower__class_Opower(X2826),X2825),X2824)),hAPP(hAPP(c_Power_Opower__class_Opower(X2826),X2825),X2823)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1475,plain,
! [X2987,X2988,X2989,X2990] :
( ~ class_Rings_Ocomm__semiring__1(X2990)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),X2989),X2988)),X2987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),X2989),X2987)),X2988) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_1476,plain,
! [X4494,X4495,X4496] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4496)
| c_Orderings_Oord__class_Oless__eq(X4496,c_Groups_Ominus__class_Ominus(X4496,c_Groups_Oabs__class_Oabs(X4496,X4495),c_Groups_Oabs__class_Oabs(X4496,X4494)),c_Groups_Oabs__class_Oabs(X4496,c_Groups_Ominus__class_Ominus(X4496,X4495,X4494))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_1477,plain,
! [X4497,X4498,X4499] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4499)
| c_Orderings_Oord__class_Oless__eq(X4499,c_Groups_Ominus__class_Ominus(X4499,c_Groups_Oabs__class_Oabs(X4499,X4498),c_Groups_Oabs__class_Oabs(X4499,X4497)),c_Groups_Oabs__class_Oabs(X4499,c_Groups_Ominus__class_Ominus(X4499,X4497,X4498))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).
fof(i_0_1478,plain,
! [X4542,X4543,X4544] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4544)
| c_Orderings_Oord__class_Oless__eq(X4544,c_Groups_Oabs__class_Oabs(X4544,c_Groups_Ominus__class_Ominus(X4544,X4543,X4542)),c_Groups_Oplus__class_Oplus(X4544,c_Groups_Oabs__class_Oabs(X4544,X4543),c_Groups_Oabs__class_Oabs(X4544,X4542))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_1479,plain,
! [X4488,X4489,X4490] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4490)
| c_Orderings_Oord__class_Oless__eq(X4490,c_Groups_Oabs__class_Oabs(X4490,c_Groups_Oplus__class_Oplus(X4490,X4489,X4488)),c_Groups_Oplus__class_Oplus(X4490,c_Groups_Oabs__class_Oabs(X4490,X4489),c_Groups_Oabs__class_Oabs(X4490,X4488))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
fof(i_0_1480,plain,
! [X2938,X2939,X2940,X2941,X2942,X2943] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2943)
| X2942 = c_Groups_Ozero__class_Ozero(X2943)
| X2941 != X2940
| X2939 = X2938
| c_Groups_Oplus__class_Oplus(X2943,X2941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2943),X2942),X2939)) != c_Groups_Oplus__class_Oplus(X2943,X2940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2943),X2942),X2938)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1481,plain,
! [X3216,X3217,X3218] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3218),X3217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3216),X3217))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3217)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3218,X3216) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3217)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3218),X3217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3216),X3217)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3218,X3216)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3218),X3217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3216),X3217)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1482,plain,
! [X3690,X3691,X3692] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3692),X3691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3692),X3690))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3691,X3690)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3692) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3691,X3690)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3692),X3691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3692),X3690))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3692) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1483,plain,
! [X3219,X3220,X3221] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3219))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3221)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3220,X3219) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3221)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3219)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3220,X3219)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3221),X3219)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1484,plain,
! [X3676,X3677,X3678] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3677),X3678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3676),X3678))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3677,X3676)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3678) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3677,X3676)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3677),X3678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3676),X3678))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3678) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1485,plain,
! [X3679,X3680,X3681] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3681),X3680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3681),X3679))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3680,X3679)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3681) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3680,X3679)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3681),X3680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3681),X3679))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3681) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1486,plain,
! [X3873,X3874,X3875] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3875),X3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3875),X3873))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3874,X3873)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3875) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3874,X3873)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3875),X3874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3875),X3873))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3875) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1487,plain,
! [X2863,X2864,X2865] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2865)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2865),X2864),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2865),X2863))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2864,X2863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1488,plain,
! [X3577,X3578,X3579] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3578),X3579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3577),X3579))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3578,X3577)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3579) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3578,X3577)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3578),X3579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3577),X3579))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3579) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1489,plain,
! [X5193,X5194] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5194),X5193)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5193,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5194),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X5193) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5194,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).
fof(i_0_1490,plain,
! [X3926,X3927,X3928] :
( ~ class_RealVector_Oreal__normed__vector(X3928)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3928,X3927),c_RealVector_Onorm__class_Onorm(X3928,X3926)),c_RealVector_Onorm__class_Onorm(X3928,c_Groups_Ominus__class_Ominus(X3928,X3927,X3926))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1491,plain,
! [X4317,X4318,X4319] :
( ~ class_RealVector_Oreal__normed__vector(X4319)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4319,X4318),c_RealVector_Onorm__class_Onorm(X4319,X4317)),c_RealVector_Onorm__class_Onorm(X4319,c_Groups_Oplus__class_Oplus(X4319,X4318,X4317))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(i_0_1492,plain,
! [X4181,X4182,X4183] :
( ~ class_RealVector_Oreal__normed__vector(X4183)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4183,c_Groups_Ominus__class_Ominus(X4183,X4182,X4181)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4183,X4182),c_RealVector_Onorm__class_Onorm(X4183,X4181))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).
fof(i_0_1493,plain,
! [X2944,X2945,X2946] :
( ~ class_RealVector_Oreal__normed__vector(X2946)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2946,c_Groups_Oplus__class_Oplus(X2946,X2945,X2944)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2946,X2945),c_RealVector_Onorm__class_Onorm(X2946,X2944))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1494,plain,
! [X4745,X4746,X4747,X4748] :
( ~ class_Rings_Ocomm__semiring__0(X4748)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4748)),c_Polynomial_Osmult(X4748,X4747,X4746)),X4745) = c_Polynomial_Osmult(X4748,X4747,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4748)),X4746),X4745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
fof(i_0_1495,plain,
! [X4767,X4768,X4769,X4770] :
( ~ class_Rings_Ocomm__ring(X4770)
| hAPP(c_Polynomial_Opoly(X4770,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4770),X4769,X4768)),X4767) = c_Groups_Ominus__class_Ominus(X4770,hAPP(c_Polynomial_Opoly(X4770,X4769),X4767),hAPP(c_Polynomial_Opoly(X4770,X4768),X4767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).
fof(i_0_1496,plain,
! [X4851,X4852,X4853,X4854] :
( ~ class_Rings_Ocomm__semiring__0(X4854)
| hAPP(c_Polynomial_Opoly(X4854,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4854),X4853,X4852)),X4851) = c_Groups_Oplus__class_Oplus(X4854,hAPP(c_Polynomial_Opoly(X4854,X4853),X4851),hAPP(c_Polynomial_Opoly(X4854,X4852),X4851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1497,plain,
! [X4298,X4299,X4300] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4298,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4299,X4300))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4298,X4300),X4299)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4300,X4299) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4298,X4300),X4299)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4298,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4299,X4300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4300,X4299) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1498,plain,
! [X4415,X4416,X4417] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4417,X4416)),X4415) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4417),X4415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4416),X4415)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1499,plain,
! [X4431,X4432,X4433] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4433,X4432)),X4431) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4433),X4431),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4432),X4431)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1500,plain,
! [X4250,X4251,X4252] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4252,X4251)),X4250) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4252),X4250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4251),X4250)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1501,plain,
! [X3273,X3274,X3275] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3275,X3274)),X3273) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3275),X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3274),X3273)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1502,plain,
! [X3407,X3408,X3409] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3409,X3408)),X3407) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3409),X3407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3408),X3407)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(i_0_1503,plain,
! [X2966,X2967,X2968] :
( ~ class_RealVector_Oreal__normed__algebra__1(X2968)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2968,hAPP(hAPP(c_Power_Opower__class_Opower(X2968),X2967),X2966)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2968,X2967)),X2966)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1504,plain,
! [X3778,X3779,X3780,X3781] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3781,c_Groups_Oplus__class_Oplus(X3781,X3780,X3779),c_Groups_Oplus__class_Oplus(X3781,X3778,X3779))
| c_Orderings_Oord__class_Oless__eq(X3781,X3780,X3778)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3781) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3781,X3780,X3778)
| c_Orderings_Oord__class_Oless__eq(X3781,c_Groups_Oplus__class_Oplus(X3781,X3780,X3779),c_Groups_Oplus__class_Oplus(X3781,X3778,X3779))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3781) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1505,plain,
! [X3757,X3758,X3759,X3760] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3760)
| ~ c_Orderings_Oord__class_Oless__eq(X3760,c_Groups_Oplus__class_Oplus(X3760,X3759,X3758),c_Groups_Oplus__class_Oplus(X3760,X3757,X3758))
| c_Orderings_Oord__class_Oless__eq(X3760,X3759,X3757) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1506,plain,
! [X3774,X3775,X3776,X3777] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3777,c_Groups_Oplus__class_Oplus(X3777,X3776,X3775),c_Groups_Oplus__class_Oplus(X3777,X3776,X3774))
| c_Orderings_Oord__class_Oless__eq(X3777,X3775,X3774)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3777) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3777,X3775,X3774)
| c_Orderings_Oord__class_Oless__eq(X3777,c_Groups_Oplus__class_Oplus(X3777,X3776,X3775),c_Groups_Oplus__class_Oplus(X3777,X3776,X3774))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3777) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_1507,plain,
! [X3753,X3754,X3755,X3756] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3756)
| ~ c_Orderings_Oord__class_Oless__eq(X3756,c_Groups_Oplus__class_Oplus(X3756,X3755,X3754),c_Groups_Oplus__class_Oplus(X3756,X3755,X3753))
| c_Orderings_Oord__class_Oless__eq(X3756,X3754,X3753) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1508,plain,
! [X3807,X3808,X3809,X3810] :
( ( ~ c_Orderings_Oord__class_Oless(X3810,c_Groups_Oplus__class_Oplus(X3810,X3809,X3808),c_Groups_Oplus__class_Oplus(X3810,X3807,X3808))
| c_Orderings_Oord__class_Oless(X3810,X3809,X3807)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3810) )
& ( ~ c_Orderings_Oord__class_Oless(X3810,X3809,X3807)
| c_Orderings_Oord__class_Oless(X3810,c_Groups_Oplus__class_Oplus(X3810,X3809,X3808),c_Groups_Oplus__class_Oplus(X3810,X3807,X3808))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3810) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1509,plain,
! [X3786,X3787,X3788,X3789] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3789)
| ~ c_Orderings_Oord__class_Oless(X3789,c_Groups_Oplus__class_Oplus(X3789,X3788,X3787),c_Groups_Oplus__class_Oplus(X3789,X3786,X3787))
| c_Orderings_Oord__class_Oless(X3789,X3788,X3786) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1510,plain,
! [X3803,X3804,X3805,X3806] :
( ( ~ c_Orderings_Oord__class_Oless(X3806,c_Groups_Oplus__class_Oplus(X3806,X3805,X3804),c_Groups_Oplus__class_Oplus(X3806,X3805,X3803))
| c_Orderings_Oord__class_Oless(X3806,X3804,X3803)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3806) )
& ( ~ c_Orderings_Oord__class_Oless(X3806,X3804,X3803)
| c_Orderings_Oord__class_Oless(X3806,c_Groups_Oplus__class_Oplus(X3806,X3805,X3804),c_Groups_Oplus__class_Oplus(X3806,X3805,X3803))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1511,plain,
! [X3782,X3783,X3784,X3785] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3785)
| ~ c_Orderings_Oord__class_Oless(X3785,c_Groups_Oplus__class_Oplus(X3785,X3784,X3783),c_Groups_Oplus__class_Oplus(X3785,X3784,X3782))
| c_Orderings_Oord__class_Oless(X3785,X3783,X3782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1512,plain,
! [X4241,X4242,X4243] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4243,X4242)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4243,X4241)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4242,X4243),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4241,X4243)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4242,X4241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1513,plain,
! [X5451,X5452,X5453,X5454] :
( ( ~ c_Rings_Odvd__class_Odvd(X5454,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5451))
| X5453 = c_Groups_Ozero__class_Ozero(X5454)
| c_Rings_Odvd__class_Odvd(X5454,X5452,X5451)
| ~ class_Rings_Oidom(X5454) )
& ( X5453 != c_Groups_Ozero__class_Ozero(X5454)
| c_Rings_Odvd__class_Odvd(X5454,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5451))
| ~ class_Rings_Oidom(X5454) )
& ( ~ c_Rings_Odvd__class_Odvd(X5454,X5452,X5451)
| c_Rings_Odvd__class_Odvd(X5454,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5454),X5453),X5451))
| ~ class_Rings_Oidom(X5454) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_1514,plain,
! [X2805,X2806,X2807] :
( ~ class_Rings_Olinordered__semidom(X2807)
| ~ c_Orderings_Oord__class_Oless(X2807,c_Groups_Oone__class_Oone(X2807),X2806)
| c_Orderings_Oord__class_Oless(X2807,c_Groups_Oone__class_Oone(X2807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2807),X2806),hAPP(hAPP(c_Power_Opower__class_Opower(X2807),X2806),X2805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1515,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk6_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
fof(i_0_1516,plain,
! [X4374,X4375,X4376] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4376),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4375,X4374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4376),X4375)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4376),X4374)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1517,plain,
! [X4708,X4709,X4710,X4711] :
( ~ class_Rings_Ocomm__semiring__0(X4711)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4711),c_Polynomial_Osmult(X4711,X4710,X4709),c_Polynomial_OpCons(X4711,X4708,X4709)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4711))
| X4709 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4711)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(i_0_1518,plain,
! [X3191,X3192,X3193] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3193,X3192),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3193,X3191))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3192,X3191) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3192,X3191)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3193,X3192),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3193,X3191)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1519,plain,
! [X3372,X3373,X3374] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3374,X3373),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3374,X3372))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3373,X3372) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3373,X3372)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3374,X3373),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3374,X3372)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1520,plain,
! [X4684,X4685,X4686] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4686)
| X4686 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4685,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4686),X4684))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4685)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4684,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).
fof(i_0_1521,plain,
! [X4644,X4645,X4646] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4646)
| X4646 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4646),X4644))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4645,X4646)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1522,plain,
! [X4738,X4739,X4740,X4741] :
( ~ class_Rings_Ocomm__ring(X4741)
| c_Polynomial_Osmult(X4741,X4740,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4741),X4739,X4738)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4741),c_Polynomial_Osmult(X4741,X4740,X4739),c_Polynomial_Osmult(X4741,X4740,X4738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__right])]) ).
fof(i_0_1523,plain,
! [X4817,X4818,X4819,X4820] :
( ~ class_Rings_Ocomm__semiring__0(X4820)
| c_Polynomial_Osmult(X4820,X4819,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4820),X4818,X4817)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4820),c_Polynomial_Osmult(X4820,X4819,X4818),c_Polynomial_Osmult(X4820,X4819,X4817)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__right])]) ).
fof(i_0_1524,plain,
! [X2870,X2871,X2872,X2873] :
( ~ class_Rings_Olinordered__semidom(X2873)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2873),X2872),X2871) != hAPP(hAPP(c_Power_Opower__class_Opower(X2873),X2870),X2871)
| ~ c_Orderings_Oord__class_Oless__eq(X2873,c_Groups_Ozero__class_Ozero(X2873),X2872)
| ~ c_Orderings_Oord__class_Oless__eq(X2873,c_Groups_Ozero__class_Ozero(X2873),X2870)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2871)
| X2872 = X2870 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1525,plain,
! [X3089,X3090,X3091] :
( ~ class_Rings_Ocomm__semiring__1(X3091)
| c_Groups_Oplus__class_Oplus(X3091,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3091),X3090),X3089),X3089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3091),c_Groups_Oplus__class_Oplus(X3091,X3090,c_Groups_Oone__class_Oone(X3091))),X3089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1526,plain,
! [X3092,X3093,X3094] :
( ~ class_Rings_Ocomm__semiring__1(X3094)
| c_Groups_Oplus__class_Oplus(X3094,X3093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3094),X3092),X3093)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3094),c_Groups_Oplus__class_Oplus(X3094,X3092,c_Groups_Oone__class_Oone(X3094))),X3093) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1527,plain,
! [X5262,X5263] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5263),X5262)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5262,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5263),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X5262) = X5263 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
fof(i_0_1528,plain,
! [X3639,X3640,X3641] :
( ~ class_Rings_Olinordered__idom(X3641)
| ~ c_Orderings_Oord__class_Oless__eq(X3641,c_Groups_Ozero__class_Ozero(X3641),X3640)
| ~ c_Orderings_Oord__class_Oless__eq(X3641,c_Groups_Ozero__class_Ozero(X3641),X3639)
| ~ c_Orderings_Oord__class_Oless__eq(X3641,X3639,c_Groups_Oone__class_Oone(X3641))
| c_Orderings_Oord__class_Oless__eq(X3641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3641),X3640),X3639),X3640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1529,plain,
! [X3642,X3643,X3644] :
( ~ class_Rings_Olinordered__idom(X3644)
| ~ c_Orderings_Oord__class_Oless__eq(X3644,c_Groups_Ozero__class_Ozero(X3644),X3643)
| ~ c_Orderings_Oord__class_Oless__eq(X3644,c_Groups_Ozero__class_Ozero(X3644),X3642)
| ~ c_Orderings_Oord__class_Oless__eq(X3644,X3642,c_Groups_Oone__class_Oone(X3644))
| c_Orderings_Oord__class_Oless__eq(X3644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3644),X3642),X3643),X3643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1530,plain,
! [X3115,X3116,X3117,X3118] :
( ~ class_RealVector_Oreal__normed__vector(X3118)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3117,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3118,X3116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3117),c_RealVector_Onorm__class_Onorm(X3118,X3115)))
| X3116 = c_Groups_Ozero__class_Ozero(X3118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1531,plain,
! [X3442,X3443,X3444,X3445] :
( ~ class_Rings_Oordered__semiring(X3445)
| ~ c_Orderings_Oord__class_Oless__eq(X3445,X3444,X3443)
| ~ c_Orderings_Oord__class_Oless__eq(X3445,c_Groups_Ozero__class_Ozero(X3445),X3442)
| c_Orderings_Oord__class_Oless__eq(X3445,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3445),X3444),X3442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3445),X3443),X3442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1532,plain,
! [X3434,X3435,X3436,X3437] :
( ~ class_Rings_Oordered__comm__semiring(X3437)
| ~ c_Orderings_Oord__class_Oless__eq(X3437,X3436,X3435)
| ~ c_Orderings_Oord__class_Oless__eq(X3437,c_Groups_Ozero__class_Ozero(X3437),X3434)
| c_Orderings_Oord__class_Oless__eq(X3437,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3437),X3434),X3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3437),X3434),X3435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1533,plain,
! [X3438,X3439,X3440,X3441] :
( ~ class_Rings_Oordered__semiring(X3441)
| ~ c_Orderings_Oord__class_Oless__eq(X3441,X3440,X3439)
| ~ c_Orderings_Oord__class_Oless__eq(X3441,c_Groups_Ozero__class_Ozero(X3441),X3438)
| c_Orderings_Oord__class_Oless__eq(X3441,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3441),X3438),X3440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3441),X3438),X3439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1534,plain,
! [X2866,X2867,X2868,X2869] :
( ~ class_Rings_Olinordered__semidom(X2869)
| ~ c_Orderings_Oord__class_Oless__eq(X2869,X2868,X2867)
| ~ c_Orderings_Oord__class_Oless__eq(X2869,c_Groups_Ozero__class_Ozero(X2869),X2868)
| c_Orderings_Oord__class_Oless__eq(X2869,hAPP(hAPP(c_Power_Opower__class_Opower(X2869),X2868),X2866),hAPP(hAPP(c_Power_Opower__class_Opower(X2869),X2867),X2866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1535,plain,
! [X3508,X3509,X3510,X3511] :
( ~ class_Rings_Olinordered__semiring__strict(X3511)
| ~ c_Orderings_Oord__class_Oless(X3511,X3510,X3509)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),X3508)
| c_Orderings_Oord__class_Oless(X3511,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3511),X3510),X3508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3511),X3509),X3508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1536,plain,
! [X3516,X3517,X3518,X3519] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3519)
| ~ c_Orderings_Oord__class_Oless(X3519,X3518,X3517)
| ~ c_Orderings_Oord__class_Oless(X3519,c_Groups_Ozero__class_Ozero(X3519),X3516)
| c_Orderings_Oord__class_Oless(X3519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3519),X3516),X3518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3519),X3516),X3517)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1537,plain,
! [X3512,X3513,X3514,X3515] :
( ~ class_Rings_Olinordered__semiring__strict(X3515)
| ~ c_Orderings_Oord__class_Oless(X3515,X3514,X3513)
| ~ c_Orderings_Oord__class_Oless(X3515,c_Groups_Ozero__class_Ozero(X3515),X3512)
| c_Orderings_Oord__class_Oless(X3515,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3515),X3512),X3514),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3515),X3512),X3513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1538,plain,
! [X3430,X3431,X3432,X3433] :
( ~ class_Rings_Oordered__ring(X3433)
| ~ c_Orderings_Oord__class_Oless__eq(X3433,X3432,X3431)
| ~ c_Orderings_Oord__class_Oless__eq(X3433,X3430,c_Groups_Ozero__class_Ozero(X3433))
| c_Orderings_Oord__class_Oless__eq(X3433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3433),X3431),X3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3433),X3432),X3430)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1539,plain,
! [X3426,X3427,X3428,X3429] :
( ~ class_Rings_Oordered__ring(X3429)
| ~ c_Orderings_Oord__class_Oless__eq(X3429,X3428,X3427)
| ~ c_Orderings_Oord__class_Oless__eq(X3429,X3426,c_Groups_Ozero__class_Ozero(X3429))
| c_Orderings_Oord__class_Oless__eq(X3429,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3429),X3426),X3427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3429),X3426),X3428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1540,plain,
! [X3520,X3521,X3522,X3523] :
( ~ class_Rings_Olinordered__ring__strict(X3523)
| ~ c_Orderings_Oord__class_Oless(X3523,X3522,X3521)
| ~ c_Orderings_Oord__class_Oless(X3523,X3520,c_Groups_Ozero__class_Ozero(X3523))
| c_Orderings_Oord__class_Oless(X3523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3523),X3521),X3520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3523),X3522),X3520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1541,plain,
! [X3524,X3525,X3526,X3527] :
( ~ class_Rings_Olinordered__ring__strict(X3527)
| ~ c_Orderings_Oord__class_Oless(X3527,X3526,X3525)
| ~ c_Orderings_Oord__class_Oless(X3527,X3524,c_Groups_Ozero__class_Ozero(X3527))
| c_Orderings_Oord__class_Oless(X3527,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3527),X3524),X3525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3527),X3524),X3526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1542,plain,
! [X4306,X4307,X4308] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4308,X4307)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4306,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4307,X4306),X4308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1543,plain,
! [X3761,X3762,X3763,X3764,X3765] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3765)
| ~ c_Orderings_Oord__class_Oless__eq(X3765,X3764,X3763)
| ~ c_Orderings_Oord__class_Oless__eq(X3765,X3762,X3761)
| c_Orderings_Oord__class_Oless__eq(X3765,c_Groups_Oplus__class_Oplus(X3765,X3764,X3762),c_Groups_Oplus__class_Oplus(X3765,X3763,X3761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1544,plain,
! [X3862,X3863,X3864,X3865,X3866] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3866)
| ~ c_Orderings_Oord__class_Oless(X3866,X3865,X3864)
| ~ c_Orderings_Oord__class_Oless__eq(X3866,X3863,X3862)
| c_Orderings_Oord__class_Oless(X3866,c_Groups_Oplus__class_Oplus(X3866,X3865,X3863),c_Groups_Oplus__class_Oplus(X3866,X3864,X3862)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1545,plain,
! [X3857,X3858,X3859,X3860,X3861] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3861)
| ~ c_Orderings_Oord__class_Oless__eq(X3861,X3860,X3859)
| ~ c_Orderings_Oord__class_Oless(X3861,X3858,X3857)
| c_Orderings_Oord__class_Oless(X3861,c_Groups_Oplus__class_Oplus(X3861,X3860,X3858),c_Groups_Oplus__class_Oplus(X3861,X3859,X3857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1546,plain,
! [X3790,X3791,X3792,X3793,X3794] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3794)
| ~ c_Orderings_Oord__class_Oless(X3794,X3793,X3792)
| ~ c_Orderings_Oord__class_Oless(X3794,X3791,X3790)
| c_Orderings_Oord__class_Oless(X3794,c_Groups_Oplus__class_Oplus(X3794,X3793,X3791),c_Groups_Oplus__class_Oplus(X3794,X3792,X3790)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1547,plain,
! [X2915,X2916,X2917,X2918] :
( ~ class_Rings_Olinordered__semidom(X2918)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2917,X2916)
| ~ c_Orderings_Oord__class_Oless__eq(X2918,c_Groups_Oone__class_Oone(X2918),X2915)
| c_Orderings_Oord__class_Oless__eq(X2918,hAPP(hAPP(c_Power_Opower__class_Opower(X2918),X2915),X2917),hAPP(hAPP(c_Power_Opower__class_Opower(X2918),X2915),X2916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1548,plain,
! [X3097,X3098,X3099,X3100] :
( ~ class_Rings_Olinordered__semidom(X3100)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3099,X3098)
| ~ c_Orderings_Oord__class_Oless(X3100,c_Groups_Oone__class_Oone(X3100),X3097)
| c_Orderings_Oord__class_Oless(X3100,hAPP(hAPP(c_Power_Opower__class_Opower(X3100),X3097),X3099),hAPP(hAPP(c_Power_Opower__class_Opower(X3100),X3097),X3098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1549,plain,
! [X4525,X4526,X4527] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4527,c_Groups_Ozero__class_Ozero(X4527),X4525)
| ~ c_Orderings_Oord__class_Oless__eq(X4527,c_Groups_Ozero__class_Ozero(X4527),X4526)
| c_Groups_Oabs__class_Oabs(X4527,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),X4526),X4525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),c_Groups_Oabs__class_Oabs(X4527,X4526)),c_Groups_Oabs__class_Oabs(X4527,X4525))
| ~ class_Rings_Oordered__ring__abs(X4527) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4527,X4525,c_Groups_Ozero__class_Ozero(X4527))
| ~ c_Orderings_Oord__class_Oless__eq(X4527,c_Groups_Ozero__class_Ozero(X4527),X4526)
| c_Groups_Oabs__class_Oabs(X4527,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),X4526),X4525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),c_Groups_Oabs__class_Oabs(X4527,X4526)),c_Groups_Oabs__class_Oabs(X4527,X4525))
| ~ class_Rings_Oordered__ring__abs(X4527) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4527,c_Groups_Ozero__class_Ozero(X4527),X4525)
| ~ c_Orderings_Oord__class_Oless__eq(X4527,X4526,c_Groups_Ozero__class_Ozero(X4527))
| c_Groups_Oabs__class_Oabs(X4527,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),X4526),X4525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),c_Groups_Oabs__class_Oabs(X4527,X4526)),c_Groups_Oabs__class_Oabs(X4527,X4525))
| ~ class_Rings_Oordered__ring__abs(X4527) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4527,X4525,c_Groups_Ozero__class_Ozero(X4527))
| ~ c_Orderings_Oord__class_Oless__eq(X4527,X4526,c_Groups_Ozero__class_Ozero(X4527))
| c_Groups_Oabs__class_Oabs(X4527,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),X4526),X4525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4527),c_Groups_Oabs__class_Oabs(X4527,X4526)),c_Groups_Oabs__class_Oabs(X4527,X4525))
| ~ class_Rings_Oordered__ring__abs(X4527) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
fof(i_0_1550,plain,
! [X4806,X4807,X4808,X4809] :
( ~ class_Groups_Oab__group__add(X4809)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4809),c_Polynomial_Omonom(X4809,X4808,X4807),c_Polynomial_Omonom(X4809,X4806,X4807)) = c_Polynomial_Omonom(X4809,c_Groups_Ominus__class_Ominus(X4809,X4808,X4806),X4807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__monom])]) ).
fof(i_0_1551,plain,
! [X4872,X4873,X4874,X4875] :
( ~ class_Groups_Ocomm__monoid__add(X4875)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4875),c_Polynomial_Omonom(X4875,X4874,X4873),c_Polynomial_Omonom(X4875,X4872,X4873)) = c_Polynomial_Omonom(X4875,c_Groups_Oplus__class_Oplus(X4875,X4874,X4872),X4873) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__monom])]) ).
fof(i_0_1552,plain,
! [X4795,X4796,X4797,X4798] :
( ~ class_Rings_Ocomm__ring(X4798)
| c_Polynomial_Osmult(X4798,c_Groups_Ominus__class_Ominus(X4798,X4797,X4796),X4795) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4798),c_Polynomial_Osmult(X4798,X4797,X4795),c_Polynomial_Osmult(X4798,X4796,X4795)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__left])]) ).
fof(i_0_1553,plain,
! [X4864,X4865,X4866,X4867] :
( ~ class_Rings_Ocomm__semiring__0(X4867)
| c_Polynomial_Osmult(X4867,c_Groups_Oplus__class_Oplus(X4867,X4866,X4865),X4864) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4867),c_Polynomial_Osmult(X4867,X4866,X4864),c_Polynomial_Osmult(X4867,X4865,X4864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
fof(i_0_1554,plain,
! [X5434,X5435,X5436,X5437,X5438] :
( ~ class_Rings_Ocomm__semiring__1(X5438)
| ~ c_Rings_Odvd__class_Odvd(X5438,X5437,X5436)
| ~ c_Rings_Odvd__class_Odvd(X5438,X5435,X5434)
| c_Rings_Odvd__class_Odvd(X5438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5438),X5437),X5435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5438),X5436),X5434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_1555,plain,
! [X4394,X4395,X4396] :
( ( X4395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4396),X4394),X4395) = c_Groups_Oone__class_Oone(X4396)
| ~ class_Power_Opower(X4396) )
& ( X4395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4396),X4394),X4395) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),X4394),hAPP(hAPP(c_Power_Opower__class_Opower(X4396),X4394),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4395,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X4396) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1556,plain,
! [X4837,X4838,X4839,X4840] :
( ~ class_Rings_Ocomm__semiring__0(X4840)
| c_Polynomial_Osmult(X4840,X4839,c_Polynomial_OpCons(X4840,X4838,X4837)) = c_Polynomial_OpCons(X4840,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4840),X4839),X4838),c_Polynomial_Osmult(X4840,X4839,X4837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
fof(i_0_1557,plain,
! [X3203,X3204,X3205,X3206] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3206,X3205)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3204,X3203)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3206,X3204),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3205,X3203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1558,plain,
! [X4612,X4613,X4614,X4615] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4615,X4614)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4613,X4612)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4615,X4613),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4614,X4612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1559,plain,
! [X4277,X4278,X4279] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4279,X4278)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4277,X4279)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4279,X4277),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4278,X4277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1560,plain,
! [X4209,X4210,X4211] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4211,X4210)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4211,X4209)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4209,X4210),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4209,X4211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1561,plain,
! [X3384,X3385,X3386,X3387] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3387,X3386)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3384)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3387,X3385),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3386,X3384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1562,plain,
! [X3867,X3868,X3869] :
( ( X3868 = c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3868),X3868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3867),X3867)) != c_Groups_Ozero__class_Ozero(X3869)
| ~ class_Rings_Olinordered__ring__strict(X3869) )
& ( X3867 = c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3868),X3868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3867),X3867)) != c_Groups_Ozero__class_Ozero(X3869)
| ~ class_Rings_Olinordered__ring__strict(X3869) )
& ( X3868 != c_Groups_Ozero__class_Ozero(X3869)
| X3867 != c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3868),X3868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3869),X3867),X3867)) = c_Groups_Ozero__class_Ozero(X3869)
| ~ class_Rings_Olinordered__ring__strict(X3869) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_1563,plain,
! [X4550,X4551,X4552] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4552,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4551),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4552),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4550)))
| X4551 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma])]) ).
fof(i_0_1564,plain,
! [X3999,X4000,X4001,X4002] :
( ~ class_RealVector_Oreal__normed__algebra(X4002)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4002),X4001),c_Groups_Ominus__class_Ominus(X4002,X4000,X3999)) = c_Groups_Ominus__class_Ominus(X4002,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4002),X4001),X4000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4002),X4001),X3999)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1565,plain,
! [X3995,X3996,X3997,X3998] :
( ~ class_RealVector_Oreal__normed__algebra(X3998)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3998),X3997),c_Groups_Ominus__class_Ominus(X3998,X3996,X3995)) = c_Groups_Ominus__class_Ominus(X3998,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3998),X3997),X3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3998),X3997),X3995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1566,plain,
! [X3060,X3061,X3062,X3063] :
( ~ class_Rings_Ocomm__semiring__1(X3063)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3063),X3062),c_Groups_Oplus__class_Oplus(X3063,X3061,X3060)) = c_Groups_Oplus__class_Oplus(X3063,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3063),X3062),X3061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3063),X3062),X3060)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1567,plain,
! [X3064,X3065,X3066,X3067] :
( ~ class_RealVector_Oreal__normed__algebra(X3067)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3067),X3066),c_Groups_Oplus__class_Oplus(X3067,X3065,X3064)) = c_Groups_Oplus__class_Oplus(X3067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3067),X3066),X3065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3067),X3066),X3064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1568,plain,
! [X3056,X3057,X3058,X3059] :
( ~ class_RealVector_Oreal__normed__algebra(X3059)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3059),X3058),c_Groups_Oplus__class_Oplus(X3059,X3057,X3056)) = c_Groups_Oplus__class_Oplus(X3059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3059),X3058),X3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3059),X3058),X3056)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1569,plain,
! [X3344,X3345,X3346] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3346)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3344)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3345,X3344)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3344)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3346)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3345,X3344)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3346),X3344)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1570,plain,
! [X3341,X3342,X3343] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3342)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3343),X3342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3341),X3342)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3343,X3341)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3343),X3342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3341),X3342)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3342)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3343,X3341)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3343),X3342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3341),X3342)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1571,plain,
! [X3495,X3496,X3497] :
( ~ class_Rings_Olinordered__semiring__strict(X3497)
| ~ c_Orderings_Oord__class_Oless(X3497,c_Groups_Ozero__class_Ozero(X3497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3497),X3496),X3495))
| ~ c_Orderings_Oord__class_Oless(X3497,c_Groups_Ozero__class_Ozero(X3497),X3495)
| c_Orderings_Oord__class_Oless(X3497,c_Groups_Ozero__class_Ozero(X3497),X3496) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1572,plain,
! [X3492,X3493,X3494] :
( ~ class_Rings_Olinordered__semiring__strict(X3494)
| ~ c_Orderings_Oord__class_Oless(X3494,c_Groups_Ozero__class_Ozero(X3494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3494),X3493),X3492))
| ~ c_Orderings_Oord__class_Oless(X3494,c_Groups_Ozero__class_Ozero(X3494),X3493)
| c_Orderings_Oord__class_Oless(X3494,c_Groups_Ozero__class_Ozero(X3494),X3492) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1573,plain,
! [X3713,X3714,X3715,X3716] :
( ~ class_Groups_Oab__semigroup__mult(X3716)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3716),X3715),X3714)),X3713) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3716),X3715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3716),X3714),X3713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1574,plain,
! [X2991,X2992,X2993,X2994] :
( ~ class_Rings_Ocomm__semiring__1(X2994)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),X2993),X2992)),X2991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),X2993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),X2992),X2991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1575,plain,
! [X3080,X3081,X3082] :
( ~ class_Groups_Omonoid__mult(X3082)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3082),hAPP(hAPP(c_Power_Opower__class_Opower(X3082),X3081),X3080)),X3081) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3082),X3081),hAPP(hAPP(c_Power_Opower__class_Opower(X3082),X3081),X3080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1576,plain,
! [X2995,X2996,X2997,X2998] :
( ~ class_Rings_Ocomm__semiring__1(X2998)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2998),X2997),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2998),X2996),X2995)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2998),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2998),X2997),X2996)),X2995) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_1577,plain,
! [X5240,X5241] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5241,X5240)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5241),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5240)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5241),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5240))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5241,X5240) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1578,plain,
! [X5242,X5243] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5243,X5242)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5243),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5242),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5243),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5242),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5243,X5242) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
fof(i_0_1579,plain,
! [X4880,X4881,X4882,X4883] :
( ~ class_Rings_Ocomm__semiring__1(X4883)
| hAPP(c_Polynomial_Opoly(X4883,c_Polynomial_Omonom(X4883,X4882,X4881)),X4880) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4883),X4882),hAPP(hAPP(c_Power_Opower__class_Opower(X4883),X4880),X4881)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(i_0_1580,plain,
! [X4911,X4912,X4913,X4914,X4915] :
( ( X4911 = hAPP(c_Polynomial_Opoly(X4915,X4914),X4913)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4915),X4914,c_Polynomial_Osmult(X4915,X4913,X4912)) != c_Polynomial_OpCons(X4915,X4911,X4912)
| ~ class_Rings_Ocomm__semiring__0(X4915) )
& ( X4912 = c_Polynomial_Osynthetic__div(X4915,X4914,X4913)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4915),X4914,c_Polynomial_Osmult(X4915,X4913,X4912)) != c_Polynomial_OpCons(X4915,X4911,X4912)
| ~ class_Rings_Ocomm__semiring__0(X4915) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
fof(i_0_1581,plain,
! [X5271] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk32_1(X5271),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5271) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5271,c_RealDef_Oreal(tc_Nat_Onat,esk32_1(X5271)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5271) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6])])])]) ).
fof(i_0_1582,plain,
! [X4907,X4908,X4909,X4910] :
( ~ class_Rings_Ocomm__semiring__0(X4910)
| c_Polynomial_Osynthetic__div(X4910,c_Polynomial_OpCons(X4910,X4909,X4908),X4907) = c_Polynomial_OpCons(X4910,hAPP(c_Polynomial_Opoly(X4910,X4908),X4907),c_Polynomial_Osynthetic__div(X4910,X4908,X4907)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons])]) ).
fof(i_0_1583,plain,
! [X2889,X2890,X2891,X2892] :
( ~ class_Groups_Omonoid__mult(X2892)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2892),X2891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2890),X2889)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2892),hAPP(hAPP(c_Power_Opower__class_Opower(X2892),X2891),X2890)),X2889) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1584,plain,
! [X2885,X2886,X2887,X2888] :
( ~ class_Rings_Ocomm__semiring__1(X2888)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2888),hAPP(hAPP(c_Power_Opower__class_Opower(X2888),X2887),X2886)),X2885) = hAPP(hAPP(c_Power_Opower__class_Opower(X2888),X2887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2886),X2885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_1585,plain,
! [X4426,X4427,X4428] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4428,X4427)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4426)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4426),X4428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4426),X4427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1586,plain,
! [X3336,X3337,X3338] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3338,X3337)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3336)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3338),X3336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3337),X3336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1587,plain,
! [X3333,X3334,X3335] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3335,X3334)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3333)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3333),X3335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3333),X3334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1588,plain,
! [X3582,X3583,X3584] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3583,X3582)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3584),X3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3584),X3582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1589,plain,
! [X4392,X4393] :
( ( X4393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4392),X4393) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4392),X4393) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4392),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4392),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4393,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).
fof(i_0_1590,plain,
! [X4309,X4310,X4311] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4311,X4310),X4309)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4311,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4309,X4310)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4311,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4309,X4310))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4311,X4310),X4309) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1591,plain,
! [X4269,X4270,X4271] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4270,X4269))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4271,X4269),X4270) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4271,X4269),X4270)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4271,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4270,X4269)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1592,plain,
! [X3159,X3160,X3161,X3162] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3162,X3161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3160,X3159)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3162),X3160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3161),X3159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1593,plain,
! [X4287,X4288,X4289] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4289,X4288)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4288,X4289),X4287) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4288,X4287),X4289) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1594,plain,
! [X4284,X4285,X4286] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4286,X4285)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4285,X4284),X4286) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4285,X4286),X4284) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1595,plain,
! [X4290,X4291,X4292] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4292,X4291)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4290,X4291),X4292) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4290,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4291,X4292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1596,plain,
! [X4312,X4313,X4314] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4314,X4313)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4312,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4313,X4314)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4312,X4314),X4313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1597,plain,
! [X4301,X4302,X4303] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4303,X4302)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4301,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4302,X4303)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4301,X4302),X4303) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1598,plain,
! [X4749,X4750,X4751,X4752] :
( ~ class_Rings_Ocomm__semiring__0(X4752)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4752)),X4751),c_Polynomial_Osmult(X4752,X4750,X4749)) = c_Polynomial_Osmult(X4752,X4750,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4752)),X4751),X4749)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(i_0_1599,plain,
! [X4833,X4834,X4835,X4836] :
( ~ class_Rings_Ocomm__semiring__0(X4836)
| hAPP(c_Polynomial_Opoly(X4836,c_Polynomial_Osmult(X4836,X4835,X4834)),X4833) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4836),X4835),hAPP(c_Polynomial_Opoly(X4836,X4834),X4833)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
fof(i_0_1600,plain,
! [X3461,X3462,X3463] :
( ( c_Orderings_Oord__class_Oless__eq(X3463,X3462,c_Groups_Ozero__class_Ozero(X3463))
| c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3462)
| ~ c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) )
& ( c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3461)
| c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3462)
| ~ c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) )
& ( c_Orderings_Oord__class_Oless__eq(X3463,X3462,c_Groups_Ozero__class_Ozero(X3463))
| c_Orderings_Oord__class_Oless__eq(X3463,X3461,c_Groups_Ozero__class_Ozero(X3463))
| ~ c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) )
& ( c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3461)
| c_Orderings_Oord__class_Oless__eq(X3463,X3461,c_Groups_Ozero__class_Ozero(X3463))
| ~ c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3462)
| ~ c_Orderings_Oord__class_Oless__eq(X3463,X3461,c_Groups_Ozero__class_Ozero(X3463))
| c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3463,X3462,c_Groups_Ozero__class_Ozero(X3463))
| ~ c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),X3461)
| c_Orderings_Oord__class_Oless__eq(X3463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3463),X3462),X3461),c_Groups_Ozero__class_Ozero(X3463))
| ~ class_Rings_Olinordered__ring__strict(X3463) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1601,plain,
! [X3464,X3465,X3466] :
( ( c_Orderings_Oord__class_Oless__eq(X3466,X3465,c_Groups_Ozero__class_Ozero(X3466))
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3465)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) )
& ( c_Orderings_Oord__class_Oless__eq(X3466,X3464,c_Groups_Ozero__class_Ozero(X3466))
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3465)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) )
& ( c_Orderings_Oord__class_Oless__eq(X3466,X3465,c_Groups_Ozero__class_Ozero(X3466))
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3464)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) )
& ( c_Orderings_Oord__class_Oless__eq(X3466,X3464,c_Groups_Ozero__class_Ozero(X3466))
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3464)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3465)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),X3464)
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3466,X3465,c_Groups_Ozero__class_Ozero(X3466))
| ~ c_Orderings_Oord__class_Oless__eq(X3466,X3464,c_Groups_Ozero__class_Ozero(X3466))
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Ozero__class_Ozero(X3466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3466),X3465),X3464))
| ~ class_Rings_Olinordered__ring__strict(X3466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1602,plain,
! [X4636,X4637] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4637)),X4636))
| X4637 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4637 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4637)),X4636)) )
& ( X4636 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4637)),X4636)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).
fof(i_0_1603,plain,
! [X4410,X4411,X4412] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4412),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4411,X4410)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4412),X4411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4412),X4410)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1604,plain,
! [X4437,X4438,X4439] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4439),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4438,X4437)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4439),X4438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4439),X4437)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1605,plain,
! [X4247,X4248,X4249] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4249),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4248,X4247)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4249),X4248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4249),X4247)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1606,plain,
! [X3270,X3271,X3272] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3272),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3271,X3270)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3272),X3271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3272),X3270)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1607,plain,
! [X4903,X4904,X4905,X4906] :
( ~ class_Rings_Ocomm__semiring__0(X4906)
| hAPP(c_Polynomial_Opoly(X4906,c_Polynomial_Opcompose(X4906,X4905,X4904)),X4903) = hAPP(c_Polynomial_Opoly(X4906,X4905),hAPP(c_Polynomial_Opoly(X4906,X4904),X4903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pcompose])]) ).
fof(i_0_1608,plain,
! [X3095,X3096] :
( ~ class_Rings_Ocomm__semiring__1(X3096)
| c_Groups_Oplus__class_Oplus(X3096,X3095,X3095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3096),c_Groups_Oplus__class_Oplus(X3096,c_Groups_Oone__class_Oone(X3096),c_Groups_Oone__class_Oone(X3096))),X3095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_1609,plain,
! [X3106,X3107,X3108] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3108)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3107,c_RealVector_Onorm__class_Onorm(X3108,X3106))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3107)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3108,c_Rings_Oinverse__class_Oinverse(X3108,X3106)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__inverse__lemma])]) ).
fof(i_0_1610,plain,
! [X3585,X3586] :
( ( X3586 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3586),X3586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3585),X3585)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3585 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3586),X3586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3585),X3585)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3586 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3585 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3586),X3586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3585),X3585)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff])])]) ).
fof(i_0_1611,plain,
! [X4700] : 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_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X4700))),
inference(variable_rename,[status(thm)],[fact_cq0]) ).
fof(i_0_1612,plain,
! [X3844,X3845,X3846] :
( ~ class_Groups_Oordered__comm__monoid__add(X3846)
| ~ c_Orderings_Oord__class_Oless__eq(X3846,X3845,c_Groups_Ozero__class_Ozero(X3846))
| ~ c_Orderings_Oord__class_Oless__eq(X3846,X3844,c_Groups_Ozero__class_Ozero(X3846))
| c_Orderings_Oord__class_Oless__eq(X3846,c_Groups_Oplus__class_Oplus(X3846,X3845,X3844),c_Groups_Ozero__class_Ozero(X3846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1613,plain,
! [X3879,X3880,X3881] :
( ~ class_Groups_Oordered__comm__monoid__add(X3881)
| ~ c_Orderings_Oord__class_Oless(X3881,X3880,c_Groups_Ozero__class_Ozero(X3881))
| ~ c_Orderings_Oord__class_Oless__eq(X3881,X3879,c_Groups_Ozero__class_Ozero(X3881))
| c_Orderings_Oord__class_Oless(X3881,c_Groups_Oplus__class_Oplus(X3881,X3880,X3879),c_Groups_Ozero__class_Ozero(X3881)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1614,plain,
! [X3876,X3877,X3878] :
( ~ class_Groups_Oordered__comm__monoid__add(X3878)
| ~ c_Orderings_Oord__class_Oless__eq(X3878,X3877,c_Groups_Ozero__class_Ozero(X3878))
| ~ c_Orderings_Oord__class_Oless(X3878,X3876,c_Groups_Ozero__class_Ozero(X3878))
| c_Orderings_Oord__class_Oless(X3878,c_Groups_Oplus__class_Oplus(X3878,X3877,X3876),c_Groups_Ozero__class_Ozero(X3878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1615,plain,
! [X3847,X3848,X3849] :
( ~ class_Groups_Oordered__comm__monoid__add(X3849)
| ~ c_Orderings_Oord__class_Oless(X3849,X3848,c_Groups_Ozero__class_Ozero(X3849))
| ~ c_Orderings_Oord__class_Oless(X3849,X3847,c_Groups_Ozero__class_Ozero(X3849))
| c_Orderings_Oord__class_Oless(X3849,c_Groups_Oplus__class_Oplus(X3849,X3848,X3847),c_Groups_Ozero__class_Ozero(X3849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1616,plain,
! [X3830,X3831,X3832] :
( ~ class_Groups_Oordered__comm__monoid__add(X3832)
| ~ c_Orderings_Oord__class_Oless__eq(X3832,c_Groups_Ozero__class_Ozero(X3832),X3831)
| ~ c_Orderings_Oord__class_Oless__eq(X3832,c_Groups_Ozero__class_Ozero(X3832),X3830)
| c_Orderings_Oord__class_Oless__eq(X3832,c_Groups_Ozero__class_Ozero(X3832),c_Groups_Oplus__class_Oplus(X3832,X3831,X3830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1617,plain,
! [X3705,X3706,X3707] :
( ~ class_Groups_Oordered__comm__monoid__add(X3707)
| ~ c_Orderings_Oord__class_Oless(X3707,c_Groups_Ozero__class_Ozero(X3707),X3706)
| ~ c_Orderings_Oord__class_Oless__eq(X3707,c_Groups_Ozero__class_Ozero(X3707),X3705)
| c_Orderings_Oord__class_Oless(X3707,c_Groups_Ozero__class_Ozero(X3707),c_Groups_Oplus__class_Oplus(X3707,X3706,X3705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1618,plain,
! [X3708,X3709,X3710] :
( ~ class_Groups_Oordered__comm__monoid__add(X3710)
| ~ c_Orderings_Oord__class_Oless__eq(X3710,c_Groups_Ozero__class_Ozero(X3710),X3709)
| ~ c_Orderings_Oord__class_Oless(X3710,c_Groups_Ozero__class_Ozero(X3710),X3708)
| c_Orderings_Oord__class_Oless(X3710,c_Groups_Ozero__class_Ozero(X3710),c_Groups_Oplus__class_Oplus(X3710,X3709,X3708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1619,plain,
! [X3850,X3851,X3852] :
( ~ class_Groups_Oordered__comm__monoid__add(X3852)
| ~ c_Orderings_Oord__class_Oless(X3852,c_Groups_Ozero__class_Ozero(X3852),X3851)
| ~ c_Orderings_Oord__class_Oless(X3852,c_Groups_Ozero__class_Ozero(X3852),X3850)
| c_Orderings_Oord__class_Oless(X3852,c_Groups_Ozero__class_Ozero(X3852),c_Groups_Oplus__class_Oplus(X3852,X3851,X3850)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1620,plain,
! [X3575,X3576] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3576,X3575))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3576)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3575) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3576)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3576,X3575)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3575)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3576,X3575)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1621,plain,
! [X4434,X4435,X4436] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4436),X4435)),X4434) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4435),X4434)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1622,plain,
! [X3143,X3144,X3145] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3145),X3144)),X3143) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3144),X3143)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1623,plain,
! [X3278,X3279,X3280] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3280),X3279)),X3278) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3279),X3278)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1624,plain,
! [X4377,X4378,X4379] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4379),X4378)),X4377) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4378),X4377)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1625,plain,
! [X3449,X3450,X3451] :
( ~ class_Rings_Oordered__cancel__semiring(X3451)
| ~ c_Orderings_Oord__class_Oless__eq(X3451,X3450,c_Groups_Ozero__class_Ozero(X3451))
| ~ c_Orderings_Oord__class_Oless__eq(X3451,c_Groups_Ozero__class_Ozero(X3451),X3449)
| c_Orderings_Oord__class_Oless__eq(X3451,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3451),X3450),X3449),c_Groups_Ozero__class_Ozero(X3451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1626,plain,
! [X3410,X3411,X3412] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3412,c_Groups_Ozero__class_Ozero(X3412),X3411)
| ~ c_Orderings_Oord__class_Oless__eq(X3412,X3410,c_Groups_Ozero__class_Ozero(X3412))
| c_Orderings_Oord__class_Oless__eq(X3412,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3412),X3411),X3410),c_Groups_Ozero__class_Ozero(X3412))
| ~ class_Rings_Oordered__cancel__semiring(X3412) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3412,X3411,c_Groups_Ozero__class_Ozero(X3412))
| ~ c_Orderings_Oord__class_Oless__eq(X3412,c_Groups_Ozero__class_Ozero(X3412),X3410)
| c_Orderings_Oord__class_Oless__eq(X3412,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3412),X3411),X3410),c_Groups_Ozero__class_Ozero(X3412))
| ~ class_Rings_Oordered__cancel__semiring(X3412) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1627,plain,
! [X3455,X3456,X3457] :
( ~ class_Rings_Oordered__cancel__semiring(X3457)
| ~ c_Orderings_Oord__class_Oless__eq(X3457,c_Groups_Ozero__class_Ozero(X3457),X3456)
| ~ c_Orderings_Oord__class_Oless__eq(X3457,X3455,c_Groups_Ozero__class_Ozero(X3457))
| c_Orderings_Oord__class_Oless__eq(X3457,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3457),X3456),X3455),c_Groups_Ozero__class_Ozero(X3457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1628,plain,
! [X3452,X3453,X3454] :
( ~ class_Rings_Oordered__cancel__semiring(X3454)
| ~ c_Orderings_Oord__class_Oless__eq(X3454,c_Groups_Ozero__class_Ozero(X3454),X3453)
| ~ c_Orderings_Oord__class_Oless__eq(X3454,X3452,c_Groups_Ozero__class_Ozero(X3454))
| c_Orderings_Oord__class_Oless__eq(X3454,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3454),X3452),X3453),c_Groups_Ozero__class_Ozero(X3454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1629,plain,
! [X3502,X3503,X3504] :
( ~ class_Rings_Olinordered__semiring__strict(X3504)
| ~ c_Orderings_Oord__class_Oless(X3504,X3503,c_Groups_Ozero__class_Ozero(X3504))
| ~ c_Orderings_Oord__class_Oless(X3504,c_Groups_Ozero__class_Ozero(X3504),X3502)
| c_Orderings_Oord__class_Oless(X3504,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3504),X3503),X3502),c_Groups_Ozero__class_Ozero(X3504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1630,plain,
! [X3486,X3487,X3488] :
( ~ class_Rings_Olinordered__semiring__strict(X3488)
| ~ c_Orderings_Oord__class_Oless(X3488,c_Groups_Ozero__class_Ozero(X3488),X3487)
| ~ c_Orderings_Oord__class_Oless(X3488,X3486,c_Groups_Ozero__class_Ozero(X3488))
| c_Orderings_Oord__class_Oless(X3488,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3488),X3487),X3486),c_Groups_Ozero__class_Ozero(X3488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1631,plain,
! [X3489,X3490,X3491] :
( ~ class_Rings_Olinordered__semiring__strict(X3491)
| ~ c_Orderings_Oord__class_Oless(X3491,c_Groups_Ozero__class_Ozero(X3491),X3490)
| ~ c_Orderings_Oord__class_Oless(X3491,X3489,c_Groups_Ozero__class_Ozero(X3491))
| c_Orderings_Oord__class_Oless(X3491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3491),X3489),X3490),c_Groups_Ozero__class_Ozero(X3491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1632,plain,
! [X3413,X3414,X3415] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3415,c_Groups_Ozero__class_Ozero(X3415),X3414)
| ~ c_Orderings_Oord__class_Oless__eq(X3415,c_Groups_Ozero__class_Ozero(X3415),X3413)
| c_Orderings_Oord__class_Oless__eq(X3415,c_Groups_Ozero__class_Ozero(X3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3415),X3414),X3413))
| ~ class_Rings_Oordered__ring(X3415) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3415,X3414,c_Groups_Ozero__class_Ozero(X3415))
| ~ c_Orderings_Oord__class_Oless__eq(X3415,X3413,c_Groups_Ozero__class_Ozero(X3415))
| c_Orderings_Oord__class_Oless__eq(X3415,c_Groups_Ozero__class_Ozero(X3415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3415),X3414),X3413))
| ~ class_Rings_Oordered__ring(X3415) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1633,plain,
! [X3458,X3459,X3460] :
( ~ class_Rings_Oordered__cancel__semiring(X3460)
| ~ c_Orderings_Oord__class_Oless__eq(X3460,c_Groups_Ozero__class_Ozero(X3460),X3459)
| ~ c_Orderings_Oord__class_Oless__eq(X3460,c_Groups_Ozero__class_Ozero(X3460),X3458)
| c_Orderings_Oord__class_Oless__eq(X3460,c_Groups_Ozero__class_Ozero(X3460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3460),X3459),X3458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1634,plain,
! [X3483,X3484,X3485] :
( ~ class_Rings_Olinordered__semiring__strict(X3485)
| ~ c_Orderings_Oord__class_Oless(X3485,c_Groups_Ozero__class_Ozero(X3485),X3484)
| ~ c_Orderings_Oord__class_Oless(X3485,c_Groups_Ozero__class_Ozero(X3485),X3483)
| c_Orderings_Oord__class_Oless(X3485,c_Groups_Ozero__class_Ozero(X3485),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3485),X3484),X3483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1635,plain,
! [X3536,X3537,X3538] :
( ~ class_Rings_Olinordered__semidom(X3538)
| ~ c_Orderings_Oord__class_Oless(X3538,c_Groups_Oone__class_Oone(X3538),X3537)
| ~ c_Orderings_Oord__class_Oless(X3538,c_Groups_Oone__class_Oone(X3538),X3536)
| c_Orderings_Oord__class_Oless(X3538,c_Groups_Oone__class_Oone(X3538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3538),X3537),X3536)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1636,plain,
! [X3446,X3447,X3448] :
( ~ class_Rings_Oordered__ring(X3448)
| ~ c_Orderings_Oord__class_Oless__eq(X3448,X3447,c_Groups_Ozero__class_Ozero(X3448))
| ~ c_Orderings_Oord__class_Oless__eq(X3448,X3446,c_Groups_Ozero__class_Ozero(X3448))
| c_Orderings_Oord__class_Oless__eq(X3448,c_Groups_Ozero__class_Ozero(X3448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3448),X3447),X3446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1637,plain,
! [X3505,X3506,X3507] :
( ~ class_Rings_Olinordered__ring__strict(X3507)
| ~ c_Orderings_Oord__class_Oless(X3507,X3506,c_Groups_Ozero__class_Ozero(X3507))
| ~ c_Orderings_Oord__class_Oless(X3507,X3505,c_Groups_Ozero__class_Ozero(X3507))
| c_Orderings_Oord__class_Oless(X3507,c_Groups_Ozero__class_Ozero(X3507),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3507),X3506),X3505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1638,plain,
! [X3770,X3771,X3772,X3773] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3773)
| ~ c_Orderings_Oord__class_Oless__eq(X3773,X3772,X3771)
| c_Orderings_Oord__class_Oless__eq(X3773,c_Groups_Oplus__class_Oplus(X3773,X3772,X3770),c_Groups_Oplus__class_Oplus(X3773,X3771,X3770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1639,plain,
! [X3766,X3767,X3768,X3769] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3769)
| ~ c_Orderings_Oord__class_Oless__eq(X3769,X3768,X3767)
| c_Orderings_Oord__class_Oless__eq(X3769,c_Groups_Oplus__class_Oplus(X3769,X3766,X3768),c_Groups_Oplus__class_Oplus(X3769,X3766,X3767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1640,plain,
! [X3799,X3800,X3801,X3802] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3802)
| ~ c_Orderings_Oord__class_Oless(X3802,X3801,X3800)
| c_Orderings_Oord__class_Oless(X3802,c_Groups_Oplus__class_Oplus(X3802,X3801,X3799),c_Groups_Oplus__class_Oplus(X3802,X3800,X3799)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1641,plain,
! [X3795,X3796,X3797,X3798] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3798)
| ~ c_Orderings_Oord__class_Oless(X3798,X3797,X3796)
| c_Orderings_Oord__class_Oless(X3798,c_Groups_Oplus__class_Oplus(X3798,X3795,X3797),c_Groups_Oplus__class_Oplus(X3798,X3795,X3796)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1642,plain,
! [X4571] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk11_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4571),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| 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_s____),X4571)),esk11_0) ) ),
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_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])])]) ).
fof(i_0_1643,plain,
! [X4565] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk10_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4565),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| 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_s____),X4565)),esk10_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096])])])]) ).
fof(i_0_1644,plain,
! [X4409] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4409),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| 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_s____),X4409)),v_m____) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_m_I2_J])]) ).
fof(i_0_1645,plain,
! [X4647] : 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_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X4647))),
inference(variable_rename,[status(thm)],[fact_c]) ).
fof(i_0_1646,plain,
! [X2963,X2964,X2965] :
( ~ class_Rings_Olinordered__semidom(X2965)
| ~ c_Orderings_Oord__class_Oless(X2965,c_Groups_Oone__class_Oone(X2965),X2964)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2963)
| c_Orderings_Oord__class_Oless(X2965,c_Groups_Oone__class_Oone(X2965),hAPP(hAPP(c_Power_Opower__class_Opower(X2965),X2964),X2963)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1647,plain,
! [X5281,X5282,X5283,X5284] :
( ( ~ c_SEQ_Odecseq(X5282,X5281)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5283,X5284)
| c_Orderings_Oord__class_Oless__eq(X5282,hAPP(X5281,X5284),hAPP(X5281,X5283))
| ~ class_Orderings_Oorder(X5282) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk34_2(X5281,X5282),esk35_2(X5281,X5282))
| c_SEQ_Odecseq(X5282,X5281)
| ~ class_Orderings_Oorder(X5282) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5282,hAPP(X5281,esk35_2(X5281,X5282)),hAPP(X5281,esk34_2(X5281,X5282)))
| c_SEQ_Odecseq(X5282,X5281)
| ~ class_Orderings_Oorder(X5282) ) ),
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_1648,plain,
! [X5260,X5261] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5261),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5260)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5261,c_RealDef_Oreal(tc_Nat_Onat,X5260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
fof(i_0_1649,plain,
! [X3836,X3837,X3838,X3839] :
( ~ class_Groups_Oordered__comm__monoid__add(X3839)
| ~ c_Orderings_Oord__class_Oless__eq(X3839,c_Groups_Ozero__class_Ozero(X3839),X3838)
| ~ c_Orderings_Oord__class_Oless__eq(X3839,X3837,X3836)
| c_Orderings_Oord__class_Oless__eq(X3839,X3837,c_Groups_Oplus__class_Oplus(X3839,X3838,X3836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1650,plain,
! [X3840,X3841,X3842,X3843] :
( ~ class_Groups_Oordered__comm__monoid__add(X3843)
| ~ c_Orderings_Oord__class_Oless__eq(X3843,c_Groups_Ozero__class_Ozero(X3843),X3842)
| ~ c_Orderings_Oord__class_Oless__eq(X3843,X3841,X3840)
| c_Orderings_Oord__class_Oless__eq(X3843,X3841,c_Groups_Oplus__class_Oplus(X3843,X3840,X3842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1651,plain,
! [X3886,X3887,X3888,X3889] :
( ~ class_Groups_Oordered__comm__monoid__add(X3889)
| ~ c_Orderings_Oord__class_Oless(X3889,c_Groups_Ozero__class_Ozero(X3889),X3888)
| ~ c_Orderings_Oord__class_Oless__eq(X3889,X3887,X3886)
| c_Orderings_Oord__class_Oless(X3889,X3887,c_Groups_Oplus__class_Oplus(X3889,X3888,X3886)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1652,plain,
! [X3882,X3883,X3884,X3885] :
( ~ class_Groups_Oordered__comm__monoid__add(X3885)
| ~ c_Orderings_Oord__class_Oless__eq(X3885,c_Groups_Ozero__class_Ozero(X3885),X3884)
| ~ c_Orderings_Oord__class_Oless(X3885,X3883,X3882)
| c_Orderings_Oord__class_Oless(X3885,X3883,c_Groups_Oplus__class_Oplus(X3885,X3884,X3882)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1653,plain,
! [X3528,X3529,X3530,X3531] :
( ~ class_Rings_Olinordered__semidom(X3531)
| ~ c_Orderings_Oord__class_Oless(X3531,c_Groups_Ozero__class_Ozero(X3531),X3530)
| ~ c_Orderings_Oord__class_Oless(X3531,X3529,X3528)
| c_Orderings_Oord__class_Oless(X3531,X3529,c_Groups_Oplus__class_Oplus(X3531,X3530,X3528)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1654,plain,
! [X4261,X4262] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4262),X4262)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4261),X4261)),
inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(i_0_1655,plain,
! [X4616,X4617,X4618] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4618,X4617)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4616,X4618),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4616,X4617)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1656,plain,
! [X4233,X4234,X4235] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4235,X4234)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4235,X4233),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4234,X4233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1657,plain,
! [X4230,X4231,X4232] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4232,X4231)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4230,X4231),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4230,X4232)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1658,plain,
! [X3200,X3201,X3202] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3202,X3201)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3202,X3200),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3201,X3200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1659,plain,
! [X3403,X3404,X3405] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3405,X3404)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3403,X3405),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3403,X3404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
fof(i_0_1660,plain,
! [X4619,X4620,X4621] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4621,X4620)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4621,X4619),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4620,X4619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1661,plain,
! [X3381,X3382,X3383] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3383,X3382)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3383,X3381),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3382,X3381)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1662,plain,
! [X4516,X4517,X4518] :
( ~ class_Rings_Olinordered__idom(X4518)
| c_Groups_Oabs__class_Oabs(X4518,hAPP(hAPP(c_Power_Opower__class_Opower(X4518),c_Groups_Ouminus__class_Ouminus(X4518,X4517)),X4516)) = c_Groups_Oabs__class_Oabs(X4518,hAPP(hAPP(c_Power_Opower__class_Opower(X4518),X4517),X4516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).
fof(i_0_1663,plain,
! [X5373,X5374,X5375,X5376] :
( ~ class_Rings_Ocomm__ring__1(X5376)
| ~ c_Rings_Odvd__class_Odvd(X5376,X5375,X5374)
| ~ c_Rings_Odvd__class_Odvd(X5376,X5375,X5373)
| c_Rings_Odvd__class_Odvd(X5376,X5375,c_Groups_Ominus__class_Ominus(X5376,X5374,X5373)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_1664,plain,
! [X5314,X5316] :
( ~ class_RealVector_Oreal__algebra__1(X5314)
| ~ class_RealVector_Oreal__normed__vector(X5314)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5314,c_RealVector_Oof__real(X5314,X5316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5316)),esk36_1(X5314))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Obounded])])])]) ).
fof(i_0_1665,plain,
! [X5142,X5144] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk26_1(X5142))
| ~ class_RealVector_Oreal__algebra__1(X5142)
| ~ class_RealVector_Oreal__normed__vector(X5142) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5142,c_RealVector_Oof__real(X5142,X5144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5144)),esk26_1(X5142)))
| ~ class_RealVector_Oreal__algebra__1(X5142)
| ~ class_RealVector_Oreal__normed__vector(X5142) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ononneg__bounded])])])])]) ).
fof(i_0_1666,plain,
! [X4919,X4921] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk21_1(X4919))
| ~ class_RealVector_Oreal__algebra__1(X4919)
| ~ class_RealVector_Oreal__normed__vector(X4919) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4919,c_RealVector_Oof__real(X4919,X4921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4921)),esk21_1(X4919)))
| ~ class_RealVector_Oreal__algebra__1(X4919)
| ~ class_RealVector_Oreal__normed__vector(X4919) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Opos__bounded])])])])]) ).
fof(i_0_1667,plain,
! [X4452,X4453,X4454] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4454)
| c_Groups_Oabs__class_Oabs(X4454,c_Groups_Oplus__class_Oplus(X4454,c_Groups_Oabs__class_Oabs(X4454,X4453),c_Groups_Oabs__class_Oabs(X4454,X4452))) = c_Groups_Oplus__class_Oplus(X4454,c_Groups_Oabs__class_Oabs(X4454,X4453),c_Groups_Oabs__class_Oabs(X4454,X4452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_1668,plain,
! [X4693,X4694] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4694)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4693)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4694,X4693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1669,plain,
! [X5389,X5390,X5391,X5392] :
( ( X5391 != c_Groups_Ozero__class_Ozero(X5392)
| X5389 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5392))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) )
& ( X5391 = c_Groups_Ozero__class_Ozero(X5392)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),X5390,X5389)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) )
& ( X5391 != c_Groups_Ozero__class_Ozero(X5392)
| X5391 = c_Groups_Ozero__class_Ozero(X5392)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),X5390,X5389)
| X5391 = c_Groups_Ozero__class_Ozero(X5392)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) )
& ( X5391 != c_Groups_Ozero__class_Ozero(X5392)
| X5389 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5392))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),X5390,X5389)
| X5389 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5392))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5392),c_Polynomial_Osmult(X5392,X5391,X5390),X5389)
| ~ class_Fields_Ofield(X5392) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__iff])])]) ).
fof(i_0_1670,plain,
! [X5416,X5417,X5418,X5419] :
( ~ class_Fields_Ofield(X5419)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5419),X5418,c_Polynomial_Osmult(X5419,X5417,X5416))
| X5417 = c_Groups_Ozero__class_Ozero(X5419)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5419),X5418,X5416) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__cancel])]) ).
fof(i_0_1671,plain,
! [X5408,X5409,X5410,X5411] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5411),X5409,c_Polynomial_Osmult(X5411,X5410,X5408))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5411),X5409,X5408)
| X5410 = c_Groups_Ozero__class_Ozero(X5411)
| ~ class_Fields_Ofield(X5411) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5411),X5409,X5408)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5411),X5409,c_Polynomial_Osmult(X5411,X5410,X5408))
| X5410 = c_Groups_Ozero__class_Ozero(X5411)
| ~ class_Fields_Ofield(X5411) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__iff])])]) ).
fof(i_0_1672,plain,
! [X4238,X4239,X4240] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4239,X4240) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4240)
| X4239 = X4238
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4240,X4238)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4240,X4239) )
& ( X4239 != X4238
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4239,X4240) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4240)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4240,X4238)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4240,X4239) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1673,plain,
! [X4259,X4260] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4260)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4259)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4259,X4260),X4259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1674,plain,
! [X5251,X5252] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5252),X5251)
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5251,c_RealDef_Oreal(tc_Nat_Onat,X5252))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X5251),X5252) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).
fof(i_0_1675,plain,
! [X5254,X5255] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5255),X5254)
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5254,c_RealDef_Oreal(tc_Nat_Onat,X5255))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X5254),X5255) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).
fof(i_0_1676,plain,
! [X5400,X5401,X5402,X5403] :
( ~ class_Rings_Ocomm__semiring__1(X5403)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5403),c_Polynomial_Osmult(X5403,X5402,X5401),X5400)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5403),X5401,X5400) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__cancel])]) ).
fof(i_0_1677,plain,
! [X3826,X3827] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3827,c_Groups_Ozero__class_Ozero(X3827),c_Groups_Oplus__class_Oplus(X3827,X3826,X3826))
| c_Orderings_Oord__class_Oless__eq(X3827,c_Groups_Ozero__class_Ozero(X3827),X3826)
| ~ class_Groups_Olinordered__ab__group__add(X3827) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3827,c_Groups_Ozero__class_Ozero(X3827),X3826)
| c_Orderings_Oord__class_Oless__eq(X3827,c_Groups_Ozero__class_Ozero(X3827),c_Groups_Oplus__class_Oplus(X3827,X3826,X3826))
| ~ class_Groups_Olinordered__ab__group__add(X3827) ) ),
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_1678,plain,
! [X3855,X3856] :
( ( ~ c_Orderings_Oord__class_Oless(X3856,c_Groups_Ozero__class_Ozero(X3856),c_Groups_Oplus__class_Oplus(X3856,X3855,X3855))
| c_Orderings_Oord__class_Oless(X3856,c_Groups_Ozero__class_Ozero(X3856),X3855)
| ~ class_Groups_Olinordered__ab__group__add(X3856) )
& ( ~ c_Orderings_Oord__class_Oless(X3856,c_Groups_Ozero__class_Ozero(X3856),X3855)
| c_Orderings_Oord__class_Oless(X3856,c_Groups_Ozero__class_Ozero(X3856),c_Groups_Oplus__class_Oplus(X3856,X3855,X3855))
| ~ class_Groups_Olinordered__ab__group__add(X3856) ) ),
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_1679,plain,
! [X3828,X3829] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3829,c_Groups_Oplus__class_Oplus(X3829,X3828,X3828),c_Groups_Ozero__class_Ozero(X3829))
| c_Orderings_Oord__class_Oless__eq(X3829,X3828,c_Groups_Ozero__class_Ozero(X3829))
| ~ class_Groups_Olinordered__ab__group__add(X3829) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3829,X3828,c_Groups_Ozero__class_Ozero(X3829))
| c_Orderings_Oord__class_Oless__eq(X3829,c_Groups_Oplus__class_Oplus(X3829,X3828,X3828),c_Groups_Ozero__class_Ozero(X3829))
| ~ class_Groups_Olinordered__ab__group__add(X3829) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
fof(i_0_1680,plain,
! [X3853,X3854] :
( ( ~ c_Orderings_Oord__class_Oless(X3854,c_Groups_Oplus__class_Oplus(X3854,X3853,X3853),c_Groups_Ozero__class_Ozero(X3854))
| c_Orderings_Oord__class_Oless(X3854,X3853,c_Groups_Ozero__class_Ozero(X3854))
| ~ class_Groups_Olinordered__ab__group__add(X3854) )
& ( ~ c_Orderings_Oord__class_Oless(X3854,X3853,c_Groups_Ozero__class_Ozero(X3854))
| c_Orderings_Oord__class_Oless(X3854,c_Groups_Oplus__class_Oplus(X3854,X3853,X3853),c_Groups_Ozero__class_Ozero(X3854))
| ~ class_Groups_Olinordered__ab__group__add(X3854) ) ),
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_1681,plain,
! [X4197,X4198] :
( ( ~ c_Orderings_Oord__class_Oless(X4198,c_Groups_Oplus__class_Oplus(X4198,X4197,X4197),c_Groups_Ozero__class_Ozero(X4198))
| c_Orderings_Oord__class_Oless(X4198,X4197,c_Groups_Ozero__class_Ozero(X4198))
| ~ class_Rings_Olinordered__idom(X4198) )
& ( ~ c_Orderings_Oord__class_Oless(X4198,X4197,c_Groups_Ozero__class_Ozero(X4198))
| c_Orderings_Oord__class_Oless(X4198,c_Groups_Oplus__class_Oplus(X4198,X4197,X4197),c_Groups_Ozero__class_Ozero(X4198))
| ~ class_Rings_Olinordered__idom(X4198) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1682,plain,
! [X3011,X3012,X3013,X3014] :
( ~ class_Rings_Ocomm__semiring__1(X3014)
| c_Groups_Oplus__class_Oplus(X3014,c_Groups_Oplus__class_Oplus(X3014,X3013,X3012),X3011) = c_Groups_Oplus__class_Oplus(X3014,c_Groups_Oplus__class_Oplus(X3014,X3013,X3011),X3012) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1683,plain,
! [X3737,X3738,X3739,X3740] :
( ~ class_Groups_Oab__semigroup__add(X3740)
| c_Groups_Oplus__class_Oplus(X3740,c_Groups_Oplus__class_Oplus(X3740,X3739,X3738),X3737) = c_Groups_Oplus__class_Oplus(X3740,X3739,c_Groups_Oplus__class_Oplus(X3740,X3738,X3737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1684,plain,
! [X3015,X3016,X3017,X3018] :
( ~ class_Rings_Ocomm__semiring__1(X3018)
| c_Groups_Oplus__class_Oplus(X3018,c_Groups_Oplus__class_Oplus(X3018,X3017,X3016),X3015) = c_Groups_Oplus__class_Oplus(X3018,X3017,c_Groups_Oplus__class_Oplus(X3018,X3016,X3015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1685,plain,
! [X3019,X3020,X3021,X3022] :
( ~ class_Rings_Ocomm__semiring__1(X3022)
| c_Groups_Oplus__class_Oplus(X3022,X3021,c_Groups_Oplus__class_Oplus(X3022,X3020,X3019)) = c_Groups_Oplus__class_Oplus(X3022,c_Groups_Oplus__class_Oplus(X3022,X3021,X3020),X3019) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1686,plain,
! [X3023,X3024,X3025,X3026] :
( ~ class_Rings_Ocomm__semiring__1(X3026)
| c_Groups_Oplus__class_Oplus(X3026,X3025,c_Groups_Oplus__class_Oplus(X3026,X3024,X3023)) = c_Groups_Oplus__class_Oplus(X3026,X3024,c_Groups_Oplus__class_Oplus(X3026,X3025,X3023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1687,plain,
! [X4555] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4555),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4555),
inference(variable_rename,[status(thm)],[i_0_1281]) ).
fof(i_0_1688,plain,
! [X4336,X4337] :
( ( ~ 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,X4337,X4336))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4337),X4336) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4337),X4336)
| 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,X4337,X4336)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).
fof(i_0_1689,plain,
! [X4340,X4341] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4341,X4340))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4341),X4340) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4341),X4340)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4341,X4340)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(i_0_1690,plain,
! [X4338,X4339] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4339,X4338),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4338,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4339)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4338,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4339))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4339,X4338),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_1691,plain,
! [X4342,X4343] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4343,X4342),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4342,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4343)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4342,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4343))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4343,X4342),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_1692,plain,
! [X3649,X3650,X3651] :
( ~ class_Fields_Olinordered__field(X3651)
| ~ c_Orderings_Oord__class_Oless__eq(X3651,c_Rings_Oinverse__class_Oinverse(X3651,X3650),c_Rings_Oinverse__class_Oinverse(X3651,X3649))
| ~ c_Orderings_Oord__class_Oless(X3651,c_Groups_Ozero__class_Ozero(X3651),X3650)
| c_Orderings_Oord__class_Oless__eq(X3651,X3649,X3650) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le])]) ).
fof(i_0_1693,plain,
! [X3548,X3549,X3550] :
( ~ class_Fields_Olinordered__field(X3550)
| ~ c_Orderings_Oord__class_Oless(X3550,c_Rings_Oinverse__class_Oinverse(X3550,X3549),c_Rings_Oinverse__class_Oinverse(X3550,X3548))
| ~ c_Orderings_Oord__class_Oless(X3550,c_Groups_Ozero__class_Ozero(X3550),X3549)
| c_Orderings_Oord__class_Oless(X3550,X3548,X3549) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).
fof(i_0_1694,plain,
! [X3646,X3647,X3648] :
( ~ class_Fields_Olinordered__field(X3648)
| ~ c_Orderings_Oord__class_Oless__eq(X3648,c_Rings_Oinverse__class_Oinverse(X3648,X3647),c_Rings_Oinverse__class_Oinverse(X3648,X3646))
| ~ c_Orderings_Oord__class_Oless(X3648,X3646,c_Groups_Ozero__class_Ozero(X3648))
| c_Orderings_Oord__class_Oless__eq(X3648,X3646,X3647) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le__neg])]) ).
fof(i_0_1695,plain,
! [X3545,X3546,X3547] :
( ~ class_Fields_Olinordered__field(X3547)
| ~ c_Orderings_Oord__class_Oless(X3547,c_Rings_Oinverse__class_Oinverse(X3547,X3546),c_Rings_Oinverse__class_Oinverse(X3547,X3545))
| ~ c_Orderings_Oord__class_Oless(X3547,X3545,c_Groups_Ozero__class_Ozero(X3547))
| c_Orderings_Oord__class_Oless(X3547,X3545,X3546) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).
fof(i_0_1696,plain,
! [X4063,X4064,X4065] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4065,X4064,X4063)
| c_Orderings_Oord__class_Oless__eq(X4065,c_Groups_Ominus__class_Ominus(X4065,X4064,X4063),c_Groups_Ozero__class_Ozero(X4065))
| ~ class_Groups_Oordered__ab__group__add(X4065) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4065,c_Groups_Ominus__class_Ominus(X4065,X4064,X4063),c_Groups_Ozero__class_Ozero(X4065))
| c_Orderings_Oord__class_Oless__eq(X4065,X4064,X4063)
| ~ class_Groups_Oordered__ab__group__add(X4065) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
fof(i_0_1697,plain,
! [X4066,X4067,X4068] :
( ( ~ c_Orderings_Oord__class_Oless(X4068,X4067,X4066)
| c_Orderings_Oord__class_Oless(X4068,c_Groups_Ominus__class_Ominus(X4068,X4067,X4066),c_Groups_Ozero__class_Ozero(X4068))
| ~ class_Groups_Oordered__ab__group__add(X4068) )
& ( ~ c_Orderings_Oord__class_Oless(X4068,c_Groups_Ominus__class_Ominus(X4068,X4067,X4066),c_Groups_Ozero__class_Ozero(X4068))
| c_Orderings_Oord__class_Oless(X4068,X4067,X4066)
| ~ class_Groups_Oordered__ab__group__add(X4068) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_1698,plain,
! [X4868,X4869,X4870,X4871] :
( ~ class_Rings_Ocomm__semiring__0(X4871)
| c_Polynomial_Osmult(X4871,X4870,c_Polynomial_Omonom(X4871,X4869,X4868)) = c_Polynomial_Omonom(X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4871),X4870),X4869),X4868) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__monom])]) ).
fof(i_0_1699,plain,
! [X4783,X4784,X4785,X4786] :
( ~ class_Rings_Ocomm__semiring__0(X4786)
| c_Polynomial_Osmult(X4786,X4785,c_Polynomial_Osmult(X4786,X4784,X4783)) = c_Polynomial_Osmult(X4786,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4786),X4785),X4784),X4783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(i_0_1700,plain,
! [X4523,X4524] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4524,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4523))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4523,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4524))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(i_0_1701,plain,
! [X4689,X4690] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4690)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4689)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4690),X4689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_1702,plain,
! [X3348,X3349] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3349)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3349),X3348)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3348)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3349),X3348)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3349)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3348)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3349),X3348)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1703,plain,
! [X3580,X3581] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3581)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3580)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3581),X3580)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1704,plain,
! [X4528,X4529,X4530] :
( ~ class_Rings_Olinordered__idom(X4530)
| ~ c_Orderings_Oord__class_Oless__eq(X4530,c_Groups_Ozero__class_Ozero(X4530),X4529)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4530),c_Groups_Oabs__class_Oabs(X4530,X4528)),X4529) = c_Groups_Oabs__class_Oabs(X4530,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4530),X4528),X4529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_1705,plain,
! [X3138] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3138),X3138))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1706,plain,
! [X3955,X3956,X3957,X3958,X3959] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3959,X3958,X3957)
| c_Orderings_Oord__class_Oless__eq(X3959,X3956,X3955)
| c_Groups_Ominus__class_Ominus(X3959,X3958,X3957) != c_Groups_Ominus__class_Ominus(X3959,X3956,X3955)
| ~ class_Groups_Oordered__ab__group__add(X3959) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3959,X3956,X3955)
| c_Orderings_Oord__class_Oless__eq(X3959,X3958,X3957)
| c_Groups_Ominus__class_Ominus(X3959,X3958,X3957) != c_Groups_Ominus__class_Ominus(X3959,X3956,X3955)
| ~ class_Groups_Oordered__ab__group__add(X3959) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_1707,plain,
! [X3969,X3970,X3971,X3972,X3973] :
( ( ~ c_Orderings_Oord__class_Oless(X3973,X3972,X3971)
| c_Orderings_Oord__class_Oless(X3973,X3970,X3969)
| c_Groups_Ominus__class_Ominus(X3973,X3972,X3971) != c_Groups_Ominus__class_Ominus(X3973,X3970,X3969)
| ~ class_Groups_Oordered__ab__group__add(X3973) )
& ( ~ c_Orderings_Oord__class_Oless(X3973,X3970,X3969)
| c_Orderings_Oord__class_Oless(X3973,X3972,X3971)
| c_Groups_Ominus__class_Ominus(X3973,X3972,X3971) != c_Groups_Ominus__class_Ominus(X3973,X3970,X3969)
| ~ class_Groups_Oordered__ab__group__add(X3973) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1708,plain,
! [X3148,X3149,X3150] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3150,X3149)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3150),X3148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3149),X3148)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1709,plain,
! [X3151,X3152,X3153] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3153,X3152)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3151),X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3151),X3152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1710,plain,
! [X2999,X3000,X3001,X3002] :
( ~ class_Rings_Ocomm__semiring__1(X3002)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3002),X3001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3002),X3000),X2999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3002),X3000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3002),X3001),X2999)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1711,plain,
! [X4222,X4223,X4224] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4224,X4223),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4224,X4222)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4223,X4222),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1712,plain,
! [X4225,X4226,X4227] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4227,X4226),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4225,X4226)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4227,X4225),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1713,plain,
! [X4423,X4424,X4425] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4425,X4424),X4423) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4425,X4423),X4424),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1714,plain,
! [X4219,X4220,X4221] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4221,X4220),X4219) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4221,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4220,X4219)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1715,plain,
! [X4622,X4623,X4624] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4624,X4623),X4622) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4624,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4623,X4622)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1716,plain,
! [X3261,X3262,X3263] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3263,X3262),X3261) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3263,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3262,X3261)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1717,plain,
! [X4625,X4626,X4627] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4627,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4626,X4625)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4626,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4627,X4625)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1718,plain,
! [X3258,X3259,X3260] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3260,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3259,X3258)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3259,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3260,X3258)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1719,plain,
! [X4602,X4603] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4603,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4602,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4603,X4602)
| X4603 = X4602 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4603,X4602)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4603,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4602,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X4603 != X4602
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4603,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4602,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).
fof(i_0_1720,plain,
! [X4604,X4605] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4605,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4604)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4605,X4604) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4605,X4604)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4605,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4604) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
fof(i_0_1721,plain,
! [X4600,X4601] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4601,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4600,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4601,X4600) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4601,X4600)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4601,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4600,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).
fof(i_0_1722,plain,
! [X4575,X4576] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4576,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4575,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4576,X4575) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4576,X4575)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4576,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4575,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_1723,plain,
! [X5443,X5444,X5445,X5446] :
( ~ class_Rings_Ocomm__semiring__1(X5446)
| ~ c_Rings_Odvd__class_Odvd(X5446,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5446),X5445),X5444),X5443)
| c_Rings_Odvd__class_Odvd(X5446,X5445,X5443) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_1724,plain,
! [X5447,X5448,X5449,X5450] :
( ~ class_Rings_Ocomm__semiring__1(X5450)
| ~ c_Rings_Odvd__class_Odvd(X5450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5450),X5449),X5448),X5447)
| c_Rings_Odvd__class_Odvd(X5450,X5448,X5447) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_1725,plain,
! [X4255,X4256] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4256,X4255)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4256,X4255),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,X4256,X4255),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4256,X4255) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_1726,plain,
! [X4573,X4574] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4574,X4573)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4574,X4573),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4574,X4573),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4574,X4573) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1727,plain,
! [X4257,X4258] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4258,X4257))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4257,X4258) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4257,X4258)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4258,X4257)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_1728,plain,
! [X3388,X3389,X3390,X3391] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3391,X3390)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3389,X3390) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3391,X3388)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,X3388) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1729,plain,
! [X5258,X5259] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5259)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5259,c_RealDef_Oreal(tc_Nat_Onat,X5258))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5259),X5258) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1730,plain,
! [X5264,X5265] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5265)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5265,c_RealDef_Oreal(tc_Nat_Onat,X5264))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5265),X5264) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1731,plain,
! [X4505,X4506,X4507] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4507)
| ~ c_Orderings_Oord__class_Oless__eq(X4507,X4506,X4505)
| ~ c_Orderings_Oord__class_Oless__eq(X4507,c_Groups_Ouminus__class_Ouminus(X4507,X4506),X4505)
| c_Orderings_Oord__class_Oless__eq(X4507,c_Groups_Oabs__class_Oabs(X4507,X4506),X4505) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).
fof(i_0_1732,plain,
! [X4502,X4503,X4504] :
( ( c_Orderings_Oord__class_Oless__eq(X4504,X4503,X4502)
| ~ c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Oabs__class_Oabs(X4504,X4503),X4502)
| ~ class_Groups_Oordered__ab__group__add__abs(X4504) )
& ( c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Ouminus__class_Ouminus(X4504,X4503),X4502)
| ~ c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Oabs__class_Oabs(X4504,X4503),X4502)
| ~ class_Groups_Oordered__ab__group__add__abs(X4504) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4504,X4503,X4502)
| ~ c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Ouminus__class_Ouminus(X4504,X4503),X4502)
| c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Oabs__class_Oabs(X4504,X4503),X4502)
| ~ class_Groups_Oordered__ab__group__add__abs(X4504) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).
fof(i_0_1733,plain,
! [X4511,X4512,X4513] :
( ( c_Orderings_Oord__class_Oless(X4513,X4512,X4511)
| ~ c_Orderings_Oord__class_Oless(X4513,c_Groups_Oabs__class_Oabs(X4513,X4512),X4511)
| ~ class_Rings_Olinordered__idom(X4513) )
& ( c_Orderings_Oord__class_Oless(X4513,c_Groups_Ouminus__class_Ouminus(X4513,X4512),X4511)
| ~ c_Orderings_Oord__class_Oless(X4513,c_Groups_Oabs__class_Oabs(X4513,X4512),X4511)
| ~ class_Rings_Olinordered__idom(X4513) )
& ( ~ c_Orderings_Oord__class_Oless(X4513,X4512,X4511)
| ~ c_Orderings_Oord__class_Oless(X4513,c_Groups_Ouminus__class_Ouminus(X4513,X4512),X4511)
| c_Orderings_Oord__class_Oless(X4513,c_Groups_Oabs__class_Oabs(X4513,X4512),X4511)
| ~ class_Rings_Olinordered__idom(X4513) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(i_0_1734,plain,
! [X3213,X3214,X3215] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3215,X3213)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3215,X3214),X3213) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3214,X3213)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3215,X3214),X3213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1282])])]) ).
fof(i_0_1735,plain,
! [X3210,X3211,X3212] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3212,X3211),X3210)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3212,X3210) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1736,plain,
! [X3207,X3208,X3209] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3209,X3208),X3207)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3208,X3207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1737,plain,
! [X3392,X3393,X3394] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3394,X3393),X3392)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3394,X3392) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1738,plain,
! [X5199,X5200] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5200,X5199)
| c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5199,X5200)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5199),c_RealDef_Oreal(tc_Nat_Onat,X5200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).
fof(i_0_1739,plain,
! [X3833,X3834,X3835] :
( ( X3834 = c_Groups_Ozero__class_Ozero(X3835)
| c_Groups_Oplus__class_Oplus(X3835,X3834,X3833) != c_Groups_Ozero__class_Ozero(X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3833)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3834)
| ~ class_Groups_Oordered__comm__monoid__add(X3835) )
& ( X3833 = c_Groups_Ozero__class_Ozero(X3835)
| c_Groups_Oplus__class_Oplus(X3835,X3834,X3833) != c_Groups_Ozero__class_Ozero(X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3833)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3834)
| ~ class_Groups_Oordered__comm__monoid__add(X3835) )
& ( X3834 != c_Groups_Ozero__class_Ozero(X3835)
| X3833 != c_Groups_Ozero__class_Ozero(X3835)
| c_Groups_Oplus__class_Oplus(X3835,X3834,X3833) = c_Groups_Ozero__class_Ozero(X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3833)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3834)
| ~ class_Groups_Oordered__comm__monoid__add(X3835) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1740,plain,
! [X3655,X3656,X3657] :
( ~ class_Fields_Olinordered__field(X3657)
| ~ c_Orderings_Oord__class_Oless__eq(X3657,X3656,X3655)
| ~ c_Orderings_Oord__class_Oless(X3657,c_Groups_Ozero__class_Ozero(X3657),X3656)
| c_Orderings_Oord__class_Oless__eq(X3657,c_Rings_Oinverse__class_Oinverse(X3657,X3655),c_Rings_Oinverse__class_Oinverse(X3657,X3656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le])]) ).
fof(i_0_1741,plain,
! [X3556,X3557,X3558] :
( ~ class_Fields_Olinordered__field(X3558)
| ~ c_Orderings_Oord__class_Oless(X3558,X3557,X3556)
| ~ c_Orderings_Oord__class_Oless(X3558,c_Groups_Ozero__class_Ozero(X3558),X3557)
| c_Orderings_Oord__class_Oless(X3558,c_Rings_Oinverse__class_Oinverse(X3558,X3556),c_Rings_Oinverse__class_Oinverse(X3558,X3557)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).
fof(i_0_1742,plain,
! [X3652,X3653,X3654] :
( ~ class_Fields_Olinordered__field(X3654)
| ~ c_Orderings_Oord__class_Oless__eq(X3654,X3653,X3652)
| ~ c_Orderings_Oord__class_Oless(X3654,X3652,c_Groups_Ozero__class_Ozero(X3654))
| c_Orderings_Oord__class_Oless__eq(X3654,c_Rings_Oinverse__class_Oinverse(X3654,X3652),c_Rings_Oinverse__class_Oinverse(X3654,X3653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le__neg])]) ).
fof(i_0_1743,plain,
! [X3553,X3554,X3555] :
( ~ class_Fields_Olinordered__field(X3555)
| ~ c_Orderings_Oord__class_Oless(X3555,X3554,X3553)
| ~ c_Orderings_Oord__class_Oless(X3555,X3553,c_Groups_Ozero__class_Ozero(X3555))
| c_Orderings_Oord__class_Oless(X3555,c_Rings_Oinverse__class_Oinverse(X3555,X3553),c_Rings_Oinverse__class_Oinverse(X3555,X3554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).
fof(i_0_1744,plain,
! [X5129,X5130,X5131,X5132] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5131,X5132),X5130,X5129)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5131,X5132),X5130,X5129)
| ~ class_Orderings_Oord(X5132) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5131,X5132),X5129,X5130)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5131,X5132),X5130,X5129)
| ~ class_Orderings_Oord(X5132) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5131,X5132),X5130,X5129)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X5131,X5132),X5129,X5130)
| c_Orderings_Oord__class_Oless(tc_fun(X5131,X5132),X5130,X5129)
| ~ class_Orderings_Oord(X5132) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1283])])]) ).
fof(i_0_1745,plain,
! [X3894,X3895] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3895),X3894))
| X3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3895) )
& ( X3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3895),X3894)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3895)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3895),X3894)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1746,plain,
! [X2846,X2847] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2847),X2846))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2847)
| X2846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2847)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2847),X2846)) )
& ( X2846 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2847),X2846)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1747,plain,
! [X5293,X5294,X5295,X5296,X5297] :
( ~ class_Groups_Ominus(X5297)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5296,X5297),X5295,X5294),X5293) = c_Groups_Ominus__class_Ominus(X5297,hAPP(X5295,X5293),hAPP(X5294,X5293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_1748,plain,
! [X3124,X3125] :
( ( c_Orderings_Oord__class_Oless(X3125,c_Groups_Ozero__class_Ozero(X3125),X3124)
| ~ c_Orderings_Oord__class_Oless__eq(X3125,c_Groups_Oone__class_Oone(X3125),c_Rings_Oinverse__class_Oinverse(X3125,X3124))
| ~ class_Fields_Olinordered__field__inverse__zero(X3125) )
& ( c_Orderings_Oord__class_Oless__eq(X3125,X3124,c_Groups_Oone__class_Oone(X3125))
| ~ c_Orderings_Oord__class_Oless__eq(X3125,c_Groups_Oone__class_Oone(X3125),c_Rings_Oinverse__class_Oinverse(X3125,X3124))
| ~ class_Fields_Olinordered__field__inverse__zero(X3125) )
& ( ~ c_Orderings_Oord__class_Oless(X3125,c_Groups_Ozero__class_Ozero(X3125),X3124)
| ~ c_Orderings_Oord__class_Oless__eq(X3125,X3124,c_Groups_Oone__class_Oone(X3125))
| c_Orderings_Oord__class_Oless__eq(X3125,c_Groups_Oone__class_Oone(X3125),c_Rings_Oinverse__class_Oinverse(X3125,X3124))
| ~ class_Fields_Olinordered__field__inverse__zero(X3125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse__iff])])]) ).
fof(i_0_1749,plain,
! [X3120,X3121] :
( ~ class_Fields_Olinordered__field(X3121)
| ~ c_Orderings_Oord__class_Oless(X3121,c_Groups_Ozero__class_Ozero(X3121),X3120)
| ~ c_Orderings_Oord__class_Oless__eq(X3121,X3120,c_Groups_Oone__class_Oone(X3121))
| c_Orderings_Oord__class_Oless__eq(X3121,c_Groups_Oone__class_Oone(X3121),c_Rings_Oinverse__class_Oinverse(X3121,X3120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse])]) ).
fof(i_0_1750,plain,
! [X3666,X3667] :
( ( c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),X3666)
| ~ c_Orderings_Oord__class_Oless(X3667,c_Groups_Oone__class_Oone(X3667),c_Rings_Oinverse__class_Oinverse(X3667,X3666))
| ~ class_Fields_Olinordered__field__inverse__zero(X3667) )
& ( c_Orderings_Oord__class_Oless(X3667,X3666,c_Groups_Oone__class_Oone(X3667))
| ~ c_Orderings_Oord__class_Oless(X3667,c_Groups_Oone__class_Oone(X3667),c_Rings_Oinverse__class_Oinverse(X3667,X3666))
| ~ class_Fields_Olinordered__field__inverse__zero(X3667) )
& ( ~ c_Orderings_Oord__class_Oless(X3667,c_Groups_Ozero__class_Ozero(X3667),X3666)
| ~ c_Orderings_Oord__class_Oless(X3667,X3666,c_Groups_Oone__class_Oone(X3667))
| c_Orderings_Oord__class_Oless(X3667,c_Groups_Oone__class_Oone(X3667),c_Rings_Oinverse__class_Oinverse(X3667,X3666))
| ~ class_Fields_Olinordered__field__inverse__zero(X3667) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff])])]) ).
fof(i_0_1751,plain,
! [X3668,X3669] :
( ~ class_Fields_Olinordered__field(X3669)
| ~ c_Orderings_Oord__class_Oless(X3669,c_Groups_Ozero__class_Ozero(X3669),X3668)
| ~ c_Orderings_Oord__class_Oless(X3669,X3668,c_Groups_Oone__class_Oone(X3669))
| c_Orderings_Oord__class_Oless(X3669,c_Groups_Oone__class_Oone(X3669),c_Rings_Oinverse__class_Oinverse(X3669,X3668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse])]) ).
fof(i_0_1752,plain,
! [X4519,X4520] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4519),X4520)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4520),X4519) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4520,X4519)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4520),X4519) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4519),X4520)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4520,X4519)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4520),X4519) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])]) ).
fof(i_0_1753,plain,
! [X5228,X5229,X5230] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5230),X5229,X5228)
| X5229 = X5228
| c_Polynomial_Opos__poly(X5230,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5230),X5228,X5229))
| ~ class_Rings_Olinordered__idom(X5230) )
& ( X5229 != X5228
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5230),X5229,X5228)
| ~ class_Rings_Olinordered__idom(X5230) )
& ( ~ c_Polynomial_Opos__poly(X5230,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5230),X5228,X5229))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5230),X5229,X5228)
| ~ class_Rings_Olinordered__idom(X5230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def])])]) ).
fof(i_0_1754,plain,
! [X5266,X5267,X5268] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5268),X5267,X5266)
| c_Polynomial_Opos__poly(X5268,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5268),X5266,X5267))
| ~ class_Rings_Olinordered__idom(X5268) )
& ( ~ c_Polynomial_Opos__poly(X5268,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5268),X5266,X5267))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5268),X5267,X5266)
| ~ class_Rings_Olinordered__idom(X5268) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])]) ).
fof(i_0_1755,plain,
! [X5412,X5413,X5414,X5415] :
( ~ class_Fields_Ofield(X5415)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5415),X5414,X5413)
| X5412 = c_Groups_Ozero__class_Ozero(X5415)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5415),c_Polynomial_Osmult(X5415,X5412,X5414),X5413) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd])]) ).
fof(i_0_1756,plain,
! [X4535,X4536,X4537] :
( ~ class_Rings_Olinordered__idom(X4537)
| c_Orderings_Oord__class_Oless__eq(X4537,c_Groups_Ozero__class_Ozero(X4537),hAPP(hAPP(c_Power_Opower__class_Opower(X4537),c_Groups_Oabs__class_Oabs(X4537,X4536)),X4535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_1757,plain,
! [X5195,X5196,X5197] :
( ( X5195 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5197))
| c_Polynomial_Opos__poly(X5197,X5195)
| ~ c_Polynomial_Opos__poly(X5197,c_Polynomial_OpCons(X5197,X5196,X5195))
| ~ class_Rings_Olinordered__idom(X5197) )
& ( c_Orderings_Oord__class_Oless(X5197,c_Groups_Ozero__class_Ozero(X5197),X5196)
| c_Polynomial_Opos__poly(X5197,X5195)
| ~ c_Polynomial_Opos__poly(X5197,c_Polynomial_OpCons(X5197,X5196,X5195))
| ~ class_Rings_Olinordered__idom(X5197) )
& ( ~ c_Polynomial_Opos__poly(X5197,X5195)
| c_Polynomial_Opos__poly(X5197,c_Polynomial_OpCons(X5197,X5196,X5195))
| ~ class_Rings_Olinordered__idom(X5197) )
& ( X5195 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5197))
| ~ c_Orderings_Oord__class_Oless(X5197,c_Groups_Ozero__class_Ozero(X5197),X5196)
| c_Polynomial_Opos__poly(X5197,c_Polynomial_OpCons(X5197,X5196,X5195))
| ~ class_Rings_Olinordered__idom(X5197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons])])]) ).
fof(i_0_1758,plain,
! [X4696] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X4696),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X4696))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X4696),esk14_1(X4696)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1284])])]) ).
fof(i_0_1759,plain,
! [X5404,X5405,X5406,X5407] :
( ~ class_Rings_Ocomm__semiring__1(X5407)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5407),X5406,X5405)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5407),X5406,c_Polynomial_Osmult(X5407,X5404,X5405)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult])]) ).
fof(i_0_1760,plain,
! [X2831,X2832,X2833,X2834] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2834),X2833),X2832) != hAPP(hAPP(c_Power_Opower__class_Opower(X2834),X2833),X2831)
| X2832 = X2831
| ~ c_Orderings_Oord__class_Oless(X2834,c_Groups_Oone__class_Oone(X2834),X2833)
| ~ class_Rings_Olinordered__semidom(X2834) )
& ( X2832 != X2831
| hAPP(hAPP(c_Power_Opower__class_Opower(X2834),X2833),X2832) = hAPP(hAPP(c_Power_Opower__class_Opower(X2834),X2833),X2831)
| ~ c_Orderings_Oord__class_Oless(X2834,c_Groups_Oone__class_Oone(X2834),X2833)
| ~ class_Rings_Olinordered__semidom(X2834) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1761,plain,
! [X5248,X5249] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5249),X5248)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5249,c_RealDef_Oreal(tc_Nat_Onat,X5248))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5249) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5249,c_RealDef_Oreal(tc_Nat_Onat,X5248))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5249),X5248)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5249) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1762,plain,
! [X5256,X5257] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5257)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5257,c_RealDef_Oreal(tc_Nat_Onat,X5256))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X5257),X5256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1763,plain,
! [X5244,X5245] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5244,c_RComplete_Onatfloor(X5245))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5244),X5245)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5245) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5244),X5245)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5244,c_RComplete_Onatfloor(X5245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5245) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
fof(i_0_1764,plain,
! [X2860,X2861,X2862] :
( ~ class_Rings_Olinordered__semidom(X2862)
| ~ c_Orderings_Oord__class_Oless__eq(X2862,c_Groups_Ozero__class_Ozero(X2862),X2861)
| c_Orderings_Oord__class_Oless__eq(X2862,c_Groups_Ozero__class_Ozero(X2862),hAPP(hAPP(c_Power_Opower__class_Opower(X2862),X2861),X2860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_1765,plain,
! [X2935,X2936,X2937] :
( ~ class_Rings_Olinordered__semidom(X2937)
| ~ c_Orderings_Oord__class_Oless__eq(X2937,c_Groups_Oone__class_Oone(X2937),X2936)
| c_Orderings_Oord__class_Oless__eq(X2937,c_Groups_Oone__class_Oone(X2937),hAPP(hAPP(c_Power_Opower__class_Opower(X2937),X2936),X2935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_1766,plain,
! [X2947,X2948,X2949] :
( ~ class_Rings_Olinordered__semidom(X2949)
| ~ c_Orderings_Oord__class_Oless(X2949,c_Groups_Ozero__class_Ozero(X2949),X2948)
| c_Orderings_Oord__class_Oless(X2949,c_Groups_Ozero__class_Ozero(X2949),hAPP(hAPP(c_Power_Opower__class_Opower(X2949),X2948),X2947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1767,plain,
! [X3658,X3659] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3659,c_Rings_Oinverse__class_Oinverse(X3659,X3658),c_Groups_Oone__class_Oone(X3659))
| c_Orderings_Oord__class_Oless__eq(X3659,X3658,c_Groups_Ozero__class_Ozero(X3659))
| c_Orderings_Oord__class_Oless__eq(X3659,c_Groups_Oone__class_Oone(X3659),X3658)
| ~ class_Fields_Olinordered__field__inverse__zero(X3659) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3659,X3658,c_Groups_Ozero__class_Ozero(X3659))
| c_Orderings_Oord__class_Oless__eq(X3659,c_Rings_Oinverse__class_Oinverse(X3659,X3658),c_Groups_Oone__class_Oone(X3659))
| ~ class_Fields_Olinordered__field__inverse__zero(X3659) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3659,c_Groups_Oone__class_Oone(X3659),X3658)
| c_Orderings_Oord__class_Oless__eq(X3659,c_Rings_Oinverse__class_Oinverse(X3659,X3658),c_Groups_Oone__class_Oone(X3659))
| ~ class_Fields_Olinordered__field__inverse__zero(X3659) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__1__iff])])]) ).
fof(i_0_1768,plain,
! [X3122,X3123] :
( ( ~ c_Orderings_Oord__class_Oless(X3123,c_Rings_Oinverse__class_Oinverse(X3123,X3122),c_Groups_Oone__class_Oone(X3123))
| c_Orderings_Oord__class_Oless__eq(X3123,X3122,c_Groups_Ozero__class_Ozero(X3123))
| c_Orderings_Oord__class_Oless(X3123,c_Groups_Oone__class_Oone(X3123),X3122)
| ~ class_Fields_Olinordered__field__inverse__zero(X3123) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3123,X3122,c_Groups_Ozero__class_Ozero(X3123))
| c_Orderings_Oord__class_Oless(X3123,c_Rings_Oinverse__class_Oinverse(X3123,X3122),c_Groups_Oone__class_Oone(X3123))
| ~ class_Fields_Olinordered__field__inverse__zero(X3123) )
& ( ~ c_Orderings_Oord__class_Oless(X3123,c_Groups_Oone__class_Oone(X3123),X3122)
| c_Orderings_Oord__class_Oless(X3123,c_Rings_Oinverse__class_Oinverse(X3123,X3122),c_Groups_Oone__class_Oone(X3123))
| ~ class_Fields_Olinordered__field__inverse__zero(X3123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__1__iff])])]) ).
fof(i_0_1769,plain,
! [X5165] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5165)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5165,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5165),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_1770,plain,
! [X5127] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5127)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5127,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5127),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_1771,plain,
! [X3569,X3570,X3571] :
( ~ class_Rings_Odivision__ring(X3571)
| X3570 = c_Groups_Ozero__class_Ozero(X3571)
| X3569 = c_Groups_Ozero__class_Ozero(X3571)
| c_Rings_Oinverse__class_Oinverse(X3571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3571),X3570),X3569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3571),c_Rings_Oinverse__class_Oinverse(X3571,X3569)),c_Rings_Oinverse__class_Oinverse(X3571,X3570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).
fof(i_0_1772,plain,
! [X3469,X3470] :
( ~ class_Rings_Olinordered__ring(X3470)
| ~ c_Orderings_Oord__class_Oless(X3470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3470),X3469),X3469),c_Groups_Ozero__class_Ozero(X3470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1285])]) ).
fof(i_0_1773,plain,
! [X4596] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4596),X4596) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1774,plain,
! [X5172,X5173] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5173)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5172)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X5173,X5172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_1775,plain,
! [X5136,X5137,X5138,X5139] : hAPP(hAPP(c_Power_Opower_Opower(X5139,X5138,X5137),X5136),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5138,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_1776,plain,
! [X4607] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4607)
| 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),X4607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_1777,plain,
! [X5343,X5344,X5345] :
( ~ class_Rings_Olinordered__idom(X5345)
| c_Groups_Osgn__class_Osgn(X5345,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5345),X5344),X5343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5345),c_Groups_Osgn__class_Osgn(X5345,X5344)),c_Groups_Osgn__class_Osgn(X5345,X5343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).
fof(i_0_1778,plain,
! [X5340,X5341,X5342] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5342)
| c_Groups_Osgn__class_Osgn(X5342,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5342),X5341),X5340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5342),c_Groups_Osgn__class_Osgn(X5342,X5341)),c_Groups_Osgn__class_Osgn(X5342,X5340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__mult])]) ).
fof(i_0_1779,plain,
! [X4459,X4460,X4461] :
( ~ class_Rings_Olinordered__idom(X4461)
| c_Groups_Oabs__class_Oabs(X4461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4461),X4460),X4459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4461),c_Groups_Oabs__class_Oabs(X4461,X4460)),c_Groups_Oabs__class_Oabs(X4461,X4459)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_1780,plain,
! [X3362,X3363,X3364] :
( ~ class_Fields_Ofield__inverse__zero(X3364)
| c_Rings_Oinverse__class_Oinverse(X3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3364),X3363),X3362)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3364),c_Rings_Oinverse__class_Oinverse(X3364,X3363)),c_Rings_Oinverse__class_Oinverse(X3364,X3362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib])]) ).
fof(i_0_1781,plain,
! [X4792,X4793,X4794] :
( ~ class_Groups_Oab__group__add(X4794)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4794),c_Polynomial_OpCons(X4794,X4793,X4792)) = c_Polynomial_OpCons(X4794,c_Groups_Ouminus__class_Ouminus(X4794,X4793),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4794),X4792)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J])]) ).
fof(i_0_1782,plain,
! [X4789,X4790,X4791] :
( ~ class_Groups_Oab__group__add(X4791)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4791),c_Polynomial_OpCons(X4791,X4790,X4789)) = c_Polynomial_OpCons(X4791,c_Groups_Ouminus__class_Ouminus(X4791,X4790),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4791),X4789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])]) ).
fof(i_0_1783,plain,
! [X5426,X5427,X5428,X5429] :
( ~ class_Rings_Ocomm__semiring__1(X5429)
| ~ c_Rings_Odvd__class_Odvd(X5429,X5428,X5427)
| c_Rings_Odvd__class_Odvd(X5429,X5428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5429),X5427),X5426)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_1784,plain,
! [X5430,X5431,X5432,X5433] :
( ~ class_Rings_Ocomm__semiring__1(X5433)
| ~ c_Rings_Odvd__class_Odvd(X5433,X5432,X5431)
| c_Rings_Odvd__class_Odvd(X5433,X5432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5433),X5430),X5431)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_1785,plain,
! [X4420,X4421,X4422] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4422)
| c_Groups_Oabs__class_Oabs(X4422,c_Groups_Ominus__class_Ominus(X4422,X4421,X4420)) = c_Groups_Oabs__class_Oabs(X4422,c_Groups_Ominus__class_Ominus(X4422,X4420,X4421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
fof(i_0_1786,plain,
! [X4056,X4057,X4058] :
( ~ class_RealVector_Oreal__normed__vector(X4058)
| c_RealVector_Onorm__class_Onorm(X4058,c_Groups_Ominus__class_Ominus(X4058,X4057,X4056)) = c_RealVector_Onorm__class_Onorm(X4058,c_Groups_Ominus__class_Ominus(X4058,X4056,X4057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(i_0_1787,plain,
! [X2815,X2816,X2817] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2817)
| c_RealVector_Onorm__class_Onorm(X2817,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2816),X2815)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2817,X2816)),c_RealVector_Onorm__class_Onorm(X2817,X2815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_1788,plain,
! [X4608,X4609] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4609,X4608)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4609,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4608) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
fof(i_0_1789,plain,
! [X3368,X3369] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3369,X3368),X3369),
inference(variable_rename,[status(thm)],[i_0_1286]) ).
fof(i_0_1790,plain,
! [X3370,X3371] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3371,X3370),X3370),
inference(variable_rename,[status(thm)],[i_0_1287]) ).
fof(i_0_1791,plain,
! [X4296,X4297] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4297,X4296)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4296,X4297),X4297) = X4296 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_1792,plain,
! [X4236,X4237] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4237,X4236)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4236,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4236,X4237)) = X4237 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_1793,plain,
! [X4304,X4305] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4305,X4304)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4305,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4304,X4305)) = X4304 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_1794,plain,
! [X4130,X4131,X4132] :
( ~ class_RealVector_Oreal__algebra__1(X4132)
| c_RealVector_Oof__real(X4132,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4131),X4130)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4132),c_RealVector_Oof__real(X4132,X4131)),c_RealVector_Oof__real(X4132,X4130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__mult])]) ).
fof(i_0_1795,plain,
! [X4984,X4985,X4986,X4987,X4988] :
( ~ class_Orderings_Oord(X4988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4987,X4988),X4986,X4985)
| c_Orderings_Oord__class_Oless__eq(X4988,hAPP(X4986,X4984),hAPP(X4985,X4984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_1796,plain,
! [X4946,X4947,X4948,X4949,X4950] :
( ~ class_Orderings_Oord(X4950)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4949,X4950),X4948,X4947)
| c_Orderings_Oord__class_Oless__eq(X4950,hAPP(X4948,X4946),hAPP(X4947,X4946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_1797,plain,
! [X4212,X4213,X4214] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4214,X4213)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4214,X4212),X4213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_1798,plain,
! [X5179,X5180,X5181] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5181,X5180)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5181,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5180,X5179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_1799,plain,
! [X3194,X3195,X3196] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3196,X3195)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3196,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3195,X3194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_1800,plain,
! [X5182,X5183,X5184] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5184,X5183)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5184,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5182,X5183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_1801,plain,
! [X3197,X3198,X3199] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3199,X3198)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3199,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_1802,plain,
! [X5188,X5189,X5190] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5190,X5189)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5190,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5189,X5188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_1803,plain,
! [X3375,X3376,X3377] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3377,X3376)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3377,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3376,X3375)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_1804,plain,
! [X5185,X5186,X5187] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5187,X5186)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5187,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5185,X5186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_1805,plain,
! [X3378,X3379,X3380] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3380,X3379)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3380,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3378,X3379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_1806,plain,
! [X3936,X3937,X3938] :
( ~ class_RealVector_Oreal__algebra__1(X3938)
| ~ class_RealVector_Oreal__normed__vector(X3938)
| c_RealVector_Oof__real(X3938,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3937,X3936)) = c_Groups_Ominus__class_Ominus(X3938,c_RealVector_Oof__real(X3938,X3937),c_RealVector_Oof__real(X3938,X3936)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Odiff])]) ).
fof(i_0_1807,plain,
! [X4136,X4137,X4138] :
( ~ class_RealVector_Oreal__algebra__1(X4138)
| ~ class_RealVector_Oreal__normed__vector(X4138)
| c_RealVector_Oof__real(X4138,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4137,X4136)) = c_Groups_Oplus__class_Oplus(X4138,c_RealVector_Oof__real(X4138,X4137),c_RealVector_Oof__real(X4138,X4136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Oadd])]) ).
fof(i_0_1808,plain,
! [X4584,X4585] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4585)),X4584)),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_1809,plain,
! [X4196] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4196),X4196))
| X4196 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4196 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4196),X4196)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1288])]) ).
fof(i_0_1810,plain,
! [X3870,X3871,X3872] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3871) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3870)
| X3871 = X3870
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3872) )
& ( X3871 != X3870
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3871) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3870)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3872) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_1811,plain,
! [X4687,X4688] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4688)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4688),X4687)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_1812,plain,
! [X4973,X4974,X4975,X4976] :
( ~ class_Orderings_Opreorder(X4976)
| ~ c_Orderings_Oord__class_Oless__eq(X4976,X4975,X4974)
| ~ c_Orderings_Oord__class_Oless__eq(X4976,X4974,X4973)
| c_Orderings_Oord__class_Oless__eq(X4976,X4975,X4973) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_1813,plain,
! [X4980,X4981,X4982,X4983] :
( ~ class_Orderings_Oorder(X4983)
| ~ c_Orderings_Oord__class_Oless__eq(X4983,X4982,X4981)
| ~ c_Orderings_Oord__class_Oless__eq(X4983,X4980,X4982)
| c_Orderings_Oord__class_Oless__eq(X4983,X4980,X4981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_1814,plain,
! [X5072,X5073,X5074,X5075] :
( ~ class_Orderings_Opreorder(X5075)
| ~ c_Orderings_Oord__class_Oless(X5075,X5074,X5073)
| ~ c_Orderings_Oord__class_Oless__eq(X5075,X5073,X5072)
| c_Orderings_Oord__class_Oless(X5075,X5074,X5072) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_1815,plain,
! [X5064,X5065,X5066,X5067] :
( ~ class_Orderings_Opreorder(X5067)
| ~ c_Orderings_Oord__class_Oless__eq(X5067,X5066,X5065)
| ~ c_Orderings_Oord__class_Oless(X5067,X5065,X5064)
| c_Orderings_Oord__class_Oless(X5067,X5066,X5064) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_1816,plain,
! [X5002,X5003,X5004,X5005] :
( ~ class_Orderings_Opreorder(X5005)
| ~ c_Orderings_Oord__class_Oless(X5005,X5004,X5003)
| ~ c_Orderings_Oord__class_Oless(X5005,X5003,X5002)
| c_Orderings_Oord__class_Oless(X5005,X5004,X5002) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_1817,plain,
! [X5068,X5069,X5070,X5071] :
( ~ class_Orderings_Oorder(X5071)
| ~ c_Orderings_Oord__class_Oless(X5071,X5070,X5069)
| ~ c_Orderings_Oord__class_Oless__eq(X5071,X5068,X5070)
| c_Orderings_Oord__class_Oless(X5071,X5068,X5069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_1818,plain,
! [X5060,X5061,X5062,X5063] :
( ~ class_Orderings_Oorder(X5063)
| ~ c_Orderings_Oord__class_Oless__eq(X5063,X5062,X5061)
| ~ c_Orderings_Oord__class_Oless(X5063,X5060,X5062)
| c_Orderings_Oord__class_Oless(X5063,X5060,X5061) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_1819,plain,
! [X4998,X4999,X5000,X5001] :
( ~ class_Orderings_Oorder(X5001)
| ~ c_Orderings_Oord__class_Oless(X5001,X5000,X4999)
| ~ c_Orderings_Oord__class_Oless(X5001,X4998,X5000)
| c_Orderings_Oord__class_Oless(X5001,X4998,X4999) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_1820,plain,
! [X5273,X5274,X5275] :
( ~ class_Groups_Oab__group__add(X5275)
| c_Groups_Ominus__class_Ominus(X5275,c_Groups_Ouminus__class_Ouminus(X5275,X5274),c_Groups_Ouminus__class_Ouminus(X5275,X5273)) = c_Groups_Ouminus__class_Ouminus(X5275,c_Groups_Ominus__class_Ominus(X5275,X5274,X5273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
fof(i_0_1821,plain,
! [X4053,X4054,X4055] :
( ~ class_Groups_Oab__group__add(X4055)
| c_Groups_Ouminus__class_Ouminus(X4055,c_Groups_Oplus__class_Oplus(X4055,X4054,X4053)) = c_Groups_Oplus__class_Oplus(X4055,c_Groups_Ouminus__class_Ouminus(X4055,X4054),c_Groups_Ouminus__class_Ouminus(X4055,X4053)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_1822,plain,
! [X4050,X4051,X4052] :
( ~ class_Groups_Ogroup__add(X4052)
| c_Groups_Ouminus__class_Ouminus(X4052,c_Groups_Oplus__class_Oplus(X4052,X4051,X4050)) = c_Groups_Oplus__class_Oplus(X4052,c_Groups_Ouminus__class_Ouminus(X4052,X4050),c_Groups_Ouminus__class_Ouminus(X4052,X4051)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_1823,plain,
! [X5250] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5250,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5250)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(i_0_1824,plain,
! [X2857,X2858,X2859] :
( ~ class_Rings_Odivision__ring(X2859)
| X2858 = c_Groups_Ozero__class_Ozero(X2859)
| c_Rings_Oinverse__class_Oinverse(X2859,hAPP(hAPP(c_Power_Opower__class_Opower(X2859),X2858),X2857)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2859),c_Rings_Oinverse__class_Oinverse(X2859,X2858)),X2857) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse])]) ).
fof(i_0_1825,plain,
! [X3933,X3934,X3935] :
( ~ class_RealVector_Oreal__algebra__1(X3935)
| c_RealVector_Oof__real(X3935,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3934,X3933)) = c_Groups_Ominus__class_Ominus(X3935,c_RealVector_Oof__real(X3935,X3934),c_RealVector_Oof__real(X3935,X3933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__diff])]) ).
fof(i_0_1826,plain,
! [X4133,X4134,X4135] :
( ~ class_RealVector_Oreal__algebra__1(X4135)
| c_RealVector_Oof__real(X4135,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4134,X4133)) = c_Groups_Oplus__class_Oplus(X4135,c_RealVector_Oof__real(X4135,X4134),c_RealVector_Oof__real(X4135,X4133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__add])]) ).
fof(i_0_1827,plain,
! [X5287,X5288,X5289] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5289,c_Groups_Ouminus__class_Ouminus(X5289,X5288),c_Groups_Ouminus__class_Ouminus(X5289,X5287))
| c_Orderings_Oord__class_Oless__eq(X5289,X5287,X5288)
| ~ class_Lattices_Oboolean__algebra(X5289) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5289,X5287,X5288)
| c_Orderings_Oord__class_Oless__eq(X5289,c_Groups_Ouminus__class_Ouminus(X5289,X5288),c_Groups_Ouminus__class_Ouminus(X5289,X5287))
| ~ class_Lattices_Oboolean__algebra(X5289) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_1828,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_Groups_Oordered__ab__group__add(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_Groups_Oordered__ab__group__add(X3982) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
fof(i_0_1829,plain,
! [X3986,X3987,X3988] :
( ( ~ c_Orderings_Oord__class_Oless(X3988,c_Groups_Ouminus__class_Ouminus(X3988,X3987),c_Groups_Ouminus__class_Ouminus(X3988,X3986))
| c_Orderings_Oord__class_Oless(X3988,X3986,X3987)
| ~ class_Groups_Oordered__ab__group__add(X3988) )
& ( ~ c_Orderings_Oord__class_Oless(X3988,X3986,X3987)
| c_Orderings_Oord__class_Oless(X3988,c_Groups_Ouminus__class_Ouminus(X3988,X3987),c_Groups_Ouminus__class_Ouminus(X3988,X3986))
| ~ class_Groups_Oordered__ab__group__add(X3988) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_1830,plain,
! [X4035,X4036,X4037] :
( ~ class_RealVector_Oreal__normed__algebra(X4037)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),c_Groups_Ouminus__class_Ouminus(X4037,X4036)),X4035) = c_Groups_Ouminus__class_Ouminus(X4037,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4036),X4035)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_1831,plain,
! [X4032,X4033,X4034] :
( ~ class_RealVector_Oreal__normed__algebra(X4034)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4034),c_Groups_Ouminus__class_Ouminus(X4034,X4033)),X4032) = c_Groups_Ouminus__class_Ouminus(X4034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4034),X4033),X4032)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_1832,plain,
! [X4468,X4469,X4470] :
( ~ class_Rings_Olinordered__idom(X4470)
| c_Groups_Oabs__class_Oabs(X4470,hAPP(hAPP(c_Power_Opower__class_Opower(X4470),X4469),X4468)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4470),c_Groups_Oabs__class_Oabs(X4470,X4469)),X4468) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_1833,plain,
! [X4014,X4015,X4016] :
( ~ class_Rings_Oring(X4016)
| c_Groups_Ouminus__class_Ouminus(X4016,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4016),X4015),X4014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4016),c_Groups_Ouminus__class_Ouminus(X4016,X4015)),X4014) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_1834,plain,
! [X2882,X2883,X2884] :
( ~ class_Rings_Odivision__ring__inverse__zero(X2884)
| c_Rings_Oinverse__class_Oinverse(X2884,hAPP(hAPP(c_Power_Opower__class_Opower(X2884),X2883),X2882)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2884),c_Rings_Oinverse__class_Oinverse(X2884,X2883)),X2882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inverse])]) ).
fof(i_0_1835,plain,
! [X4742,X4743,X4744] :
( ~ class_Rings_Ocomm__ring(X4744)
| c_Polynomial_Osmult(X4744,X4743,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4744),X4742)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4744),c_Polynomial_Osmult(X4744,X4743,X4742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__right])]) ).
fof(i_0_1836,plain,
! [X4293,X4294,X4295] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4294,X4295) != X4293
| X4294 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4293,X4295)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4295,X4294) )
& ( X4294 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4293,X4295)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4294,X4295) = X4293
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4295,X4294) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_1837,plain,
! [X2811,X2812,X2813] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2813)
| c_RealVector_Onorm__class_Onorm(X2813,hAPP(hAPP(c_Power_Opower__class_Opower(X2813),X2812),X2811)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2813,X2812)),X2811) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_1838,plain,
! [X4047,X4048,X4049] :
( ~ class_Groups_Ogroup__add(X4049)
| c_Groups_Oplus__class_Oplus(X4049,X4048,c_Groups_Oplus__class_Oplus(X4049,c_Groups_Ouminus__class_Ouminus(X4049,X4048),X4047)) = X4047 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_1839,plain,
! [X4651,X4652,X4653] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4653,X4652)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4652,X4651)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4653,X4651) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_1840,plain,
! [X3154,X3155,X3156] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3156,X3155)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3155,X3154)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3156,X3154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_1841,plain,
! [X3237,X3238,X3239] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3239,X3238)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3238,X3237)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3239,X3237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_1842,plain,
! [X5217,X5218,X5219] :
( ~ class_Rings_Olinordered__idom(X5219)
| ~ c_Polynomial_Opos__poly(X5219,X5218)
| ~ c_Polynomial_Opos__poly(X5219,X5217)
| c_Polynomial_Opos__poly(X5219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5219)),X5218),X5217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__mult])]) ).
fof(i_0_1843,plain,
! [X5215,X5216] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5216),X5215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5216)),c_RealDef_Oreal(tc_Nat_Onat,X5215)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
fof(i_0_1844,plain,
! [X4142,X4143,X4144] :
( ~ class_RealVector_Oreal__algebra__1(X4144)
| c_RealVector_Oof__real(X4144,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X4143),X4142)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4144),c_RealVector_Oof__real(X4144,X4143)),X4142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__power])]) ).
fof(i_0_1845,plain,
! [X4771,X4772,X4773] :
( ~ class_Rings_Ocomm__ring(X4773)
| hAPP(c_Polynomial_Opoly(X4773,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4773),X4772)),X4771) = c_Groups_Ouminus__class_Ouminus(X4773,hAPP(c_Polynomial_Opoly(X4773,X4772),X4771)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_1846,plain,
! [X4508,X4509,X4510] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4510)
| ~ c_Orderings_Oord__class_Oless__eq(X4510,c_Groups_Oabs__class_Oabs(X4510,X4509),X4508)
| c_Orderings_Oord__class_Oless__eq(X4510,c_Groups_Ouminus__class_Ouminus(X4510,X4509),X4508) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).
fof(i_0_1847,plain,
! [X3977,X3978,X3979] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3979,c_Groups_Ouminus__class_Ouminus(X3979,X3978),X3977)
| c_Orderings_Oord__class_Oless__eq(X3979,c_Groups_Ouminus__class_Ouminus(X3979,X3977),X3978)
| ~ class_Groups_Oordered__ab__group__add(X3979) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3979,c_Groups_Ouminus__class_Ouminus(X3979,X3977),X3978)
| c_Orderings_Oord__class_Oless__eq(X3979,c_Groups_Ouminus__class_Ouminus(X3979,X3978),X3977)
| ~ class_Groups_Oordered__ab__group__add(X3979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_1848,plain,
! [X3989,X3990,X3991] :
( ( ~ c_Orderings_Oord__class_Oless(X3991,c_Groups_Ouminus__class_Ouminus(X3991,X3990),X3989)
| c_Orderings_Oord__class_Oless(X3991,c_Groups_Ouminus__class_Ouminus(X3991,X3989),X3990)
| ~ class_Groups_Oordered__ab__group__add(X3991) )
& ( ~ c_Orderings_Oord__class_Oless(X3991,c_Groups_Ouminus__class_Ouminus(X3991,X3989),X3990)
| c_Orderings_Oord__class_Oless(X3991,c_Groups_Ouminus__class_Ouminus(X3991,X3990),X3989)
| ~ class_Groups_Oordered__ab__group__add(X3991) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_1849,plain,
! [X3974,X3975,X3976] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3976,X3975,c_Groups_Ouminus__class_Ouminus(X3976,X3974))
| c_Orderings_Oord__class_Oless__eq(X3976,X3974,c_Groups_Ouminus__class_Ouminus(X3976,X3975))
| ~ class_Groups_Oordered__ab__group__add(X3976) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3976,X3974,c_Groups_Ouminus__class_Ouminus(X3976,X3975))
| c_Orderings_Oord__class_Oless__eq(X3976,X3975,c_Groups_Ouminus__class_Ouminus(X3976,X3974))
| ~ class_Groups_Oordered__ab__group__add(X3976) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_1850,plain,
! [X3992,X3993,X3994] :
( ( ~ c_Orderings_Oord__class_Oless(X3994,X3993,c_Groups_Ouminus__class_Ouminus(X3994,X3992))
| c_Orderings_Oord__class_Oless(X3994,X3992,c_Groups_Ouminus__class_Ouminus(X3994,X3993))
| ~ class_Groups_Oordered__ab__group__add(X3994) )
& ( ~ c_Orderings_Oord__class_Oless(X3994,X3992,c_Groups_Ouminus__class_Ouminus(X3994,X3993))
| c_Orderings_Oord__class_Oless(X3994,X3993,c_Groups_Ouminus__class_Ouminus(X3994,X3992))
| ~ class_Groups_Oordered__ab__group__add(X3994) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_1851,plain,
! [X5209,X5210] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5210,X5209)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5210),c_RealDef_Oreal(tc_Nat_Onat,X5209)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_1852,plain,
! [X4632,X4633] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4633,X4632)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4633),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4632)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_1853,plain,
! [X4810,X4811,X4812] :
( ~ class_Groups_Oab__group__add(X4812)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4812),c_Polynomial_Omonom(X4812,X4811,X4810)) = c_Polynomial_Omonom(X4812,c_Groups_Ouminus__class_Ouminus(X4812,X4811),X4810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__monom])]) ).
fof(i_0_1854,plain,
! [X4799,X4800,X4801] :
( ~ class_Rings_Ocomm__ring(X4801)
| c_Polynomial_Osmult(X4801,c_Groups_Ouminus__class_Ouminus(X4801,X4800),X4799) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4801),c_Polynomial_Osmult(X4801,X4800,X4799)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__left])]) ).
fof(i_0_1855,plain,
! [X5302,X5303,X5304] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5304)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5304),X5303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5304),X5303),X5302)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5304),X5303),X5302) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_1856,plain,
! [X4563] : 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,X4563))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(i_0_1857,plain,
! [X4272,X4273] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4273,X4272)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4272,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4273,X4272)) = X4273 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1289])]) ).
fof(i_0_1858,plain,
! [X3561,X3562] :
( ~ class_Fields_Olinordered__field(X3562)
| ~ c_Orderings_Oord__class_Oless(X3562,c_Groups_Ozero__class_Ozero(X3562),c_Rings_Oinverse__class_Oinverse(X3562,X3561))
| X3561 = c_Groups_Ozero__class_Ozero(X3562)
| c_Orderings_Oord__class_Oless(X3562,c_Groups_Ozero__class_Ozero(X3562),X3561) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).
fof(i_0_1859,plain,
! [X3551,X3552] :
( ~ class_Fields_Olinordered__field(X3552)
| ~ c_Orderings_Oord__class_Oless(X3552,c_Rings_Oinverse__class_Oinverse(X3552,X3551),c_Groups_Ozero__class_Ozero(X3552))
| X3551 = c_Groups_Ozero__class_Ozero(X3552)
| c_Orderings_Oord__class_Oless(X3552,X3551,c_Groups_Ozero__class_Ozero(X3552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).
fof(i_0_1860,plain,
! [X5225,X5226] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5226),c_RealDef_Oreal(tc_Nat_Onat,X5225))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5226,X5225) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5226,X5225)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5226),c_RealDef_Oreal(tc_Nat_Onat,X5225)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_1861,plain,
! [X5201,X5202] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5202),c_RealDef_Oreal(tc_Nat_Onat,X5201))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5202,X5201) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5202,X5201)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5202),c_RealDef_Oreal(tc_Nat_Onat,X5201)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_1862,plain,
! [X4071,X4072] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4072,c_Groups_Ouminus__class_Ouminus(X4072,X4071),c_Groups_Ozero__class_Ozero(X4072))
| c_Orderings_Oord__class_Oless__eq(X4072,c_Groups_Ozero__class_Ozero(X4072),X4071)
| ~ class_Groups_Oordered__ab__group__add(X4072) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4072,c_Groups_Ozero__class_Ozero(X4072),X4071)
| c_Orderings_Oord__class_Oless__eq(X4072,c_Groups_Ouminus__class_Ouminus(X4072,X4071),c_Groups_Ozero__class_Ozero(X4072))
| ~ class_Groups_Oordered__ab__group__add(X4072) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_1863,plain,
! [X4081,X4082] :
( ( ~ c_Orderings_Oord__class_Oless(X4082,c_Groups_Ouminus__class_Ouminus(X4082,X4081),c_Groups_Ozero__class_Ozero(X4082))
| c_Orderings_Oord__class_Oless(X4082,c_Groups_Ozero__class_Ozero(X4082),X4081)
| ~ class_Groups_Oordered__ab__group__add(X4082) )
& ( ~ c_Orderings_Oord__class_Oless(X4082,c_Groups_Ozero__class_Ozero(X4082),X4081)
| c_Orderings_Oord__class_Oless(X4082,c_Groups_Ouminus__class_Ouminus(X4082,X4081),c_Groups_Ozero__class_Ozero(X4082))
| ~ class_Groups_Oordered__ab__group__add(X4082) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_1864,plain,
! [X3543,X3544] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3544,c_Groups_Ozero__class_Ozero(X3544),c_Rings_Oinverse__class_Oinverse(X3544,X3543))
| c_Orderings_Oord__class_Oless__eq(X3544,c_Groups_Ozero__class_Ozero(X3544),X3543)
| ~ class_Fields_Olinordered__field__inverse__zero(X3544) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3544,c_Groups_Ozero__class_Ozero(X3544),X3543)
| c_Orderings_Oord__class_Oless__eq(X3544,c_Groups_Ozero__class_Ozero(X3544),c_Rings_Oinverse__class_Oinverse(X3544,X3543))
| ~ class_Fields_Olinordered__field__inverse__zero(X3544) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative])])]) ).
fof(i_0_1865,plain,
! [X5321,X5322] :
( ( ~ c_Orderings_Oord__class_Oless(X5322,c_Groups_Ozero__class_Ozero(X5322),c_Groups_Osgn__class_Osgn(X5322,X5321))
| c_Orderings_Oord__class_Oless(X5322,c_Groups_Ozero__class_Ozero(X5322),X5321)
| ~ class_Rings_Olinordered__idom(X5322) )
& ( ~ c_Orderings_Oord__class_Oless(X5322,c_Groups_Ozero__class_Ozero(X5322),X5321)
| c_Orderings_Oord__class_Oless(X5322,c_Groups_Ozero__class_Ozero(X5322),c_Groups_Osgn__class_Osgn(X5322,X5321))
| ~ class_Rings_Olinordered__idom(X5322) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).
fof(i_0_1866,plain,
! [X3567,X3568] :
( ( ~ c_Orderings_Oord__class_Oless(X3568,c_Groups_Ozero__class_Ozero(X3568),c_Rings_Oinverse__class_Oinverse(X3568,X3567))
| c_Orderings_Oord__class_Oless(X3568,c_Groups_Ozero__class_Ozero(X3568),X3567)
| ~ class_Fields_Olinordered__field__inverse__zero(X3568) )
& ( ~ c_Orderings_Oord__class_Oless(X3568,c_Groups_Ozero__class_Ozero(X3568),X3567)
| c_Orderings_Oord__class_Oless(X3568,c_Groups_Ozero__class_Ozero(X3568),c_Rings_Oinverse__class_Oinverse(X3568,X3567))
| ~ class_Fields_Olinordered__field__inverse__zero(X3568) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).
fof(i_0_1867,plain,
! [X3541,X3542] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3542,c_Rings_Oinverse__class_Oinverse(X3542,X3541),c_Groups_Ozero__class_Ozero(X3542))
| c_Orderings_Oord__class_Oless__eq(X3542,X3541,c_Groups_Ozero__class_Ozero(X3542))
| ~ class_Fields_Olinordered__field__inverse__zero(X3542) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3542,X3541,c_Groups_Ozero__class_Ozero(X3542))
| c_Orderings_Oord__class_Oless__eq(X3542,c_Rings_Oinverse__class_Oinverse(X3542,X3541),c_Groups_Ozero__class_Ozero(X3542))
| ~ class_Fields_Olinordered__field__inverse__zero(X3542) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive])])]) ).
fof(i_0_1868,plain,
! [X5319,X5320] :
( ( ~ c_Orderings_Oord__class_Oless(X5320,c_Groups_Osgn__class_Osgn(X5320,X5319),c_Groups_Ozero__class_Ozero(X5320))
| c_Orderings_Oord__class_Oless(X5320,X5319,c_Groups_Ozero__class_Ozero(X5320))
| ~ class_Rings_Olinordered__idom(X5320) )
& ( ~ c_Orderings_Oord__class_Oless(X5320,X5319,c_Groups_Ozero__class_Ozero(X5320))
| c_Orderings_Oord__class_Oless(X5320,c_Groups_Osgn__class_Osgn(X5320,X5319),c_Groups_Ozero__class_Ozero(X5320))
| ~ class_Rings_Olinordered__idom(X5320) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).
fof(i_0_1869,plain,
! [X3565,X3566] :
( ( ~ c_Orderings_Oord__class_Oless(X3566,c_Rings_Oinverse__class_Oinverse(X3566,X3565),c_Groups_Ozero__class_Ozero(X3566))
| c_Orderings_Oord__class_Oless(X3566,X3565,c_Groups_Ozero__class_Ozero(X3566))
| ~ class_Fields_Olinordered__field__inverse__zero(X3566) )
& ( ~ c_Orderings_Oord__class_Oless(X3566,X3565,c_Groups_Ozero__class_Ozero(X3566))
| c_Orderings_Oord__class_Oless(X3566,c_Rings_Oinverse__class_Oinverse(X3566,X3565),c_Groups_Ozero__class_Ozero(X3566))
| ~ class_Fields_Olinordered__field__inverse__zero(X3566) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).
fof(i_0_1870,plain,
! [X4075,X4076] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4076,c_Groups_Ozero__class_Ozero(X4076),c_Groups_Ouminus__class_Ouminus(X4076,X4075))
| c_Orderings_Oord__class_Oless__eq(X4076,X4075,c_Groups_Ozero__class_Ozero(X4076))
| ~ class_Groups_Oordered__ab__group__add(X4076) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4076,X4075,c_Groups_Ozero__class_Ozero(X4076))
| c_Orderings_Oord__class_Oless__eq(X4076,c_Groups_Ozero__class_Ozero(X4076),c_Groups_Ouminus__class_Ouminus(X4076,X4075))
| ~ class_Groups_Oordered__ab__group__add(X4076) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_1871,plain,
! [X4083,X4084] :
( ( ~ c_Orderings_Oord__class_Oless(X4084,c_Groups_Ozero__class_Ozero(X4084),c_Groups_Ouminus__class_Ouminus(X4084,X4083))
| c_Orderings_Oord__class_Oless(X4084,X4083,c_Groups_Ozero__class_Ozero(X4084))
| ~ class_Groups_Oordered__ab__group__add(X4084) )
& ( ~ c_Orderings_Oord__class_Oless(X4084,X4083,c_Groups_Ozero__class_Ozero(X4084))
| c_Orderings_Oord__class_Oless(X4084,c_Groups_Ozero__class_Ozero(X4084),c_Groups_Ouminus__class_Ouminus(X4084,X4083))
| ~ class_Groups_Oordered__ab__group__add(X4084) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_1872,plain,
! [X5112,X5113,X5114] :
( ( c_Orderings_Oord__class_Oless__eq(X5114,X5113,X5112)
| ~ c_Orderings_Oord__class_Oless(X5114,X5113,X5112)
| ~ class_Orderings_Opreorder(X5114) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5114,X5112,X5113)
| ~ c_Orderings_Oord__class_Oless(X5114,X5113,X5112)
| ~ class_Orderings_Opreorder(X5114) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5114,X5113,X5112)
| c_Orderings_Oord__class_Oless__eq(X5114,X5112,X5113)
| c_Orderings_Oord__class_Oless(X5114,X5113,X5112)
| ~ class_Orderings_Opreorder(X5114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])])]) ).
fof(i_0_1873,plain,
! [X4029,X4030,X4031] :
( ~ class_RealVector_Oreal__normed__algebra(X4031)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4030),c_Groups_Ouminus__class_Ouminus(X4031,X4029)) = c_Groups_Ouminus__class_Ouminus(X4031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4030),X4029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_1874,plain,
! [X4026,X4027,X4028] :
( ~ class_RealVector_Oreal__normed__algebra(X4028)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4028),X4027),c_Groups_Ouminus__class_Ouminus(X4028,X4026)) = c_Groups_Ouminus__class_Ouminus(X4028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4028),X4027),X4026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_1875,plain,
! [X4011,X4012,X4013] :
( ~ class_Rings_Oring(X4013)
| c_Groups_Ouminus__class_Ouminus(X4013,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4013),X4012),X4011)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4013),X4012),c_Groups_Ouminus__class_Ouminus(X4013,X4011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_1876,plain,
! [X5290,X5291,X5292] :
( ~ class_Lattices_Oboolean__algebra(X5292)
| ~ c_Orderings_Oord__class_Oless__eq(X5292,X5291,X5290)
| c_Orderings_Oord__class_Oless__eq(X5292,c_Groups_Ouminus__class_Ouminus(X5292,X5290),c_Groups_Ouminus__class_Ouminus(X5292,X5291)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_1877,plain,
! [X3983,X3984,X3985] :
( ~ class_Groups_Oordered__ab__group__add(X3985)
| ~ c_Orderings_Oord__class_Oless__eq(X3985,X3984,X3983)
| c_Orderings_Oord__class_Oless__eq(X3985,c_Groups_Ouminus__class_Ouminus(X3985,X3983),c_Groups_Ouminus__class_Ouminus(X3985,X3984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
fof(i_0_1878,plain,
! [X3645] :
( ~ class_Rings_Olinordered__semidom(X3645)
| c_Orderings_Oord__class_Oless(X3645,c_Groups_Ozero__class_Ozero(X3645),c_Groups_Oplus__class_Oplus(X3645,c_Groups_Oone__class_Oone(X3645),c_Groups_Oone__class_Oone(X3645))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_1879,plain,
! [X5253] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5253,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5253))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(i_0_1880,plain,
! [X4044,X4045,X4046] :
( ~ class_Groups_Ogroup__add(X4046)
| c_Groups_Oplus__class_Oplus(X4046,c_Groups_Ouminus__class_Ouminus(X4046,X4045),c_Groups_Oplus__class_Oplus(X4046,X4045,X4044)) = X4044 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_1881,plain,
! [X4069,X4070] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4070,c_Groups_Ouminus__class_Ouminus(X4070,X4069),X4069)
| c_Orderings_Oord__class_Oless__eq(X4070,c_Groups_Ozero__class_Ozero(X4070),X4069)
| ~ class_Groups_Olinordered__ab__group__add(X4070) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4070,c_Groups_Ozero__class_Ozero(X4070),X4069)
| c_Orderings_Oord__class_Oless__eq(X4070,c_Groups_Ouminus__class_Ouminus(X4070,X4069),X4069)
| ~ class_Groups_Olinordered__ab__group__add(X4070) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_1882,plain,
! [X4079,X4080] :
( ( ~ c_Orderings_Oord__class_Oless(X4080,c_Groups_Ouminus__class_Ouminus(X4080,X4079),X4079)
| c_Orderings_Oord__class_Oless(X4080,c_Groups_Ozero__class_Ozero(X4080),X4079)
| ~ class_Groups_Olinordered__ab__group__add(X4080) )
& ( ~ c_Orderings_Oord__class_Oless(X4080,c_Groups_Ozero__class_Ozero(X4080),X4079)
| c_Orderings_Oord__class_Oless(X4080,c_Groups_Ouminus__class_Ouminus(X4080,X4079),X4079)
| ~ class_Groups_Olinordered__ab__group__add(X4080) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_1883,plain,
! [X4073,X4074] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4074,X4073,c_Groups_Ouminus__class_Ouminus(X4074,X4073))
| c_Orderings_Oord__class_Oless__eq(X4074,X4073,c_Groups_Ozero__class_Ozero(X4074))
| ~ class_Groups_Olinordered__ab__group__add(X4074) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4074,X4073,c_Groups_Ozero__class_Ozero(X4074))
| c_Orderings_Oord__class_Oless__eq(X4074,X4073,c_Groups_Ouminus__class_Ouminus(X4074,X4073))
| ~ class_Groups_Olinordered__ab__group__add(X4074) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_1884,plain,
! [X4077,X4078] :
( ( ~ c_Orderings_Oord__class_Oless(X4078,X4077,c_Groups_Ouminus__class_Ouminus(X4078,X4077))
| c_Orderings_Oord__class_Oless(X4078,X4077,c_Groups_Ozero__class_Ozero(X4078))
| ~ class_Rings_Olinordered__idom(X4078) )
& ( ~ c_Orderings_Oord__class_Oless(X4078,X4077,c_Groups_Ozero__class_Ozero(X4078))
| c_Orderings_Oord__class_Oless(X4078,X4077,c_Groups_Ouminus__class_Ouminus(X4078,X4077))
| ~ class_Rings_Olinordered__idom(X4078) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_1885,plain,
! [X4413,X4414] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4414)),X4413) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4414),X4413)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_1886,plain,
! [X4147,X4148] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X4148)),X4147) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X4148),X4147)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__power]) ).
fof(i_0_1887,plain,
! [X5205,X5206] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5206)),X5205) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5206),X5205)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_1888,plain,
! [X5207,X5208] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5208),X5207)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5208)),X5207),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
fof(i_0_1889,plain,
! [X3243,X3244,X3245] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3244,X3245)
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| X3245 = X3244
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3245,X3244) )
& ( ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| X3245 = X3244
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3245,X3244) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3244,X3245)
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3245,X3244) )
& ( ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3245,X3244) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3244,X3245)
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| X3245 = X3244
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245)) )
& ( ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| X3245 = X3244
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3244,X3245)
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245)) )
& ( ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245))
| ~ hBOOL(hAPP(hAPP(X3243,X3244),X3245)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_1890,plain,
! [X3559,X3560] :
( ~ class_Fields_Olinordered__field(X3560)
| ~ c_Orderings_Oord__class_Oless(X3560,X3559,c_Groups_Ozero__class_Ozero(X3560))
| c_Orderings_Oord__class_Oless(X3560,c_Rings_Oinverse__class_Oinverse(X3560,X3559),c_Groups_Ozero__class_Ozero(X3560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).
fof(i_0_1891,plain,
! [X3563,X3564] :
( ~ class_Fields_Olinordered__field(X3564)
| ~ c_Orderings_Oord__class_Oless(X3564,c_Groups_Ozero__class_Ozero(X3564),X3563)
| c_Orderings_Oord__class_Oless(X3564,c_Groups_Ozero__class_Ozero(X3564),c_Rings_Oinverse__class_Oinverse(X3564,X3563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).
fof(i_0_1892,plain,
! [X4860,X4861,X4862,X4863] :
( ~ class_Rings_Ocomm__semiring__0(X4863)
| c_Polynomial_Osmult(X4863,X4862,X4861) != c_Polynomial_OpCons(X4863,X4860,X4861)
| X4861 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
fof(i_0_1893,plain,
! [X4457,X4458] :
( ~ class_Rings_Olinordered__idom(X4458)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4458),c_Groups_Oabs__class_Oabs(X4458,X4457)),c_Groups_Oabs__class_Oabs(X4458,X4457)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4458),X4457),X4457) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_1894,plain,
! [X4020,X4021,X4022] :
( ~ class_Rings_Oring(X4022)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4022),c_Groups_Ouminus__class_Ouminus(X4022,X4021)),c_Groups_Ouminus__class_Ouminus(X4022,X4020)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4022),X4021),X4020) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_1895,plain,
! [X4017,X4018,X4019] :
( ~ class_Rings_Oring(X4019)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4019),c_Groups_Ouminus__class_Ouminus(X4019,X4018)),X4017) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4019),X4018),c_Groups_Ouminus__class_Ouminus(X4019,X4017)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_1896,plain,
! [X5370,X5371,X5372] :
( ( ~ c_Rings_Odvd__class_Odvd(X5372,c_Groups_Ouminus__class_Ouminus(X5372,X5371),X5370)
| c_Rings_Odvd__class_Odvd(X5372,X5371,X5370)
| ~ class_Rings_Ocomm__ring__1(X5372) )
& ( ~ c_Rings_Odvd__class_Odvd(X5372,X5371,X5370)
| c_Rings_Odvd__class_Odvd(X5372,c_Groups_Ouminus__class_Ouminus(X5372,X5371),X5370)
| ~ class_Rings_Ocomm__ring__1(X5372) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_1897,plain,
! [X4447,X4448,X4449] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4449)
| ~ c_Orderings_Oord__class_Oless__eq(X4449,c_Groups_Oabs__class_Oabs(X4449,X4448),X4447)
| c_Orderings_Oord__class_Oless__eq(X4449,X4448,X4447) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_1898,plain,
! [X5367,X5368,X5369] :
( ( ~ c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Ouminus__class_Ouminus(X5369,X5367))
| c_Rings_Odvd__class_Odvd(X5369,X5368,X5367)
| ~ class_Rings_Ocomm__ring__1(X5369) )
& ( ~ c_Rings_Odvd__class_Odvd(X5369,X5368,X5367)
| c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Ouminus__class_Ouminus(X5369,X5367))
| ~ class_Rings_Ocomm__ring__1(X5369) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_1899,plain,
! [X4023,X4024,X4025] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)
| X4024 = X4023
| X4024 = c_Groups_Ouminus__class_Ouminus(X4025,X4023)
| ~ class_Rings_Oidom(X4025) )
& ( X4024 != X4023
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)
| ~ class_Rings_Oidom(X4025) )
& ( X4024 != c_Groups_Ouminus__class_Ouminus(X4025,X4023)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)
| ~ class_Rings_Oidom(X4025) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_1900,plain,
! [X5220,X5221,X5222] :
( ~ class_Rings_Olinordered__idom(X5222)
| ~ c_Polynomial_Opos__poly(X5222,X5221)
| ~ c_Polynomial_Opos__poly(X5222,X5220)
| c_Polynomial_Opos__poly(X5222,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5222),X5221,X5220)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])]) ).
fof(i_0_1901,plain,
! [X3921,X3922,X3923,X3924,X3925] :
( ( X3924 != X3923
| X3922 = X3921
| c_Groups_Ominus__class_Ominus(X3925,X3924,X3923) != c_Groups_Ominus__class_Ominus(X3925,X3922,X3921)
| ~ class_Groups_Oab__group__add(X3925) )
& ( X3922 != X3921
| X3924 = X3923
| c_Groups_Ominus__class_Ominus(X3925,X3924,X3923) != c_Groups_Ominus__class_Ominus(X3925,X3922,X3921)
| ~ class_Groups_Oab__group__add(X3925) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_1902,plain,
! [X5237,X5238] :
( X5238 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5238))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5238),X5237)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5238)),X5237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_1903,plain,
! [X5085,X5086,X5087] :
( ( c_Orderings_Oord__class_Oless(X5087,X5086,X5085)
| X5086 = X5085
| ~ c_Orderings_Oord__class_Oless__eq(X5087,X5086,X5085)
| ~ class_Orderings_Olinorder(X5087) )
& ( X5086 != X5085
| ~ c_Orderings_Oord__class_Oless(X5087,X5086,X5085)
| ~ c_Orderings_Oord__class_Oless__eq(X5087,X5086,X5085)
| ~ class_Orderings_Olinorder(X5087) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1291])])]) ).
fof(i_0_1904,plain,
! [X3909,X3910,X3911] :
( ~ class_Groups_Oab__group__add(X3911)
| c_Groups_Ouminus__class_Ouminus(X3911,c_Groups_Ominus__class_Ominus(X3911,X3910,X3909)) = c_Groups_Ominus__class_Ominus(X3911,X3909,X3910) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_1905,plain,
! [X4977,X4978,X4979] :
( ~ class_Orderings_Oorder(X4979)
| ~ c_Orderings_Oord__class_Oless__eq(X4979,X4978,X4977)
| ~ c_Orderings_Oord__class_Oless__eq(X4979,X4977,X4978)
| X4977 = X4978 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_1906,plain,
! [X4970,X4971,X4972] :
( ~ class_Orderings_Oorder(X4972)
| ~ c_Orderings_Oord__class_Oless__eq(X4972,X4971,X4970)
| ~ c_Orderings_Oord__class_Oless__eq(X4972,X4970,X4971)
| X4971 = X4970 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_1907,plain,
! [X4951,X4952,X4953] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4953,X4951,X4952)
| X4951 = X4952
| ~ c_Orderings_Oord__class_Oless__eq(X4953,X4952,X4951)
| ~ class_Orderings_Oorder(X4953) )
& ( X4951 != X4952
| c_Orderings_Oord__class_Oless__eq(X4953,X4951,X4952)
| ~ c_Orderings_Oord__class_Oless__eq(X4953,X4952,X4951)
| ~ class_Orderings_Oorder(X4953) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_1908,plain,
! [X4940,X4941,X4942] :
( ( c_Orderings_Oord__class_Oless__eq(X4942,X4941,X4940)
| X4941 != X4940
| ~ class_Orderings_Oorder(X4942) )
& ( c_Orderings_Oord__class_Oless__eq(X4942,X4940,X4941)
| X4941 != X4940
| ~ class_Orderings_Oorder(X4942) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4942,X4941,X4940)
| ~ c_Orderings_Oord__class_Oless__eq(X4942,X4940,X4941)
| X4941 = X4940
| ~ class_Orderings_Oorder(X4942) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_1909,plain,
! [X5239] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5239))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5239) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5239)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5239)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_1910,plain,
! [X3539,X3540] :
( ~ class_Rings_Olinordered__semidom(X3540)
| c_Orderings_Oord__class_Oless(X3540,X3539,c_Groups_Oplus__class_Oplus(X3540,X3539,c_Groups_Oone__class_Oone(X3540))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_1911,plain,
! [X4733,X4734,X4735,X4736,X4737] :
( ( X4736 = X4734
| c_Polynomial_OpCons(X4737,X4736,X4735) != c_Polynomial_OpCons(X4737,X4734,X4733)
| ~ class_Groups_Ozero(X4737) )
& ( X4735 = X4733
| c_Polynomial_OpCons(X4737,X4736,X4735) != c_Polynomial_OpCons(X4737,X4734,X4733)
| ~ class_Groups_Ozero(X4737) )
& ( X4736 != X4734
| X4735 != X4733
| c_Polynomial_OpCons(X4737,X4736,X4735) = c_Polynomial_OpCons(X4737,X4734,X4733)
| ~ class_Groups_Ozero(X4737) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
fof(i_0_1912,plain,
! [X4757,X4758,X4759,X4760] :
( ( c_Polynomial_Omonom(X4760,X4759,X4758) != c_Polynomial_Omonom(X4760,X4757,X4758)
| X4759 = X4757
| ~ class_Groups_Ozero(X4760) )
& ( X4759 != X4757
| c_Polynomial_Omonom(X4760,X4759,X4758) = c_Polynomial_Omonom(X4760,X4757,X4758)
| ~ class_Groups_Ozero(X4760) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__iff])])]) ).
fof(i_0_1913,plain,
! [X3729,X3730,X3731,X3732] :
( ( c_Groups_Oplus__class_Oplus(X3732,X3731,X3730) != c_Groups_Oplus__class_Oplus(X3732,X3729,X3730)
| X3731 = X3729
| ~ class_Groups_Ocancel__semigroup__add(X3732) )
& ( X3731 != X3729
| c_Groups_Oplus__class_Oplus(X3732,X3731,X3730) = c_Groups_Oplus__class_Oplus(X3732,X3729,X3730)
| ~ class_Groups_Ocancel__semigroup__add(X3732) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_1914,plain,
! [X3717,X3718,X3719,X3720] :
( ~ class_Groups_Ocancel__semigroup__add(X3720)
| c_Groups_Oplus__class_Oplus(X3720,X3719,X3718) != c_Groups_Oplus__class_Oplus(X3720,X3717,X3718)
| X3719 = X3717 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_1915,plain,
! [X3721,X3722,X3723,X3724] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3724)
| c_Groups_Oplus__class_Oplus(X3724,X3723,X3722) != c_Groups_Oplus__class_Oplus(X3724,X3723,X3721)
| X3722 = X3721 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_1916,plain,
! [X3733,X3734,X3735,X3736] :
( ( c_Groups_Oplus__class_Oplus(X3736,X3735,X3734) != c_Groups_Oplus__class_Oplus(X3736,X3735,X3733)
| X3734 = X3733
| ~ class_Groups_Ocancel__semigroup__add(X3736) )
& ( X3734 != X3733
| c_Groups_Oplus__class_Oplus(X3736,X3735,X3734) = c_Groups_Oplus__class_Oplus(X3736,X3735,X3733)
| ~ class_Groups_Ocancel__semigroup__add(X3736) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_1917,plain,
! [X3725,X3726,X3727,X3728] :
( ~ class_Groups_Ocancel__semigroup__add(X3728)
| c_Groups_Oplus__class_Oplus(X3728,X3727,X3726) != c_Groups_Oplus__class_Oplus(X3728,X3727,X3725)
| X3726 = X3725 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_1918,plain,
! [X4581,X4582] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4582),X4581)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4582) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])]) ).
fof(i_0_1919,plain,
! [X5022,X5023,X5024] :
( ~ class_Orderings_Oorder(X5024)
| ~ c_Orderings_Oord__class_Oless(X5024,X5023,X5022)
| ~ c_Orderings_Oord__class_Oless(X5024,X5022,X5023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1292])]) ).
fof(i_0_1920,plain,
! [X5121,X5122,X5123] :
( ( c_Orderings_Oord__class_Oless__eq(X5123,X5122,X5121)
| c_Orderings_Oord__class_Oless(X5123,X5121,X5122)
| ~ class_Orderings_Olinorder(X5123) )
& ( ~ c_Orderings_Oord__class_Oless(X5123,X5121,X5122)
| ~ c_Orderings_Oord__class_Oless__eq(X5123,X5122,X5121)
| ~ class_Orderings_Olinorder(X5123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1293])])]) ).
fof(i_0_1921,plain,
! [X5124,X5125,X5126] :
( ( c_Orderings_Oord__class_Oless(X5126,X5125,X5124)
| c_Orderings_Oord__class_Oless__eq(X5126,X5124,X5125)
| ~ class_Orderings_Olinorder(X5126) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5126,X5124,X5125)
| ~ c_Orderings_Oord__class_Oless(X5126,X5125,X5124)
| ~ class_Orderings_Olinorder(X5126) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1294])])]) ).
fof(i_0_1922,plain,
! [X5091,X5092,X5093] :
( ~ class_Orderings_Olinorder(X5093)
| ~ c_Orderings_Oord__class_Oless__eq(X5093,X5092,X5091)
| ~ c_Orderings_Oord__class_Oless(X5093,X5091,X5092) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1295])]) ).
fof(i_0_1923,plain,
! [X5052,X5053,X5054] :
( ( c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| c_Orderings_Oord__class_Oless(X5054,X5052,X5053)
| X5053 = X5052
| ~ class_Orderings_Olinorder(X5054) )
& ( ~ c_Orderings_Oord__class_Oless(X5054,X5052,X5053)
| ~ c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| ~ class_Orderings_Olinorder(X5054) )
& ( X5053 != X5052
| ~ c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| ~ class_Orderings_Olinorder(X5054) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1296])])]) ).
fof(i_0_1924,plain,
! [X5037,X5038,X5039] :
( ~ class_Orderings_Opreorder(X5039)
| ~ c_Orderings_Oord__class_Oless(X5039,X5038,X5037)
| ~ c_Orderings_Oord__class_Oless(X5039,X5037,X5038) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1297])]) ).
fof(i_0_1925,plain,
! [X5034,X5035,X5036] :
( ~ class_Orderings_Opreorder(X5036)
| ~ c_Orderings_Oord__class_Oless(X5036,X5035,X5034)
| ~ c_Orderings_Oord__class_Oless(X5036,X5034,X5035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1298])]) ).
fof(i_0_1926,plain,
! [X5025,X5026,X5027] :
( ~ class_Orderings_Opreorder(X5027)
| ~ c_Orderings_Oord__class_Oless(X5027,X5026,X5025)
| ~ c_Orderings_Oord__class_Oless(X5027,X5025,X5026) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1299])]) ).
fof(i_0_1927,plain,
! [X4995,X4996,X4997] :
( ~ class_Orderings_Opreorder(X4997)
| ~ c_Orderings_Oord__class_Oless(X4997,X4996,X4995)
| ~ c_Orderings_Oord__class_Oless(X4997,X4995,X4996) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1300])]) ).
fof(i_0_1928,plain,
! [X5235,X5236] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5236,c_RealDef_Oreal(tc_Nat_Onat,X5235))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5236),X5235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_1929,plain,
! [X5233,X5234] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5234),X5233)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5234,c_RComplete_Onatfloor(X5233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
fof(i_0_1930,plain,
! [X4922,X4923,X4924] :
( ( hAPP(c_Polynomial_Opoly(X4924,X4923),X4922) != c_Groups_Ozero__class_Ozero(X4924)
| X4923 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4924))
| c_Polynomial_Oorder(X4924,X4922,X4923) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X4924) )
& ( X4923 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4924))
| hAPP(c_Polynomial_Opoly(X4924,X4923),X4922) = c_Groups_Ozero__class_Ozero(X4924)
| ~ class_Rings_Oidom(X4924) )
& ( c_Polynomial_Oorder(X4924,X4922,X4923) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X4924,X4923),X4922) = c_Groups_Ozero__class_Ozero(X4924)
| ~ class_Rings_Oidom(X4924) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_1931,plain,
! [X4204,X4205] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4205,X4204) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4204,X4205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4205 = X4204 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_1932,plain,
! [X5232] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5232)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5232)),X5232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
fof(i_0_1933,plain,
! [X5317,X5318] :
( ( X5317 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318))
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5318),X5317) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318))
| ~ class_Rings_Olinordered__idom(X5318) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5318),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318)),X5317)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5318),X5317) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5318))
| X5317 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318))
| ~ class_Rings_Olinordered__idom(X5318) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5318),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318)),X5317)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5318),X5317) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5318),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5318)))
| X5317 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5318))
| ~ class_Rings_Olinordered__idom(X5318) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1301])])]) ).
fof(i_0_1934,plain,
! [X4728,X4729] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4729),X4728,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4729)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4729),X4728) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4729),X4728)
| ~ class_Rings_Olinordered__idom(X4729) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4729),X4728,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4729)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4729),X4728) = X4728
| ~ class_Rings_Olinordered__idom(X4729) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1302])])]) ).
fof(i_0_1935,plain,
! [X3467,X3468] :
( ~ class_Rings_Olinordered__ring(X3468)
| c_Orderings_Oord__class_Oless__eq(X3468,c_Groups_Ozero__class_Ozero(X3468),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3468),X3467),X3467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_1936,plain,
! [X4654,X4655] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4655,X4654)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4654,X4655)
| X4655 = X4654 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_1937,plain,
! [X3157,X3158] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3158,X3157)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3157,X3158)
| X3158 = X3157 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_1938,plain,
! [X3235,X3236] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3236,X3235)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3235,X3236)
| X3236 = X3235 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_1939,plain,
! [X4038,X4039,X4040] :
( ~ class_Groups_Ogroup__add(X4040)
| c_Groups_Ominus__class_Ominus(X4040,c_Groups_Oplus__class_Oplus(X4040,X4039,X4038),X4038) = X4039 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_1940,plain,
! [X4041,X4042,X4043] :
( ~ class_Groups_Ogroup__add(X4043)
| c_Groups_Oplus__class_Oplus(X4043,c_Groups_Ominus__class_Ominus(X4043,X4042,X4041),X4041) = X4042 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_1941,plain,
! [X4429,X4430] :
( ( X4430 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4430),X4429) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4430) )
& ( X4429 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4430),X4429) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4430) )
& ( X4430 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4429 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4430),X4429) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4430) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
fof(i_0_1942,plain,
! [X3267,X3268,X3269] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,X3268) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3267,X3268)
| X3269 = X3267 )
& ( X3269 != X3267
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3269,X3268) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3267,X3268) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_1943,plain,
! [X3264,X3265,X3266] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3266,X3265) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3266,X3264)
| X3265 = X3264 )
& ( X3265 != X3264
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3266,X3265) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3266,X3264) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_1944,plain,
! [X5164] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk31_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk31_0),X5164) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X5164)) ),
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_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])])]) ).
fof(i_0_1945,plain,
! [X4699] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk15_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk15_0),X4699) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X4699)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096])])]) ).
fof(i_0_1946,plain,
! [X4695] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4695) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X4695)),
inference(variable_rename,[status(thm)],[fact_q_I2_J]) ).
fof(i_0_1947,plain,
! [X5420,X5421,X5422] :
( ~ class_Rings_Ocomm__semiring__1(X5422)
| c_Rings_Odvd__class_Odvd(X5422,X5421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5422),X5421),X5420)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_1948,plain,
! [X5423,X5424,X5425] :
( ~ class_Rings_Ocomm__semiring__1(X5425)
| c_Rings_Odvd__class_Odvd(X5425,X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5425),X5423),X5424)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
fof(i_0_1949,plain,
! [X3185,X3186,X3188,X3189,X3190] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3186,X3185)
| X3185 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3186,esk5_2(X3185,X3186)) )
& ( X3188 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3189,X3190)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3189,X3188) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).
fof(i_0_1950,plain,
! [X3179,X3180,X3182,X3183,X3184] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3180,X3179)
| X3179 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3180,esk4_2(X3179,X3180)) )
& ( X3182 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3183,X3184)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3183,X3182) ) ),
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_1951,plain,
! [X4263,X4264] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4264,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4264,X4263)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_1952,plain,
! [X4217,X4218] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4218,X4217),X4218) = X4217,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_1953,plain,
! [X4215,X4216] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4216,X4215),X4215) = X4216,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_1954,plain,
! [X4228,X4229] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4229,X4228),X4229),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_1955,plain,
! [X3177,X3178] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3178,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3178,X3177)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_1956,plain,
! [X3175,X3176] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3176,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3175,X3176)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_1957,plain,
! [X5174] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5174))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5174) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5174)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5174)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_1958,plain,
! [X5141] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5141),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5141,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5141,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5141),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_1959,plain,
! [X4479,X4480] :
( ( ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Groups_Oabs__class_Oabs(X4480,X4479))
| X4479 != c_Groups_Ozero__class_Ozero(X4480)
| ~ class_Groups_Oordered__ab__group__add__abs(X4480) )
& ( X4479 = c_Groups_Ozero__class_Ozero(X4480)
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Groups_Oabs__class_Oabs(X4480,X4479))
| ~ class_Groups_Oordered__ab__group__add__abs(X4480) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
fof(i_0_1960,plain,
! [X3132] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X3132))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3132) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X3132),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3132) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X3132),X3132)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3132) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096])])])]) ).
fof(i_0_1961,plain,
! [X3225,X3226,X3227] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3227),X3226) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3225),X3226)
| X3227 = X3225
| X3226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3227 != X3225
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3227),X3226) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3225),X3226) )
& ( X3226 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3227),X3226) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3225),X3226) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_1962,plain,
! [X3395,X3396,X3397] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3396),X3397) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3395),X3397)
| X3396 = X3395
| X3397 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3396 != X3395
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3396),X3397) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3395),X3397)
| X3397 = 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_1963,plain,
! [X3819,X3820,X3821] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3820) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3819)
| X3821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3820 = X3819 )
& ( X3821 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3820) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3819) )
& ( X3820 != X3819
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3820) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3821),X3819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_1964,plain,
! [X3228,X3229,X3230] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3229) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3228)
| X3229 = X3228
| X3230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3229 != X3228
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3228) )
& ( X3230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3230),X3228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_1965,plain,
! [X3398,X3399,X3400] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3400),X3399) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3400),X3398)
| X3399 = X3398
| X3400 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3399 != X3398
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3400),X3399) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3400),X3398)
| X3400 = 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_1966,plain,
! [X5175,X5176] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5176,X5175)
| c_Nat__Transfer_Otsub(X5175,X5176) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5175,X5176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_1967,plain,
! [X5166,X5167] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5167,X5166)
| c_Nat__Transfer_Otsub(X5166,X5167) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5166,X5167) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5167,X5166)
| c_Nat__Transfer_Otsub(X5166,X5167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1303])]) ).
fof(i_0_1968,plain,
! [X5115,X5116,X5117] :
( ( c_Orderings_Oord__class_Oless__eq(X5117,X5116,X5115)
| ~ c_Orderings_Oord__class_Oless(X5117,X5116,X5115)
| ~ class_Orderings_Oorder(X5117) )
& ( X5116 != X5115
| ~ c_Orderings_Oord__class_Oless(X5117,X5116,X5115)
| ~ class_Orderings_Oorder(X5117) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5117,X5116,X5115)
| X5116 = X5115
| c_Orderings_Oord__class_Oless(X5117,X5116,X5115)
| ~ class_Orderings_Oorder(X5117) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_1969,plain,
! [X5109,X5110,X5111] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5111,X5110,X5109)
| c_Orderings_Oord__class_Oless(X5111,X5110,X5109)
| X5110 = X5109
| ~ class_Orderings_Oorder(X5111) )
& ( ~ c_Orderings_Oord__class_Oless(X5111,X5110,X5109)
| c_Orderings_Oord__class_Oless__eq(X5111,X5110,X5109)
| ~ class_Orderings_Oorder(X5111) )
& ( X5110 != X5109
| c_Orderings_Oord__class_Oless__eq(X5111,X5110,X5109)
| ~ class_Orderings_Oorder(X5111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_1970,plain,
! [X5097,X5098,X5099] :
( ~ class_Orderings_Oorder(X5099)
| X5098 = X5097
| ~ c_Orderings_Oord__class_Oless__eq(X5099,X5098,X5097)
| c_Orderings_Oord__class_Oless(X5099,X5098,X5097) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_1971,plain,
! [X5082,X5083,X5084] :
( ~ class_Orderings_Oorder(X5084)
| ~ c_Orderings_Oord__class_Oless__eq(X5084,X5083,X5082)
| c_Orderings_Oord__class_Oless(X5084,X5083,X5082)
| X5083 = X5082 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_1972,plain,
! [X5079,X5080,X5081] :
( ~ class_Orderings_Oorder(X5081)
| ~ c_Orderings_Oord__class_Oless__eq(X5081,X5080,X5079)
| X5080 = X5079
| c_Orderings_Oord__class_Oless(X5081,X5080,X5079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_1973,plain,
! [X5076,X5077,X5078] :
( ~ class_Orderings_Oorder(X5078)
| ~ c_Orderings_Oord__class_Oless__eq(X5078,X5077,X5076)
| X5076 = X5077
| c_Orderings_Oord__class_Oless(X5078,X5077,X5076) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_1974,plain,
! [X5100,X5101,X5102] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5102,X5101,X5100)
| X5101 = X5100
| c_Orderings_Oord__class_Oless(X5102,X5101,X5100)
| ~ class_Orderings_Olinorder(X5102) )
& ( X5101 != X5100
| c_Orderings_Oord__class_Oless__eq(X5102,X5101,X5100)
| c_Orderings_Oord__class_Oless(X5102,X5101,X5100)
| ~ class_Orderings_Olinorder(X5102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1304])])]) ).
fof(i_0_1975,plain,
! [X5094,X5095,X5096] :
( ~ class_Orderings_Oorder(X5096)
| X5095 = X5094
| ~ c_Orderings_Oord__class_Oless__eq(X5096,X5094,X5095)
| c_Orderings_Oord__class_Oless(X5096,X5094,X5095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_1976,plain,
! [X4128,X4129] :
( ~ class_Rings_Ocomm__ring__1(X4129)
| c_Groups_Ouminus__class_Ouminus(X4129,X4128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4129),c_Groups_Ouminus__class_Ouminus(X4129,c_Groups_Oone__class_Oone(X4129))),X4128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_1977,plain,
! [X5168,X5169] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5169,X5168)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X5169),c_RComplete_Onatfloor(X5168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_1978,plain,
! [X5134,X5135] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5135,X5134)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5135),c_RComplete_Onatceiling(X5134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_1979,plain,
! [X4473,X4474] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4474,c_Groups_Oabs__class_Oabs(X4474,X4473),c_Groups_Ozero__class_Ozero(X4474))
| X4473 = c_Groups_Ozero__class_Ozero(X4474)
| ~ class_Groups_Oordered__ab__group__add__abs(X4474) )
& ( X4473 != c_Groups_Ozero__class_Ozero(X4474)
| c_Orderings_Oord__class_Oless__eq(X4474,c_Groups_Oabs__class_Oabs(X4474,X4473),c_Groups_Ozero__class_Ozero(X4474))
| ~ class_Groups_Oordered__ab__group__add__abs(X4474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_1980,plain,
! [X5088,X5089,X5090] :
( ~ class_Orderings_Opreorder(X5090)
| ~ c_Orderings_Oord__class_Oless(X5090,X5089,X5088)
| c_Orderings_Oord__class_Oless__eq(X5090,X5089,X5088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_1981,plain,
! [X5439,X5440,X5441,X5442] :
( ~ class_Rings_Odvd(X5442)
| X5441 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5442),X5440),X5439)
| c_Rings_Odvd__class_Odvd(X5442,X5440,X5441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
fof(i_0_1982,plain,
! [X4531,X4532] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4532)
| c_Orderings_Oord__class_Oless__eq(X4532,c_Groups_Ouminus__class_Ouminus(X4532,c_Groups_Oabs__class_Oabs(X4532,X4531)),c_Groups_Ozero__class_Ozero(X4532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).
fof(i_0_1983,plain,
! [X4598] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4598)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4598) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4598)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4598) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_1984,plain,
! [X2925,X2926] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2926,X2925))
| X2925 != c_Groups_Ozero__class_Ozero(X2926)
| ~ class_RealVector_Oreal__normed__vector(X2926) )
& ( X2925 = c_Groups_Ozero__class_Ozero(X2926)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2926,X2925))
| ~ class_RealVector_Oreal__normed__vector(X2926) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_1985,plain,
! [X4253] : 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,X4253)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4253)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(i_0_1986,plain,
! [X4481,X4482] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4482)
| ~ c_Orderings_Oord__class_Oless(X4482,c_Groups_Oabs__class_Oabs(X4482,X4481),c_Groups_Ozero__class_Ozero(X4482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1305])]) ).
fof(i_0_1987,plain,
! [X3137] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3137),X3137)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_1988,plain,
! [X3904,X3905,X3906] :
( ~ class_Groups_Ogroup__add(X3906)
| c_Groups_Ominus__class_Ominus(X3906,X3905,c_Groups_Ouminus__class_Ouminus(X3906,X3904)) = c_Groups_Oplus__class_Oplus(X3906,X3905,X3904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_1989,plain,
! [X3942,X3943,X3944] :
( ~ class_Rings_Ocomm__ring__1(X3944)
| c_Groups_Ominus__class_Ominus(X3944,X3943,X3942) = c_Groups_Oplus__class_Oplus(X3944,X3943,c_Groups_Ouminus__class_Ouminus(X3944,X3942)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_1990,plain,
! [X3901,X3902,X3903] :
( ~ class_Groups_Oab__group__add(X3903)
| c_Groups_Ominus__class_Ominus(X3903,X3902,X3901) = c_Groups_Oplus__class_Oplus(X3903,X3902,c_Groups_Ouminus__class_Ouminus(X3903,X3901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_1991,plain,
! [X3898,X3899,X3900] :
( ~ class_Groups_Ogroup__add(X3900)
| c_Groups_Ominus__class_Ominus(X3900,X3899,X3898) = c_Groups_Oplus__class_Oplus(X3900,X3899,c_Groups_Ouminus__class_Ouminus(X3900,X3898)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_1992,plain,
! [X2850,X2851] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2851,X2850),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X2850 = c_Groups_Ozero__class_Ozero(X2851)
| ~ class_RealVector_Oreal__normed__vector(X2851) )
& ( X2850 != c_Groups_Ozero__class_Ozero(X2851)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2851,X2850),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2851) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_1993,plain,
! [X4267,X4268] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4268,X4267) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4268,X4267) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4268,X4267)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4268,X4267) = 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_1994,plain,
! [X4628,X4629] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4629,X4628)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4629,X4628) )
& ( X4629 != X4628
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4629,X4628) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4629,X4628)
| X4629 = X4628
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4629,X4628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_1995,plain,
! [X3173,X3174] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3174,X3173)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3174,X3173) )
& ( X3174 != X3173
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3174,X3173) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3174,X3173)
| X3174 = X3173
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3174,X3173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_1996,plain,
! [X3171,X3172] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3172,X3171)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3172,X3171)
| X3172 = X3171 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3172,X3171)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3172,X3171) )
& ( X3172 != X3171
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3172,X3171) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_1997,plain,
! [X3167,X3168] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3168,X3167)
| X3168 = X3167
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3168,X3167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_1998,plain,
! [X3354,X3355] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3355,X3354)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3355,X3354)
| X3355 = X3354 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3355,X3354)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3355,X3354) )
& ( X3355 != X3354
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3355,X3354) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_1999,plain,
! [X3352,X3353] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3353,X3352)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3353,X3352) )
& ( X3353 != X3352
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3353,X3352) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3353,X3352)
| X3353 = X3352
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3353,X3352) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2000,plain,
! [X4265,X4266] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4266,X4265)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4266,X4265) = 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_2001,plain,
! [X4254] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X4254)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4254),
inference(variable_rename,[status(thm)],[fact_complex__i__mult__minus]) ).
fof(i_0_2002,plain,
! [X5307,X5308,X5309,X5310] :
( ~ class_Groups_Ouminus(X5310)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5309,X5310),X5308),X5307) = c_Groups_Ouminus__class_Ouminus(X5310,hAPP(X5308,X5307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_2003,plain,
! [X5326,X5327] :
( ~ class_Rings_Olinordered__idom(X5327)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5327),c_Groups_Osgn__class_Osgn(X5327,X5326)),c_Groups_Oabs__class_Oabs(X5327,X5326)) = X5326 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).
fof(i_0_2004,plain,
! [X4717,X4718] :
( ~ class_Groups_Ozero(X4718)
| c_Polynomial_Omonom(X4718,X4717,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X4718,X4717,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4718))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__0])]) ).
fof(i_0_2005,plain,
! [X5352,X5353] :
( ~ class_Rings_Olinordered__idom(X5353)
| ~ c_Orderings_Oord__class_Oless(X5353,X5352,c_Groups_Ozero__class_Ozero(X5353))
| c_Groups_Osgn__class_Osgn(X5353,X5352) = c_Groups_Ouminus__class_Ouminus(X5353,c_Groups_Oone__class_Oone(X5353)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).
fof(i_0_2006,plain,
! [X5350,X5351] :
( ( c_Groups_Osgn__class_Osgn(X5351,X5350) != c_Groups_Ouminus__class_Ouminus(X5351,c_Groups_Oone__class_Oone(X5351))
| c_Orderings_Oord__class_Oless(X5351,X5350,c_Groups_Ozero__class_Ozero(X5351))
| ~ class_Rings_Olinordered__idom(X5351) )
& ( ~ c_Orderings_Oord__class_Oless(X5351,X5350,c_Groups_Ozero__class_Ozero(X5351))
| c_Groups_Osgn__class_Osgn(X5351,X5350) = c_Groups_Ouminus__class_Ouminus(X5351,c_Groups_Oone__class_Oone(X5351))
| ~ class_Rings_Olinordered__idom(X5351) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).
fof(i_0_2007,plain,
! [X5191,X5192] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5192,X5191)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5192,X5191) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2008,plain,
! [X3169,X3170] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3170,X3169)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3170,X3169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2009,plain,
! [X3165,X3166] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3166,X3165)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3166,X3165) )
& ( X3166 != X3165
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3166,X3165) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2010,plain,
! [X2954,X2955] :
( ~ class_RealVector_Oreal__normed__vector(X2955)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2955,X2954),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])]) ).
fof(i_0_2011,plain,
! [X4538,X4539] :
( ( ~ c_Orderings_Oord__class_Oless(X4539,X4538,c_Groups_Ozero__class_Ozero(X4539))
| c_Groups_Oabs__class_Oabs(X4539,X4538) = c_Groups_Ouminus__class_Ouminus(X4539,X4538)
| ~ class_Groups_Oabs__if(X4539) )
& ( c_Orderings_Oord__class_Oless(X4539,X4538,c_Groups_Ozero__class_Ozero(X4539))
| c_Groups_Oabs__class_Oabs(X4539,X4538) = X4538
| ~ class_Groups_Oabs__if(X4539) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1307])])]) ).
fof(i_0_2012,plain,
! [X4533,X4534] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4534)
| ~ c_Orderings_Oord__class_Oless__eq(X4534,X4533,c_Groups_Ozero__class_Ozero(X4534))
| c_Groups_Oabs__class_Oabs(X4534,X4533) = c_Groups_Ouminus__class_Ouminus(X4534,X4533) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
fof(i_0_2013,plain,
! [X4540,X4541] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4541)
| ~ c_Orderings_Oord__class_Oless(X4541,X4540,c_Groups_Ozero__class_Ozero(X4541))
| c_Groups_Oabs__class_Oabs(X4541,X4540) = c_Groups_Ouminus__class_Ouminus(X4541,X4540) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).
fof(i_0_2014,plain,
! [X4723,X4724] :
( ~ class_Rings_Ocomm__semiring__0(X4724)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4724)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4724))),X4723) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_2015,plain,
! [X4577,X4578] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4578,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4577)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4578,X4577),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_2016,plain,
! [X4579,X4580] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4580,X4579) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4580,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4579)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_2017,plain,
! [X4194,X4195] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4195,X4194) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4195,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4194)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(i_0_2018,plain,
! [X4202,X4203] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4203,X4202) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4203,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4202)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(i_0_2019,plain,
! [X4200,X4201] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4201,X4200) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4201,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4200)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(i_0_2020,plain,
! [X4583] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4583),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X4583 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X4583 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4583),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_2021,plain,
! [X5223] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5223),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X5223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5223 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5223),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_2022,plain,
! [X2797,X2798] :
( hAPP(X2798,esk1_2(X2797,X2798)) != hAPP(X2797,esk1_2(X2797,X2798))
| X2798 = X2797 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_2023,plain,
! [X5354,X5355] :
( ( X5354 != c_Groups_Ozero__class_Ozero(X5355)
| c_Groups_Osgn__class_Osgn(X5355,X5354) = c_Groups_Ozero__class_Ozero(X5355)
| ~ class_Groups_Osgn__if(X5355) )
& ( ~ c_Orderings_Oord__class_Oless(X5355,c_Groups_Ozero__class_Ozero(X5355),X5354)
| c_Groups_Osgn__class_Osgn(X5355,X5354) = c_Groups_Oone__class_Oone(X5355)
| X5354 = c_Groups_Ozero__class_Ozero(X5355)
| ~ class_Groups_Osgn__if(X5355) )
& ( c_Orderings_Oord__class_Oless(X5355,c_Groups_Ozero__class_Ozero(X5355),X5354)
| c_Groups_Osgn__class_Osgn(X5355,X5354) = c_Groups_Ouminus__class_Ouminus(X5355,c_Groups_Oone__class_Oone(X5355))
| X5354 = c_Groups_Ozero__class_Ozero(X5355)
| ~ class_Groups_Osgn__if(X5355) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])])]) ).
fof(i_0_2024,plain,
! [X4827,X4828,X4829] :
( ( c_Polynomial_Osmult(X4829,X4828,X4827) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4829))
| X4828 = c_Groups_Ozero__class_Ozero(X4829)
| X4827 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4829))
| ~ class_Rings_Oidom(X4829) )
& ( X4828 != c_Groups_Ozero__class_Ozero(X4829)
| c_Polynomial_Osmult(X4829,X4828,X4827) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4829))
| ~ class_Rings_Oidom(X4829) )
& ( X4827 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4829))
| c_Polynomial_Osmult(X4829,X4828,X4827) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4829))
| ~ class_Rings_Oidom(X4829) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff])])]) ).
fof(i_0_2025,plain,
! [X4282,X4283] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4283,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4282)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4283 = X4282 )
& ( X4283 != X4282
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4283,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4282)) = 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_2026,plain,
! [X5203] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5203),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1309]) ).
fof(i_0_2027,plain,
! [X2852,X2853,X2854] :
( ( X2853 = c_Groups_Ozero__class_Ozero(X2854)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2854),X2853),X2852) != c_Groups_Ozero__class_Ozero(X2854)
| ~ class_Power_Opower(X2854)
| ~ class_Rings_Omult__zero(X2854)
| ~ class_Rings_Ono__zero__divisors(X2854)
| ~ class_Rings_Ozero__neq__one(X2854) )
& ( X2852 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2854),X2853),X2852) != c_Groups_Ozero__class_Ozero(X2854)
| ~ class_Power_Opower(X2854)
| ~ class_Rings_Omult__zero(X2854)
| ~ class_Rings_Ono__zero__divisors(X2854)
| ~ class_Rings_Ozero__neq__one(X2854) )
& ( X2853 != c_Groups_Ozero__class_Ozero(X2854)
| X2852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2854),X2853),X2852) = c_Groups_Ozero__class_Ozero(X2854)
| ~ class_Power_Opower(X2854)
| ~ class_Rings_Omult__zero(X2854)
| ~ class_Rings_Ono__zero__divisors(X2854)
| ~ class_Rings_Ozero__neq__one(X2854) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2028,plain,
! [X4126,X4127] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4127),X4126),X4126) != c_Groups_Oone__class_Oone(X4127)
| X4126 = c_Groups_Oone__class_Oone(X4127)
| X4126 = c_Groups_Ouminus__class_Ouminus(X4127,c_Groups_Oone__class_Oone(X4127))
| ~ class_Rings_Oring__1__no__zero__divisors(X4127) )
& ( X4126 != c_Groups_Oone__class_Oone(X4127)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4127),X4126),X4126) = c_Groups_Oone__class_Oone(X4127)
| ~ class_Rings_Oring__1__no__zero__divisors(X4127) )
& ( X4126 != c_Groups_Ouminus__class_Ouminus(X4127,c_Groups_Oone__class_Oone(X4127))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4127),X4126),X4126) = c_Groups_Oone__class_Oone(X4127)
| ~ class_Rings_Oring__1__no__zero__divisors(X4127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_2029,plain,
! [X5348,X5349] :
( ~ class_Rings_Olinordered__idom(X5349)
| ~ c_Orderings_Oord__class_Oless(X5349,c_Groups_Ozero__class_Ozero(X5349),X5348)
| c_Groups_Osgn__class_Osgn(X5349,X5348) = c_Groups_Oone__class_Oone(X5349) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).
fof(i_0_2030,plain,
! [X5346,X5347] :
( ( c_Groups_Osgn__class_Osgn(X5347,X5346) != c_Groups_Oone__class_Oone(X5347)
| c_Orderings_Oord__class_Oless(X5347,c_Groups_Ozero__class_Ozero(X5347),X5346)
| ~ class_Rings_Olinordered__idom(X5347) )
& ( ~ c_Orderings_Oord__class_Oless(X5347,c_Groups_Ozero__class_Ozero(X5347),X5346)
| c_Groups_Osgn__class_Osgn(X5347,X5346) = c_Groups_Oone__class_Oone(X5347)
| ~ class_Rings_Olinordered__idom(X5347) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).
fof(i_0_2031,plain,
! [X3672,X3673] :
( ~ class_Fields_Ofield(X3673)
| X3672 = c_Groups_Ozero__class_Ozero(X3673)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3673),c_Rings_Oinverse__class_Oinverse(X3673,X3672)),X3672) = c_Groups_Oone__class_Oone(X3673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).
fof(i_0_2032,plain,
! [X3674,X3675] :
( ~ class_Rings_Odivision__ring(X3675)
| X3674 = c_Groups_Ozero__class_Ozero(X3675)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3675),c_Rings_Oinverse__class_Oinverse(X3675,X3674)),X3674) = c_Groups_Oone__class_Oone(X3675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).
fof(i_0_2033,plain,
! [X4823,X4824,X4825] :
( ( X4824 = c_Groups_Ozero__class_Ozero(X4825)
| c_Polynomial_OpCons(X4825,X4824,X4823) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4825))
| ~ class_Groups_Ozero(X4825) )
& ( X4823 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4825))
| c_Polynomial_OpCons(X4825,X4824,X4823) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4825))
| ~ class_Groups_Ozero(X4825) )
& ( X4824 != c_Groups_Ozero__class_Ozero(X4825)
| X4823 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4825))
| c_Polynomial_OpCons(X4825,X4824,X4823) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4825))
| ~ class_Groups_Ozero(X4825) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(i_0_2034,plain,
! [X5055,X5056,X5057] :
( ( X5056 = X5055
| c_Orderings_Oord__class_Oless(X5057,X5056,X5055)
| c_Orderings_Oord__class_Oless(X5057,X5055,X5056)
| ~ class_Orderings_Olinorder(X5057) )
& ( ~ c_Orderings_Oord__class_Oless(X5057,X5056,X5055)
| X5056 != X5055
| ~ class_Orderings_Olinorder(X5057) )
& ( ~ c_Orderings_Oord__class_Oless(X5057,X5055,X5056)
| X5056 != X5055
| ~ class_Orderings_Olinorder(X5057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2035,plain,
! [X5049,X5050,X5051] :
( ~ class_Orderings_Olinorder(X5051)
| c_Orderings_Oord__class_Oless(X5051,X5050,X5049)
| X5050 = X5049
| c_Orderings_Oord__class_Oless(X5051,X5049,X5050) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2036,plain,
! [X5046,X5047,X5048] :
( ( c_Orderings_Oord__class_Oless(X5048,X5046,X5047)
| X5046 = X5047
| c_Orderings_Oord__class_Oless(X5048,X5047,X5046)
| ~ class_Orderings_Olinorder(X5048) )
& ( X5046 != X5047
| ~ c_Orderings_Oord__class_Oless(X5048,X5046,X5047)
| c_Orderings_Oord__class_Oless(X5048,X5047,X5046)
| ~ class_Orderings_Olinorder(X5048) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1310])])]) ).
fof(i_0_2037,plain,
! [X5043,X5044,X5045] :
( ~ class_Orderings_Olinorder(X5045)
| X5044 = X5043
| c_Orderings_Oord__class_Oless(X5045,X5044,X5043)
| c_Orderings_Oord__class_Oless(X5045,X5043,X5044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1311])]) ).
fof(i_0_2038,plain,
! [X4992,X4993,X4994] :
( ~ class_Orderings_Olinorder(X4994)
| c_Orderings_Oord__class_Oless(X4994,X4993,X4992)
| X4993 = X4992
| c_Orderings_Oord__class_Oless(X4994,X4992,X4993) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1312])]) ).
fof(i_0_2039,plain,
! [X3222,X3223,X3224] :
( ~ class_Rings_Olinordered__idom(X3224)
| X3223 = X3222
| c_Orderings_Oord__class_Oless(X3224,X3223,X3222)
| c_Orderings_Oord__class_Oless(X3224,X3222,X3223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1313])]) ).
fof(i_0_2040,plain,
! [X4586,X4587,X4588,X4589,X4590,X4591,X4594,X4595] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4588,X4587,X4586)
| hAPP(X4586,X4589) = hAPP(X4586,X4590) )
& ( hAPP(X4591,esk12_1(X4591)) != hAPP(X4591,esk13_1(X4591))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4595,X4594,X4591) ) ),
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_constant__def])])])])]) ).
fof(i_0_2041,plain,
! [X4471,X4472] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4472)
| ~ c_Orderings_Oord__class_Oless__eq(X4472,c_Groups_Ozero__class_Ozero(X4472),X4471)
| c_Groups_Oabs__class_Oabs(X4472,X4471) = X4471 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_2042,plain,
! [X4477,X4478] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4478)
| ~ c_Orderings_Oord__class_Oless(X4478,c_Groups_Ozero__class_Ozero(X4478),X4477)
| c_Groups_Oabs__class_Oabs(X4478,X4477) = X4477 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_2043,plain,
! [X4989,X4990,X4991] :
( ~ class_Orderings_Olinorder(X4991)
| c_Orderings_Oord__class_Oless__eq(X4991,X4990,X4989)
| c_Orderings_Oord__class_Oless__eq(X4991,X4989,X4990) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1314])]) ).
fof(i_0_2044,plain,
! [X4937,X4938,X4939] :
( ~ class_Orderings_Olinorder(X4939)
| c_Orderings_Oord__class_Oless__eq(X4939,X4938,X4937)
| c_Orderings_Oord__class_Oless__eq(X4939,X4937,X4938) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2045,plain,
! [X5106,X5107,X5108] :
( ~ class_Orderings_Olinorder(X5108)
| c_Orderings_Oord__class_Oless(X5108,X5107,X5106)
| c_Orderings_Oord__class_Oless__eq(X5108,X5106,X5107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1315])]) ).
fof(i_0_2046,plain,
! [X5118,X5119,X5120] :
( ~ class_Orderings_Olinorder(X5120)
| c_Orderings_Oord__class_Oless__eq(X5120,X5119,X5118)
| c_Orderings_Oord__class_Oless(X5120,X5118,X5119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2047,plain,
! [X5103,X5104,X5105] :
( ~ class_Orderings_Olinorder(X5105)
| c_Orderings_Oord__class_Oless__eq(X5105,X5104,X5103)
| c_Orderings_Oord__class_Oless(X5105,X5103,X5104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1316])]) ).
fof(i_0_2048,plain,
! [X3027,X3028,X3029] :
( ~ class_Rings_Ocomm__semiring__1(X3029)
| c_Groups_Oplus__class_Oplus(X3029,X3028,X3027) = c_Groups_Oplus__class_Oplus(X3029,X3027,X3028) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2049,plain,
! [X4092,X4093,X4094] :
( ~ class_Groups_Ogroup__add(X4094)
| c_Groups_Oplus__class_Oplus(X4094,X4093,X4092) != c_Groups_Ozero__class_Ozero(X4094)
| c_Groups_Ouminus__class_Ouminus(X4094,X4093) = X4092 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2050,plain,
! [X4099,X4100,X4101] :
( ( X4100 != c_Groups_Ouminus__class_Ouminus(X4101,X4099)
| c_Groups_Oplus__class_Oplus(X4101,X4100,X4099) = c_Groups_Ozero__class_Ozero(X4101)
| ~ class_Groups_Ogroup__add(X4101) )
& ( c_Groups_Oplus__class_Oplus(X4101,X4100,X4099) != c_Groups_Ozero__class_Ozero(X4101)
| X4100 = c_Groups_Ouminus__class_Ouminus(X4101,X4099)
| ~ class_Groups_Ogroup__add(X4101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2051,plain,
! [X4089,X4090,X4091] :
( ( c_Groups_Oplus__class_Oplus(X4091,X4090,X4089) != c_Groups_Ozero__class_Ozero(X4091)
| X4089 = c_Groups_Ouminus__class_Ouminus(X4091,X4090)
| ~ class_Groups_Ogroup__add(X4091) )
& ( X4089 != c_Groups_Ouminus__class_Ouminus(X4091,X4090)
| c_Groups_Oplus__class_Oplus(X4091,X4090,X4089) = c_Groups_Ozero__class_Ozero(X4091)
| ~ class_Groups_Ogroup__add(X4091) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2052,plain,
! [X4848,X4849,X4850] :
( ( c_Polynomial_Omonom(X4850,X4849,X4848) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4850))
| X4849 = c_Groups_Ozero__class_Ozero(X4850)
| ~ class_Groups_Ozero(X4850) )
& ( X4849 != c_Groups_Ozero__class_Ozero(X4850)
| c_Polynomial_Omonom(X4850,X4849,X4848) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4850))
| ~ class_Groups_Ozero(X4850) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff])])]) ).
fof(i_0_2053,plain,
! [X4500,X4501] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4501)
| c_Orderings_Oord__class_Oless__eq(X4501,c_Groups_Ouminus__class_Ouminus(X4501,X4500),c_Groups_Oabs__class_Oabs(X4501,X4500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).
fof(i_0_2054,plain,
! [X4572] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4572,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4572) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4572) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4572,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4572) = X4572 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1317])]) ).
fof(i_0_2055,plain,
! [X4554] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4554,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4554) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4554) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4554,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4554) = X4554 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1318])]) ).
fof(i_0_2056,plain,
! [X4553] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4553,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4553) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4553) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4553,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4553) = X4553 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1319])]) ).
fof(i_0_2057,plain,
! [X3533] :
( ~ class_Rings_Olinordered__semidom(X3533)
| ~ c_Orderings_Oord__class_Oless__eq(X3533,c_Groups_Oone__class_Oone(X3533),c_Groups_Ozero__class_Ozero(X3533)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1320])]) ).
fof(i_0_2058,plain,
! [X3534] :
( ~ class_Rings_Olinordered__semidom(X3534)
| ~ c_Orderings_Oord__class_Oless(X3534,c_Groups_Oone__class_Oone(X3534),c_Groups_Ozero__class_Ozero(X3534)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1321])]) ).
fof(i_0_2059,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(fof_simplification,[status(thm)],[fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096]) ).
fof(i_0_2060,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(fof_simplification,[status(thm)],[fact_qnc]) ).
fof(i_0_2061,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(fof_simplification,[status(thm)],[fact_less_Oprems]) ).
fof(i_0_2062,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(fof_simplification,[status(thm)],[fact_assms]) ).
fof(i_0_2063,plain,
! [X4725,X4726] :
( ~ class_Rings_Ocomm__semiring__0(X4726)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4726)),X4725),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4726))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
fof(i_0_2064,plain,
! [X3003,X3004,X3005] :
( ~ class_Rings_Ocomm__semiring__1(X3005)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3005),X3004),X3003) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3005),X3003),X3004) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2065,plain,
! [X3572,X3573,X3574] :
( ~ class_Rings_Odivision__ring(X3574)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3574),X3573),X3572) != c_Groups_Oone__class_Oone(X3574)
| c_Rings_Oinverse__class_Oinverse(X3574,X3573) = X3572 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).
fof(i_0_2066,plain,
! [X4610,X4611] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4611,X4610)
| X4611 = X4610
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4610,X4611) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2067,plain,
! [X3253,X3254] :
( ( X3254 = X3253
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3254,X3253)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3253,X3254) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3254,X3253)
| X3254 != X3253 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3253,X3254)
| X3254 != X3253 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2068,plain,
! [X3251,X3252] :
( X3252 = X3251
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3252,X3251)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3251,X3252) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1322])]) ).
fof(i_0_2069,plain,
! [X4649,X4650] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4650,X4649)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4649,X4650) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2070,plain,
! [X3141,X3142] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3142,X3141)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3141,X3142) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2071,plain,
! [X3240,X3241] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3241,X3240)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3240,X3241) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2072,plain,
! [X3299,X3300,X3301] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3300),X3299) != c_Groups_Ozero__class_Ozero(X3301)
| X3300 = c_Groups_Ozero__class_Ozero(X3301)
| X3299 = c_Groups_Ozero__class_Ozero(X3301)
| ~ class_Rings_Oring__no__zero__divisors(X3301) )
& ( X3300 != c_Groups_Ozero__class_Ozero(X3301)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3300),X3299) = c_Groups_Ozero__class_Ozero(X3301)
| ~ class_Rings_Oring__no__zero__divisors(X3301) )
& ( X3299 != c_Groups_Ozero__class_Ozero(X3301)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3300),X3299) = c_Groups_Ozero__class_Ozero(X3301)
| ~ class_Rings_Oring__no__zero__divisors(X3301) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2073,plain,
! [X3305,X3306,X3307] :
( ~ class_Rings_Ono__zero__divisors(X3307)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3307),X3306),X3305) != c_Groups_Ozero__class_Ozero(X3307)
| X3306 = c_Groups_Ozero__class_Ozero(X3307)
| X3305 = c_Groups_Ozero__class_Ozero(X3307) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2074,plain,
! [X3302,X3303,X3304] :
( ~ class_Rings_Ono__zero__divisors(X3304)
| X3303 = c_Groups_Ozero__class_Ozero(X3304)
| X3302 = c_Groups_Ozero__class_Ozero(X3304)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3304),X3303),X3302) != c_Groups_Ozero__class_Ozero(X3304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2075,plain,
! [X4719,X4720] :
( ~ class_Groups_Oab__group__add(X4720)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4720),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4720)),X4719) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4720),X4719) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).
fof(i_0_2076,plain,
! [X4630,X4631] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4631,X4630) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4630,X4631),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2077,plain,
! [X3256,X3257] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3257,X3256) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3256,X3257),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2078,plain,
! [X4400,X4401] :
( ( c_Groups_Oplus__class_Oplus(X4401,X4400,X4400) != c_Groups_Ozero__class_Ozero(X4401)
| X4400 = c_Groups_Ozero__class_Ozero(X4401)
| ~ class_Groups_Olinordered__ab__group__add(X4401) )
& ( X4400 != c_Groups_Ozero__class_Ozero(X4401)
| c_Groups_Oplus__class_Oplus(X4401,X4400,X4400) = c_Groups_Ozero__class_Ozero(X4401)
| ~ class_Groups_Olinordered__ab__group__add(X4401) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2079,plain,
! [X3747,X3748] :
( ( c_Groups_Ozero__class_Ozero(X3748) != c_Groups_Oplus__class_Oplus(X3748,X3747,X3747)
| X3747 = c_Groups_Ozero__class_Ozero(X3748)
| ~ class_Groups_Olinordered__ab__group__add(X3748) )
& ( X3747 != c_Groups_Ozero__class_Ozero(X3748)
| c_Groups_Ozero__class_Ozero(X3748) = c_Groups_Oplus__class_Oplus(X3748,X3747,X3747)
| ~ class_Groups_Olinordered__ab__group__add(X3748) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2080,plain,
! [X3949,X3950,X3951] :
( ( X3950 != X3949
| c_Groups_Ominus__class_Ominus(X3951,X3950,X3949) = c_Groups_Ozero__class_Ozero(X3951)
| ~ class_Groups_Oab__group__add(X3951) )
& ( c_Groups_Ominus__class_Ominus(X3951,X3950,X3949) != c_Groups_Ozero__class_Ozero(X3951)
| X3950 = X3949
| ~ class_Groups_Oab__group__add(X3951) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2081,plain,
! [X3952,X3953,X3954] :
( ( c_Groups_Ominus__class_Ominus(X3954,X3953,X3952) != c_Groups_Ozero__class_Ozero(X3954)
| X3953 = X3952
| ~ class_Groups_Ogroup__add(X3954) )
& ( X3953 != X3952
| c_Groups_Ominus__class_Ominus(X3954,X3953,X3952) = c_Groups_Ozero__class_Ozero(X3954)
| ~ class_Groups_Ogroup__add(X3954) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2082,plain,
! [X2912,X2913,X2914] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2914)
| X2913 = c_Groups_Ozero__class_Ozero(X2914)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2914),X2913),X2912) != c_Groups_Ozero__class_Ozero(X2914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2083,plain,
! [X4280,X4281] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4281,X4280) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4280 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4281) )
& ( X4280 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4281)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4281,X4280) = 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_2084,plain,
! [X2905,X2906,X2907] :
( ( X2906 != c_Groups_Oplus__class_Oplus(X2907,X2906,X2905)
| X2905 = c_Groups_Ozero__class_Ozero(X2907)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2907) )
& ( X2905 != c_Groups_Ozero__class_Ozero(X2907)
| X2906 = c_Groups_Oplus__class_Oplus(X2907,X2906,X2905)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2907) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2085,plain,
! [X5328,X5329] :
( ~ class_Rings_Olinordered__idom(X5329)
| c_Groups_Oabs__class_Oabs(X5329,X5328) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5329),X5328),c_Groups_Osgn__class_Osgn(X5329,X5328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).
fof(i_0_2086,plain,
! [X4802,X4803] :
( ( c_Polynomial_Opoly(X4803,X4802) != c_Polynomial_Opoly(X4803,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4803)))
| X4802 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4803))
| ~ class_Int_Oring__char__0(X4803)
| ~ class_Rings_Oidom(X4803) )
& ( X4802 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4803))
| c_Polynomial_Opoly(X4803,X4802) = c_Polynomial_Opoly(X4803,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4803)))
| ~ class_Int_Oring__char__0(X4803)
| ~ class_Rings_Oidom(X4803) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2087,plain,
! [X3134] :
( X3134 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3134)),X3134) = 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_2088,plain,
! [X5040,X5041,X5042] :
( ~ class_Orderings_Oorder(X5042)
| ~ c_Orderings_Oord__class_Oless(X5042,X5041,X5040)
| X5041 != X5040 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2089,plain,
! [X5031,X5032,X5033] :
( ~ class_Orderings_Oorder(X5033)
| ~ c_Orderings_Oord__class_Oless(X5033,X5032,X5031)
| X5032 != X5031 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2090,plain,
! [X5028,X5029,X5030] :
( ~ class_Orderings_Oorder(X5030)
| ~ c_Orderings_Oord__class_Oless(X5030,X5029,X5028)
| X5028 != X5029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2091,plain,
! [X4826] :
( ~ class_Groups_Ozero(X4826)
| c_Polynomial_OpCons(X4826,c_Groups_Ozero__class_Ozero(X4826),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4826))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])]) ).
fof(i_0_2092,plain,
! [X4832] :
( ~ class_Rings_Ocomm__semiring__1(X4832)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4832)) = c_Polynomial_OpCons(X4832,c_Groups_Oone__class_Oone(X4832),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4832))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(i_0_2093,plain,
! [X5171] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5171,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X5171) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).
fof(i_0_2094,plain,
! [X5140] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5140,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X5140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).
fof(i_0_2095,plain,
! [X3670,X3671] :
( ~ class_Rings_Odivision__ring(X3671)
| X3670 = c_Groups_Ozero__class_Ozero(X3671)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3671),X3670),c_Rings_Oinverse__class_Oinverse(X3671,X3670)) = c_Groups_Oone__class_Oone(X3671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).
fof(i_0_2096,plain,
! [X3350] :
( ( X3350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3350) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3350)
| X3350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2097,plain,
! [X4475,X4476] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4476)
| c_Orderings_Oord__class_Oless__eq(X4476,c_Groups_Ozero__class_Ozero(X4476),c_Groups_Oabs__class_Oabs(X4476,X4475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_2098,plain,
! [X5058,X5059] :
( ~ class_Orderings_Opreorder(X5059)
| ~ c_Orderings_Oord__class_Oless(X5059,X5058,X5058) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])]) ).
fof(i_0_2099,plain,
! [X2844,X2845] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2845)
| ~ class_Rings_Odivision__ring__inverse__zero(X2845)
| c_RealVector_Onorm__class_Onorm(X2845,c_Rings_Oinverse__class_Oinverse(X2845,X2844)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2845,X2844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__inverse])]) ).
fof(i_0_2100,plain,
! [X4514,X4515] :
( ~ class_Fields_Olinordered__field(X4515)
| X4514 = c_Groups_Ozero__class_Ozero(X4515)
| c_Groups_Oabs__class_Oabs(X4515,c_Rings_Oinverse__class_Oinverse(X4515,X4514)) = c_Rings_Oinverse__class_Oinverse(X4515,c_Groups_Oabs__class_Oabs(X4515,X4514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__inverse])]) ).
fof(i_0_2101,plain,
! [X4140,X4141] :
( ~ class_Rings_Odivision__ring(X4141)
| X4140 = c_Groups_Ozero__class_Ozero(X4141)
| c_Rings_Oinverse__class_Oinverse(X4141,c_Groups_Ouminus__class_Ouminus(X4141,X4140)) = c_Groups_Ouminus__class_Ouminus(X4141,c_Rings_Oinverse__class_Oinverse(X4141,X4140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).
fof(i_0_2102,plain,
! [X3163] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3163,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
fof(i_0_2103,plain,
! [X4440,X4441] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4441),X4440) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4440),X4441),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2104,plain,
! [X3139,X3140] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3140),X3139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3139),X3140),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2105,plain,
! [X3276,X3277] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3277),X3276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3276),X3277),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2106,plain,
! [X4095,X4096] :
( ~ class_Groups_Oab__group__add(X4096)
| c_Groups_Oplus__class_Oplus(X4096,c_Groups_Ouminus__class_Ouminus(X4096,X4095),X4095) = c_Groups_Ozero__class_Ozero(X4096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_2107,plain,
! [X4097,X4098] :
( ~ class_Groups_Ogroup__add(X4098)
| c_Groups_Oplus__class_Oplus(X4098,c_Groups_Ouminus__class_Ouminus(X4098,X4097),X4097) = c_Groups_Ozero__class_Ozero(X4098) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_2108,plain,
! [X4102,X4103] :
( ~ class_Groups_Ogroup__add(X4103)
| c_Groups_Oplus__class_Oplus(X4103,X4102,c_Groups_Ouminus__class_Ouminus(X4103,X4102)) = c_Groups_Ozero__class_Ozero(X4103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2109,plain,
! [X3931,X3932] :
( ~ class_RealVector_Oreal__algebra__1(X3932)
| ~ class_RealVector_Oreal__normed__vector(X3932)
| c_RealVector_Oof__real(X3932,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3931)) = c_Groups_Ouminus__class_Ouminus(X3932,c_RealVector_Oof__real(X3932,X3931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ominus])]) ).
fof(i_0_2110,plain,
! [X4145,X4146] :
( ~ class_RealVector_Oreal__div__algebra(X4146)
| ~ class_Rings_Odivision__ring__inverse__zero(X4146)
| c_RealVector_Oof__real(X4146,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4145)) = c_Rings_Oinverse__class_Oinverse(X4146,c_RealVector_Oof__real(X4146,X4145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__inverse])]) ).
fof(i_0_2111,plain,
! [X3358,X3359] :
( ( X3359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3359,X3358) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3359,X3358) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3358 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3359,X3358) = 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_2112,plain,
! [X2855,X2856] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2856)
| X2855 = c_Groups_Ozero__class_Ozero(X2856)
| c_RealVector_Onorm__class_Onorm(X2856,c_Rings_Oinverse__class_Oinverse(X2856,X2855)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2856,X2855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__inverse])]) ).
fof(i_0_2113,plain,
! [X4901,X4902] :
( ~ class_Rings_Ocomm__semiring__0(X4902)
| c_Polynomial_Opcompose(X4902,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4902)),X4901) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__0])]) ).
fof(i_0_2114,plain,
! [X4899,X4900] :
( ~ class_Rings_Ocomm__semiring__0(X4900)
| c_Polynomial_Osynthetic__div(X4900,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4900)),X4899) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4900)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__0])]) ).
fof(i_0_2115,plain,
! [X4804,X4805] :
( ~ class_Rings_Ocomm__semiring__0(X4805)
| c_Polynomial_Osmult(X4805,X4804,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4805))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
fof(i_0_2116,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk16_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096])])]) ).
fof(i_0_2117,plain,
! [X3339,X3340] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3340,X3339)
| X3339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).
fof(i_0_2118,plain,
! [X2839,X2840] :
( ~ class_RealVector_Oreal__normed__vector(X2840)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2840,X2839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2119,plain,
! [X2923,X2924] :
( ( X2923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2924),c_Groups_Ozero__class_Ozero(X2924)),X2923) = c_Groups_Oone__class_Oone(X2924)
| ~ class_Power_Opower(X2924)
| ~ class_Rings_Osemiring__0(X2924) )
& ( X2923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2924),c_Groups_Ozero__class_Ozero(X2924)),X2923) = c_Groups_Ozero__class_Ozero(X2924)
| ~ class_Power_Opower(X2924)
| ~ class_Rings_Osemiring__0(X2924) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2120,plain,
! [X3360,X3361] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3361,X3360) != X3361
| X3360 = 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_2121,plain,
! [X3351] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3351,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1324]) ).
fof(i_0_2122,plain,
! [X3347] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1325]) ).
fof(i_0_2123,plain,
! [X3119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3119,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1326]) ).
fof(i_0_2124,plain,
! [X5224] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5224,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X5224))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2125,plain,
! [X4184,X4185] :
( ~ class_RealVector_Oreal__div__algebra(X4185)
| X4184 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X4185,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4184)) = c_Rings_Oinverse__class_Oinverse(X4185,c_RealVector_Oof__real(X4185,X4184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__of__real__inverse])]) ).
fof(i_0_2126,plain,
! [X4821,X4822] :
( ~ class_Rings_Ocomm__semiring__0(X4822)
| hAPP(c_Polynomial_Opoly(X4822,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4822))),X4821) = c_Groups_Ozero__class_Ozero(X4822) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2127,plain,
! [X4765,X4766] :
( ~ class_Rings_Ocomm__semiring__1(X4766)
| hAPP(c_Polynomial_Opoly(X4766,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4766))),X4765) = c_Groups_Oone__class_Oone(X4766) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2128,plain,
! [X4450,X4451] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4451)
| c_Orderings_Oord__class_Oless__eq(X4451,X4450,c_Groups_Oabs__class_Oabs(X4451,X4450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_2129,plain,
! [X3248,X3249] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3249,X3248)
| X3248 != X3249 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2130,plain,
! [X3246,X3247] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3247,X3246)
| X3247 != X3246 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2131,plain,
! [X5324,X5325] :
( ~ class_RealVector_Oreal__normed__vector(X5325)
| c_Groups_Osgn__class_Osgn(X5325,c_Groups_Ouminus__class_Ouminus(X5325,X5324)) = c_Groups_Ouminus__class_Ouminus(X5325,c_Groups_Osgn__class_Osgn(X5325,X5324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__minus])]) ).
fof(i_0_2132,plain,
! [X4466,X4467] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4467)
| c_Groups_Oabs__class_Oabs(X4467,c_Rings_Oinverse__class_Oinverse(X4467,X4466)) = c_Rings_Oinverse__class_Oinverse(X4467,c_Groups_Oabs__class_Oabs(X4467,X4466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__inverse])]) ).
fof(i_0_2133,plain,
! [X4061,X4062] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4062)
| c_Rings_Oinverse__class_Oinverse(X4062,c_Groups_Ouminus__class_Ouminus(X4062,X4061)) = c_Groups_Ouminus__class_Ouminus(X4062,c_Rings_Oinverse__class_Oinverse(X4062,X4061)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).
fof(i_0_2134,plain,
! [X4815,X4816] :
( ~ class_Groups_Ocomm__monoid__add(X4816)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4816),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4816)),X4815) = X4815 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_2135,plain,
! [X4721,X4722] :
( ~ class_Groups_Oab__group__add(X4722)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4722),X4721,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4722))) = X4721 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).
fof(i_0_2136,plain,
! [X4813,X4814] :
( ~ class_Groups_Ocomm__monoid__add(X4814)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4814),X4813,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4814))) = X4813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2137,plain,
! [X5246,X5247] :
( ~ class_Rings_Olinordered__idom(X5247)
| X5246 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5247))
| c_Polynomial_Opos__poly(X5247,X5246)
| c_Polynomial_Opos__poly(X5247,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5247),X5246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__total])]) ).
fof(i_0_2138,plain,
! [X3231,X3232] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3232),X3231) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3232 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3232),X3231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3232),X3231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).
fof(i_0_2139,plain,
! [X3929,X3930] :
( ~ class_RealVector_Oreal__algebra__1(X3930)
| c_RealVector_Oof__real(X3930,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3929)) = c_Groups_Ouminus__class_Ouminus(X3930,c_RealVector_Oof__real(X3930,X3929)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__minus])]) ).
fof(i_0_2140,plain,
! [X5330,X5331] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5331)
| c_Groups_Osgn__class_Osgn(X5331,c_RealVector_Oof__real(X5331,X5330)) = c_RealVector_Oof__real(X5331,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X5330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__of__real])]) ).
fof(i_0_2141,plain,
! [X3255] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3255,X3255),
inference(variable_rename,[status(thm)],[i_0_1327]) ).
fof(i_0_2142,plain,
! [X3250] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3250,X3250),
inference(variable_rename,[status(thm)],[i_0_1328]) ).
fof(i_0_2143,plain,
! [X3401,X3402] :
( X3402 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3402),X3401)
| X3401 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).
fof(i_0_2144,plain,
! [X3896,X3897] :
( ~ class_Groups_Ogroup__add(X3897)
| c_Groups_Ominus__class_Ominus(X3897,c_Groups_Ozero__class_Ozero(X3897),X3896) = c_Groups_Ouminus__class_Ouminus(X3897,X3896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_2145,plain,
! [X3293,X3294] :
( ( X3294 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3294),X3293) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3293 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3294),X3293) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3294 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3293 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3294),X3293) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).
fof(i_0_2146,plain,
! [X3290,X3291] :
( ( X3291 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3291),X3290) )
& ( X3290 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3291),X3290) )
& ( X3291 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3290 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3291),X3290) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2147,plain,
! [X5198] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5198)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2148,plain,
! [X4635] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4635),X4635) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2149,plain,
! [X4846,X4847] :
( ~ class_Groups_Ozero(X4847)
| c_Polynomial_Omonom(X4847,c_Groups_Ozero__class_Ozero(X4847),X4846) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0])]) ).
fof(i_0_2150,plain,
! [X4830,X4831] :
( ~ class_Rings_Ocomm__semiring__0(X4831)
| c_Polynomial_Osmult(X4831,c_Groups_Ozero__class_Ozero(X4831),X4830) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(i_0_2151,plain,
! [X5128] :
( ~ class_Power_Opower(X5128)
| c_Power_Opower__class_Opower(X5128) = c_Power_Opower_Opower(X5128,c_Groups_Oone__class_Oone(X5128),c_Groups_Otimes__class_Otimes(X5128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2152,plain,
! [X3295,X3296] :
( ~ class_Rings_Omult__zero(X3296)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3296),c_Groups_Ozero__class_Ozero(X3296)),X3295) = c_Groups_Ozero__class_Ozero(X3296) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2153,plain,
! [X2903,X2904] :
( ~ class_Rings_Ocomm__semiring__1(X2904)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2904),c_Groups_Ozero__class_Ozero(X2904)),X2903) = c_Groups_Ozero__class_Ozero(X2904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2154,plain,
! [X2901,X2902] :
( ~ class_RealVector_Oreal__normed__algebra(X2902)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2902),c_Groups_Ozero__class_Ozero(X2902)),X2901) = c_Groups_Ozero__class_Ozero(X2902) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2155,plain,
! [X2899,X2900] :
( ~ class_RealVector_Oreal__normed__algebra(X2900)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2900),c_Groups_Ozero__class_Ozero(X2900)),X2899) = c_Groups_Ozero__class_Ozero(X2900) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2156,plain,
! [X3083,X3084] :
( ~ class_Groups_Omonoid__mult(X3084)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3084),c_Groups_Oone__class_Oone(X3084)),X3083) = c_Groups_Oone__class_Oone(X3084) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2157,plain,
! [X3532] :
( ~ class_Rings_Olinordered__semidom(X3532)
| c_Orderings_Oord__class_Oless__eq(X3532,c_Groups_Ozero__class_Ozero(X3532),c_Groups_Oone__class_Oone(X3532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2158,plain,
! [X3535] :
( ~ class_Rings_Olinordered__semidom(X3535)
| c_Orderings_Oord__class_Oless(X3535,c_Groups_Ozero__class_Ozero(X3535),c_Groups_Oone__class_Oone(X3535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2159,plain,
! [X3815,X3816] :
( ~ class_Groups_Ocomm__monoid__mult(X3816)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3816),c_Groups_Oone__class_Oone(X3816)),X3815) = X3815 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2160,plain,
! [X3070,X3071] :
( ~ class_Rings_Ocomm__semiring__1(X3071)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3071),c_Groups_Oone__class_Oone(X3071)),X3070) = X3070 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2161,plain,
! [X3817,X3818] :
( ~ class_Groups_Omonoid__mult(X3818)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3818),c_Groups_Oone__class_Oone(X3818)),X3817) = X3817 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2162,plain,
! [X3297,X3298] :
( ~ class_Rings_Omult__zero(X3298)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3298),X3297),c_Groups_Ozero__class_Ozero(X3298)) = c_Groups_Ozero__class_Ozero(X3298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2163,plain,
! [X2897,X2898] :
( ~ class_Rings_Ocomm__semiring__1(X2898)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2898),X2897),c_Groups_Ozero__class_Ozero(X2898)) = c_Groups_Ozero__class_Ozero(X2898) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2164,plain,
! [X2895,X2896] :
( ~ class_RealVector_Oreal__normed__algebra(X2896)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2896),X2895),c_Groups_Ozero__class_Ozero(X2896)) = c_Groups_Ozero__class_Ozero(X2896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2165,plain,
! [X2893,X2894] :
( ~ class_RealVector_Oreal__normed__algebra(X2894)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2894),X2893),c_Groups_Ozero__class_Ozero(X2894)) = c_Groups_Ozero__class_Ozero(X2894) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2166,plain,
! [X4787,X4788] :
( ~ class_Rings_Ocomm__semiring__1(X4788)
| c_Polynomial_Osmult(X4788,c_Groups_Oone__class_Oone(X4788),X4787) = X4787 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
fof(i_0_2167,plain,
! [X3751,X3752] :
( ~ class_Groups_Omonoid__add(X3752)
| c_Groups_Oplus__class_Oplus(X3752,c_Groups_Ozero__class_Ozero(X3752),X3751) = X3751 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2168,plain,
! [X3749,X3750] :
( ~ class_Groups_Ocomm__monoid__add(X3750)
| c_Groups_Oplus__class_Oplus(X3750,c_Groups_Ozero__class_Ozero(X3750),X3749) = X3749 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2169,plain,
! [X2910,X2911] :
( ~ class_Rings_Ocomm__semiring__1(X2911)
| c_Groups_Oplus__class_Oplus(X2911,c_Groups_Ozero__class_Ozero(X2911),X2910) = X2910 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2170,plain,
! [X3945,X3946] :
( ~ class_Groups_Ogroup__add(X3946)
| c_Groups_Ominus__class_Ominus(X3946,X3945,c_Groups_Ozero__class_Ozero(X3946)) = X3945 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2171,plain,
! [X3745,X3746] :
( ~ class_Groups_Omonoid__add(X3746)
| c_Groups_Oplus__class_Oplus(X3746,X3745,c_Groups_Ozero__class_Ozero(X3746)) = X3745 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2172,plain,
! [X3743,X3744] :
( ~ class_Groups_Ocomm__monoid__add(X3744)
| c_Groups_Oplus__class_Oplus(X3744,X3743,c_Groups_Ozero__class_Ozero(X3744)) = X3743 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2173,plain,
! [X2908,X2909] :
( ~ class_Rings_Ocomm__semiring__1(X2909)
| c_Groups_Oplus__class_Oplus(X2909,X2908,c_Groups_Ozero__class_Ozero(X2909)) = X2908 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2174,plain,
! [X5365,X5366] :
( ~ class_Rings_Ocomm__semiring__1(X5366)
| c_Rings_Odvd__class_Odvd(X5366,X5365,c_Groups_Ozero__class_Ozero(X5366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_2175,plain,
! [X2952,X2953] :
( ~ class_Power_Opower(X2953)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2953),X2952),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2176,plain,
! [X2950,X2951] :
( ~ class_Rings_Ocomm__semiring__1(X2951)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2951),X2950),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2951) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2177,plain,
! [X3811,X3812] :
( ~ class_Groups_Ocomm__monoid__mult(X3812)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3812),X3811),c_Groups_Oone__class_Oone(X3812)) = X3811 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2178,plain,
! [X3068,X3069] :
( ~ class_Rings_Ocomm__semiring__1(X3069)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3069),X3068),c_Groups_Oone__class_Oone(X3069)) = X3068 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2179,plain,
! [X3813,X3814] :
( ~ class_Groups_Omonoid__mult(X3814)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3814),X3813),c_Groups_Oone__class_Oone(X3814)) = X3813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2180,plain,
! [X3947,X3948] :
( ~ class_Groups_Ogroup__add(X3948)
| c_Groups_Ominus__class_Ominus(X3948,X3947,X3947) = c_Groups_Ozero__class_Ozero(X3948) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2181,plain,
! [X4943,X4944,X4945] :
( ~ class_Orderings_Opreorder(X4945)
| X4944 != X4943
| c_Orderings_Oord__class_Oless__eq(X4945,X4944,X4943) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2182,plain,
! [X3319,X3320,X3321] :
( ~ class_Rings_Odivision__ring(X3321)
| c_Rings_Oinverse__class_Oinverse(X3321,X3320) != c_Rings_Oinverse__class_Oinverse(X3321,X3319)
| X3320 = c_Groups_Ozero__class_Ozero(X3321)
| X3319 = c_Groups_Ozero__class_Ozero(X3321)
| X3320 = X3319 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).
fof(i_0_2183,plain,
! [X3085,X3086] :
( ~ class_Rings_Ocomm__semiring__1(X3086)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3086),X3085),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3085 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2184,plain,
! [X3087,X3088] :
( ~ class_Groups_Omonoid__mult(X3088)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3088),X3087),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3087 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2185,plain,
! [X5170] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X5170)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2186,plain,
! [X5133] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X5133)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2187,plain,
! [X4925,X4926] :
( ~ class_Orderings_Opreorder(X4926)
| c_Orderings_Oord__class_Oless__eq(X4926,X4925,X4925) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_2188,plain,
! [X5332,X5333] :
( ~ class_Rings_Olinordered__idom(X5333)
| c_Groups_Osgn__class_Osgn(X5333,c_Groups_Osgn__class_Osgn(X5333,X5332)) = c_Groups_Osgn__class_Osgn(X5333,X5332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).
fof(i_0_2189,plain,
! [X4455,X4456] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4456)
| c_Groups_Oabs__class_Oabs(X4456,c_Groups_Oabs__class_Oabs(X4456,X4455)) = c_Groups_Oabs__class_Oabs(X4456,X4455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_2190,plain,
! [X4418,X4419] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4419)
| c_Groups_Oabs__class_Oabs(X4419,c_Groups_Ouminus__class_Ouminus(X4419,X4418)) = c_Groups_Oabs__class_Oabs(X4419,X4418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(i_0_2191,plain,
! [X4059,X4060] :
( ~ class_RealVector_Oreal__normed__vector(X4060)
| c_RealVector_Onorm__class_Onorm(X4060,c_Groups_Ouminus__class_Ouminus(X4060,X4059)) = c_RealVector_Onorm__class_Onorm(X4060,X4059) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
fof(i_0_2192,plain,
! [X4730,X4731,X4732] :
( ( c_Polynomial_Opoly(X4732,X4731) != c_Polynomial_Opoly(X4732,X4730)
| X4731 = X4730
| ~ class_Int_Oring__char__0(X4732)
| ~ class_Rings_Oidom(X4732) )
& ( X4731 != X4730
| c_Polynomial_Opoly(X4732,X4731) = c_Polynomial_Opoly(X4732,X4730)
| ~ class_Int_Oring__char__0(X4732)
| ~ class_Rings_Oidom(X4732) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2193,plain,
! [X5300,X5301] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5301)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5301),X5300),X5300) = X5300 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_2194,plain,
! [X5298,X5299] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5299)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5299),X5298),X5298) = X5298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_2195,plain,
! [X3332] :
( X3332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2196,plain,
! [X4464,X4465] :
( ~ class_RealVector_Oreal__normed__vector(X4465)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4465,X4464)) = c_RealVector_Onorm__class_Onorm(X4465,X4464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(i_0_2197,plain,
! [X4521,X4522] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4522)
| c_RealVector_Onorm__class_Onorm(X4522,c_RealVector_Oof__real(X4522,X4521)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(i_0_2198,plain,
! [X5214] :
( ~ class_Rings_Olinordered__idom(X5214)
| ~ c_Polynomial_Opos__poly(X5214,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5214))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1329])]) ).
fof(i_0_2199,plain,
! [X4208] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4208) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2200,plain,
! [X5356,X5357] :
( ( X5356 != c_Groups_Ozero__class_Ozero(X5357)
| c_RealVector_Onorm__class_Onorm(X5357,c_Groups_Osgn__class_Osgn(X5357,X5356)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5357) )
& ( X5356 = c_Groups_Ozero__class_Ozero(X5357)
| c_RealVector_Onorm__class_Onorm(X5357,c_Groups_Osgn__class_Osgn(X5357,X5356)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5357) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__sgn])])]) ).
fof(i_0_2201,plain,
! [X4597] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4597) = X4597,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2202,plain,
! [X3356] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3356) = X3356,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2203,plain,
! [X4207] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4207,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4207,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2204,plain,
! [X4599] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4599,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4599,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2205,plain,
! [X3357] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3357,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3357,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2206,plain,
! [X3146,X3147] :
( X3147 != X3146
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3147,X3146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2207,plain,
! [X3164] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3164),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2208,plain,
! [X3135] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3135),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2209,plain,
! [X4727] :
( ~ class_Groups_Oab__group__add(X4727)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4727),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4727))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4727)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2210,plain,
! [X4206] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4206,X4206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2211,plain,
! [X3234] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2212,plain,
! [X3939,X3940,X3941] :
( ( c_RealVector_Oof__real(X3941,X3940) != c_RealVector_Oof__real(X3941,X3939)
| X3940 = X3939
| ~ class_RealVector_Oreal__algebra__1(X3941) )
& ( X3940 != X3939
| c_RealVector_Oof__real(X3941,X3940) = c_RealVector_Oof__real(X3941,X3939)
| ~ class_RealVector_Oreal__algebra__1(X3941) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__iff])])]) ).
fof(i_0_2213,plain,
! [X5311,X5312,X5313] :
( ( c_Groups_Ouminus__class_Ouminus(X5313,X5312) != c_Groups_Ouminus__class_Ouminus(X5313,X5311)
| X5312 = X5311
| ~ class_Lattices_Oboolean__algebra(X5313) )
& ( X5312 != X5311
| c_Groups_Ouminus__class_Ouminus(X5313,X5312) = c_Groups_Ouminus__class_Ouminus(X5313,X5311)
| ~ class_Lattices_Oboolean__algebra(X5313) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_2214,plain,
! [X3918,X3919,X3920] :
( ( c_Groups_Ouminus__class_Ouminus(X3920,X3919) != c_Groups_Ouminus__class_Ouminus(X3920,X3918)
| X3919 = X3918
| ~ class_Groups_Ogroup__add(X3920) )
& ( X3919 != X3918
| c_Groups_Ouminus__class_Ouminus(X3920,X3919) = c_Groups_Ouminus__class_Ouminus(X3920,X3918)
| ~ class_Groups_Ogroup__add(X3920) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2215,plain,
! [X3284,X3285,X3286] :
( ( c_Rings_Oinverse__class_Oinverse(X3286,X3285) != c_Rings_Oinverse__class_Oinverse(X3286,X3284)
| X3285 = X3284
| ~ class_Rings_Odivision__ring__inverse__zero(X3286) )
& ( X3285 != X3284
| c_Rings_Oinverse__class_Oinverse(X3286,X3285) = c_Rings_Oinverse__class_Oinverse(X3286,X3284)
| ~ class_Rings_Odivision__ring__inverse__zero(X3286) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq])])]) ).
fof(i_0_2216,plain,
! [X3281,X3282,X3283] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3283)
| c_Rings_Oinverse__class_Oinverse(X3283,X3282) != c_Rings_Oinverse__class_Oinverse(X3283,X3281)
| X3282 = X3281 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq])]) ).
fof(i_0_2217,plain,
! [X3324,X3325] :
( ~ class_Rings_Odivision__ring(X3325)
| X3324 = c_Groups_Ozero__class_Ozero(X3325)
| c_Rings_Oinverse__class_Oinverse(X3325,c_Rings_Oinverse__class_Oinverse(X3325,X3324)) = X3324 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).
fof(i_0_2218,plain,
! [X4443] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4443) = X4443,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2219,plain,
! [X3289] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3289) = X3289,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2220,plain,
! [X3406] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3406) = X3406,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2221,plain,
! [X4648] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4648,X4648),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2222,plain,
! [X3136] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3136,X3136),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2223,plain,
! [X3242] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3242,X3242),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2224,plain,
! [X3233] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3233),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).
fof(i_0_2225,plain,
! [X4442] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4442),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4442,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2226,plain,
! [X3292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3292),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3292,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2227,plain,
! [X5305,X5306] :
( ~ class_Lattices_Oboolean__algebra(X5306)
| c_Groups_Ouminus__class_Ouminus(X5306,c_Groups_Ouminus__class_Ouminus(X5306,X5305)) = X5305 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_2228,plain,
! [X3907,X3908] :
( ~ class_Groups_Ogroup__add(X3908)
| c_Groups_Ouminus__class_Ouminus(X3908,c_Groups_Ouminus__class_Ouminus(X3908,X3907)) = X3907 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2229,plain,
! [X3287,X3288] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3288)
| c_Rings_Oinverse__class_Oinverse(X3288,c_Rings_Oinverse__class_Oinverse(X3288,X3287)) = X3287 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
fof(i_0_2230,plain,
! [X5204] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5204)) = c_RealDef_Oreal(tc_Nat_Onat,X5204),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(i_0_2231,plain,
! [X3915,X3916,X3917] :
( ( c_Groups_Ouminus__class_Ouminus(X3917,X3916) != X3915
| c_Groups_Ouminus__class_Ouminus(X3917,X3915) = X3916
| ~ class_Groups_Ogroup__add(X3917) )
& ( c_Groups_Ouminus__class_Ouminus(X3917,X3915) != X3916
| c_Groups_Ouminus__class_Ouminus(X3917,X3916) = X3915
| ~ class_Groups_Ogroup__add(X3917) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2232,plain,
! [X3912,X3913,X3914] :
( ( X3913 != c_Groups_Ouminus__class_Ouminus(X3914,X3912)
| X3912 = c_Groups_Ouminus__class_Ouminus(X3914,X3913)
| ~ class_Groups_Ogroup__add(X3914) )
& ( X3912 != c_Groups_Ouminus__class_Ouminus(X3914,X3913)
| X3913 = c_Groups_Ouminus__class_Ouminus(X3914,X3912)
| ~ class_Groups_Ogroup__add(X3914) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2233,plain,
! [X4691,X4692] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4692,X4691) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4691 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4692))
| ~ class_Groups_Ozero(X4692) )
& ( X4691 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4692))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4692,X4691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X4692) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2234,plain,
! [X5211,X5212] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5212) != c_RealDef_Oreal(tc_Nat_Onat,X5211)
| X5212 = X5211 )
& ( X5212 != X5211
| c_RealDef_Oreal(tc_Nat_Onat,X5212) = c_RealDef_Oreal(tc_Nat_Onat,X5211) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2235,plain,
! [X3961,X3962] :
( ( c_Groups_Ozero__class_Ozero(X3962) != c_Groups_Ouminus__class_Ouminus(X3962,X3961)
| c_Groups_Ozero__class_Ozero(X3962) = X3961
| ~ class_Groups_Ogroup__add(X3962) )
& ( c_Groups_Ozero__class_Ozero(X3962) != X3961
| c_Groups_Ozero__class_Ozero(X3962) = c_Groups_Ouminus__class_Ouminus(X3962,X3961)
| ~ class_Groups_Ogroup__add(X3962) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_2236,plain,
! [X5338,X5339] :
( ( c_Groups_Osgn__class_Osgn(X5339,X5338) != c_Groups_Ozero__class_Ozero(X5339)
| X5338 = c_Groups_Ozero__class_Ozero(X5339)
| ~ class_Rings_Olinordered__idom(X5339) )
& ( X5338 != c_Groups_Ozero__class_Ozero(X5339)
| c_Groups_Osgn__class_Osgn(X5339,X5338) = c_Groups_Ozero__class_Ozero(X5339)
| ~ class_Rings_Olinordered__idom(X5339) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).
fof(i_0_2237,plain,
! [X5336,X5337] :
( ( c_Groups_Osgn__class_Osgn(X5337,X5336) != c_Groups_Ozero__class_Ozero(X5337)
| X5336 = c_Groups_Ozero__class_Ozero(X5337)
| ~ class_RealVector_Oreal__normed__vector(X5337) )
& ( X5336 != c_Groups_Ozero__class_Ozero(X5337)
| c_Groups_Osgn__class_Osgn(X5337,X5336) = c_Groups_Ozero__class_Ozero(X5337)
| ~ class_RealVector_Oreal__normed__vector(X5337) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff])])]) ).
fof(i_0_2238,plain,
! [X4444,X4445] :
( ( c_Groups_Oabs__class_Oabs(X4445,X4444) != c_Groups_Ozero__class_Ozero(X4445)
| X4444 = c_Groups_Ozero__class_Ozero(X4445)
| ~ class_Groups_Oordered__ab__group__add__abs(X4445) )
& ( X4444 != c_Groups_Ozero__class_Ozero(X4445)
| c_Groups_Oabs__class_Oabs(X4445,X4444) = c_Groups_Ozero__class_Ozero(X4445)
| ~ class_Groups_Oordered__ab__group__add__abs(X4445) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_2239,plain,
! [X3965,X3966] :
( ( c_Groups_Ouminus__class_Ouminus(X3966,X3965) != c_Groups_Ozero__class_Ozero(X3966)
| X3965 = c_Groups_Ozero__class_Ozero(X3966)
| ~ class_Groups_Ogroup__add(X3966) )
& ( X3965 != c_Groups_Ozero__class_Ozero(X3966)
| c_Groups_Ouminus__class_Ouminus(X3966,X3965) = c_Groups_Ozero__class_Ozero(X3966)
| ~ class_Groups_Ogroup__add(X3966) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2240,plain,
! [X3326,X3327] :
( ~ class_Rings_Odivision__ring(X3327)
| X3326 = c_Groups_Ozero__class_Ozero(X3327)
| c_Rings_Oinverse__class_Oinverse(X3327,X3326) != c_Groups_Ozero__class_Ozero(X3327) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).
fof(i_0_2241,plain,
! [X3322,X3323] :
( ~ class_Rings_Odivision__ring(X3323)
| c_Rings_Oinverse__class_Oinverse(X3323,X3322) != c_Groups_Ozero__class_Ozero(X3323)
| X3322 = c_Groups_Ozero__class_Ozero(X3323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).
fof(i_0_2242,plain,
! [X3328,X3329] :
( ( c_Rings_Oinverse__class_Oinverse(X3329,X3328) != c_Groups_Ozero__class_Ozero(X3329)
| X3328 = c_Groups_Ozero__class_Ozero(X3329)
| ~ class_Rings_Odivision__ring__inverse__zero(X3329) )
& ( X3328 != c_Groups_Ozero__class_Ozero(X3329)
| c_Rings_Oinverse__class_Oinverse(X3329,X3328) = c_Groups_Ozero__class_Ozero(X3329)
| ~ class_Rings_Odivision__ring__inverse__zero(X3329) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
fof(i_0_2243,plain,
! [X3366,X3367] :
( ( c_Rings_Oinverse__class_Oinverse(X3367,X3366) != c_Groups_Oone__class_Oone(X3367)
| X3366 = c_Groups_Oone__class_Oone(X3367)
| ~ class_Fields_Ofield__inverse__zero(X3367) )
& ( X3366 != c_Groups_Oone__class_Oone(X3367)
| c_Rings_Oinverse__class_Oinverse(X3367,X3366) = c_Groups_Oone__class_Oone(X3367)
| ~ class_Fields_Ofield__inverse__zero(X3367) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).
fof(i_0_2244,plain,
! [X4085,X4086] :
( ( c_RealVector_Oof__real(X4086,X4085) != c_Groups_Ozero__class_Ozero(X4086)
| X4085 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X4086) )
& ( X4085 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X4086,X4085) = c_Groups_Ozero__class_Ozero(X4086)
| ~ class_RealVector_Oreal__algebra__1(X4086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__0__iff])])]) ).
fof(i_0_2245,plain,
! [X2848,X2849] :
( ( c_RealVector_Onorm__class_Onorm(X2849,X2848) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2848 = c_Groups_Ozero__class_Ozero(X2849)
| ~ class_RealVector_Oreal__normed__vector(X2849) )
& ( X2848 != c_Groups_Ozero__class_Ozero(X2849)
| c_RealVector_Onorm__class_Onorm(X2849,X2848) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2849) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2246,plain,
! [X5464,X5465] :
( ~ class_Groups_Ouminus(X5465)
| class_Groups_Ouminus(tc_fun(X5464,X5465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_2247,plain,
! [X5466,X5467] :
( ~ class_Groups_Ominus(X5467)
| class_Groups_Ominus(tc_fun(X5466,X5467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_2248,plain,
! [X5456,X5457] :
( ~ class_Lattices_Oboolean__algebra(X5457)
| class_Lattices_Oboolean__algebra(tc_fun(X5456,X5457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_2249,plain,
! [X5460,X5461] :
( ~ class_Orderings_Oorder(X5461)
| class_Orderings_Oorder(tc_fun(X5460,X5461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2250,plain,
! [X5462,X5463] :
( ~ class_Orderings_Oord(X5463)
| class_Orderings_Oord(tc_fun(X5462,X5463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2251,plain,
! [X5458,X5459] :
( ~ class_Orderings_Opreorder(X5459)
| class_Orderings_Opreorder(tc_fun(X5458,X5459)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2252,plain,
! [X4634] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4634)) = X4634,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2253,plain,
! [X3967,X3968] :
( ( c_Groups_Ouminus__class_Ouminus(X3968,X3967) != X3967
| X3967 = c_Groups_Ozero__class_Ozero(X3968)
| ~ class_Groups_Olinordered__ab__group__add(X3968) )
& ( X3967 != c_Groups_Ozero__class_Ozero(X3968)
| c_Groups_Ouminus__class_Ouminus(X3968,X3967) = X3967
| ~ class_Groups_Olinordered__ab__group__add(X3968) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2254,plain,
! [X3963,X3964] :
( ( X3963 != c_Groups_Ouminus__class_Ouminus(X3964,X3963)
| X3963 = c_Groups_Ozero__class_Ozero(X3964)
| ~ class_Groups_Olinordered__ab__group__add(X3964) )
& ( X3963 != c_Groups_Ozero__class_Ozero(X3964)
| X3963 = c_Groups_Ouminus__class_Ouminus(X3964,X3963)
| ~ class_Groups_Olinordered__ab__group__add(X3964) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2255,plain,
! [X4087] :
( ~ class_RealVector_Oreal__algebra__1(X4087)
| ~ class_RealVector_Oreal__normed__vector(X4087)
| c_RealVector_Oof__real(X4087,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X4087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ozero])]) ).
fof(i_0_2256,plain,
! [X5334] :
( ~ class_Groups_Osgn__if(X5334)
| c_Groups_Osgn__class_Osgn(X5334,c_Groups_Ozero__class_Ozero(X5334)) = c_Groups_Ozero__class_Ozero(X5334) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).
fof(i_0_2257,plain,
! [X5335] :
( ~ class_RealVector_Oreal__normed__vector(X5335)
| c_Groups_Osgn__class_Osgn(X5335,c_Groups_Ozero__class_Ozero(X5335)) = c_Groups_Ozero__class_Ozero(X5335) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero])]) ).
fof(i_0_2258,plain,
! [X5323] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5323)
| c_Groups_Osgn__class_Osgn(X5323,c_Groups_Oone__class_Oone(X5323)) = c_Groups_Oone__class_Oone(X5323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__one])]) ).
fof(i_0_2259,plain,
! [X4446] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4446)
| c_Groups_Oabs__class_Oabs(X4446,c_Groups_Ozero__class_Ozero(X4446)) = c_Groups_Ozero__class_Ozero(X4446) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_2260,plain,
! [X4462] :
( ~ class_Rings_Olinordered__idom(X4462)
| c_Groups_Oabs__class_Oabs(X4462,c_Groups_Oone__class_Oone(X4462)) = c_Groups_Oone__class_Oone(X4462) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_2261,plain,
! [X3960] :
( ~ class_Groups_Ogroup__add(X3960)
| c_Groups_Ouminus__class_Ouminus(X3960,c_Groups_Ozero__class_Ozero(X3960)) = c_Groups_Ozero__class_Ozero(X3960) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2262,plain,
! [X3331] :
( ~ class_Fields_Ofield__inverse__zero(X3331)
| c_Rings_Oinverse__class_Oinverse(X3331,c_Groups_Ozero__class_Ozero(X3331)) = c_Groups_Ozero__class_Ozero(X3331) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).
fof(i_0_2263,plain,
! [X3330] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3330)
| c_Rings_Oinverse__class_Oinverse(X3330,c_Groups_Ozero__class_Ozero(X3330)) = c_Groups_Ozero__class_Ozero(X3330) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).
fof(i_0_2264,plain,
! [X3365] :
( ~ class_Rings_Odivision__ring(X3365)
| c_Rings_Oinverse__class_Oinverse(X3365,c_Groups_Oone__class_Oone(X3365)) = c_Groups_Oone__class_Oone(X3365) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).
fof(i_0_2265,plain,
! [X2841] :
( ~ class_RealVector_Oreal__normed__vector(X2841)
| c_RealVector_Onorm__class_Onorm(X2841,c_Groups_Ozero__class_Ozero(X2841)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2266,plain,
! [X2814] :
( ~ class_RealVector_Oreal__normed__algebra__1(X2814)
| c_RealVector_Onorm__class_Onorm(X2814,c_Groups_Oone__class_Oone(X2814)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2267,plain,
! [X4088] :
( ~ class_RealVector_Oreal__algebra__1(X4088)
| c_RealVector_Oof__real(X4088,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X4088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__0])]) ).
fof(i_0_2268,plain,
! [X4139] :
( ~ class_RealVector_Oreal__algebra__1(X4139)
| c_RealVector_Oof__real(X4139,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X4139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])]) ).
fof(i_0_2269,plain,
! [X5231] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X5231)) = X5231,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2270,plain,
! [X5227] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X5227)) = X5227,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2271,plain,
! [X5213] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5213) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X5213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X5213) = 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_2272,plain,
! [X4463] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4463) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4463),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(i_0_2273,plain,
! [X3309] :
( ~ class_Rings_Ozero__neq__one(X3309)
| c_Groups_Ozero__class_Ozero(X3309) != c_Groups_Oone__class_Oone(X3309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2274,plain,
! [X3308] :
( ~ class_Rings_Ozero__neq__one(X3308)
| c_Groups_Oone__class_Oone(X3308) != c_Groups_Ozero__class_Ozero(X3308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2275,plain,
! [X5455] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5455)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5455)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2276,plain,
! [X5527] :
( ~ class_Rings_Ocomm__semiring__1(X5527)
| class_Rings_Odvd(tc_Polynomial_Opoly(X5527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd])]) ).
fof(i_0_2277,plain,
! [X5518] :
( ~ class_Rings_Olinordered__idom(X5518)
| class_Groups_Osgn__if(tc_Polynomial_Opoly(X5518)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if])]) ).
fof(i_0_2278,plain,
! [X5517] :
( ~ class_Groups_Oab__group__add(X5517)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X5517)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).
fof(i_0_2279,plain,
! [X5521] :
( ~ class_Groups_Oab__group__add(X5521)
| class_Groups_Ominus(tc_Polynomial_Opoly(X5521)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])]) ).
fof(i_0_2280,plain,
! [X5513] :
( ~ class_Rings_Olinordered__idom(X5513)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2281,plain,
! [X5505] :
( ~ class_Rings_Olinordered__idom(X5505)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2282,plain,
! [X5516] :
( ~ class_Rings_Olinordered__idom(X5516)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2283,plain,
! [X5504] :
( ~ class_Rings_Olinordered__idom(X5504)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2284,plain,
! [X5512] :
( ~ class_Rings_Ocomm__ring(X5512)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2285,plain,
! [X5514] :
( ~ class_Rings_Olinordered__idom(X5514)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2286,plain,
! [X5499] :
( ~ class_Rings_Ocomm__semiring__0(X5499)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2287,plain,
! [X5519] :
( ~ class_Rings_Olinordered__idom(X5519)
| class_Groups_Oabs__if(tc_Polynomial_Opoly(X5519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if])]) ).
fof(i_0_2288,plain,
! [X5493] :
( ~ class_Rings_Olinordered__idom(X5493)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X5493)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs])]) ).
fof(i_0_2289,plain,
! [X5475] :
( ~ class_Rings_Olinordered__idom(X5475)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X5475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])]) ).
fof(i_0_2290,plain,
! [X5520] :
( ~ class_Rings_Ocomm__ring__1(X5520)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2291,plain,
! [X5525] :
( ~ class_Rings_Oidom(X5525)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2292,plain,
! [X5524] :
( ~ class_Rings_Ocomm__ring(X5524)
| class_Rings_Oring(tc_Polynomial_Opoly(X5524)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2293,plain,
! [X5485] :
( ~ class_Rings_Olinordered__idom(X5485)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2294,plain,
! [X5507] :
( ~ class_Rings_Ocomm__ring__1(X5507)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2295,plain,
! [X5501] :
( ~ class_Groups_Oab__group__add(X5501)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2296,plain,
! [X5510] :
( ~ class_Groups_Oab__group__add(X5510)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2297,plain,
! [X5469] :
( ~ class_Rings_Olinordered__idom(X5469)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2298,plain,
! [X5474] :
( ~ class_Rings_Olinordered__idom(X5474)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2299,plain,
! [X5470] :
( ~ class_Rings_Olinordered__idom(X5470)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2300,plain,
! [X5477] :
( ~ class_Rings_Olinordered__idom(X5477)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2301,plain,
! [X5508] :
( ~ class_Groups_Ocomm__monoid__add(X5508)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2302,plain,
! [X5495] :
( ~ class_Groups_Ocomm__monoid__add(X5495)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5495)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2303,plain,
! [X5526] :
( ~ class_Rings_Ocomm__semiring__1(X5526)
| class_Groups_Oone(tc_Polynomial_Opoly(X5526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2304,plain,
! [X5491] :
( ~ class_Groups_Ocomm__monoid__add(X5491)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2305,plain,
! [X5478] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5478)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2306,plain,
! [X5486] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5486)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2307,plain,
! [X5489] :
( ~ class_Rings_Ocomm__semiring__0(X5489)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2308,plain,
! [X5523] :
( ~ class_Groups_Ozero(X5523)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2309,plain,
! [X5476] :
( ~ class_Rings_Olinordered__idom(X5476)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2310,plain,
! [X5487] :
( ~ class_Rings_Olinordered__idom(X5487)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5487)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2311,plain,
! [X5471] :
( ~ class_Rings_Olinordered__idom(X5471)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2312,plain,
! [X5473] :
( ~ class_Rings_Olinordered__idom(X5473)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2313,plain,
! [X5496] :
( ~ class_Rings_Olinordered__idom(X5496)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2314,plain,
! [X5481] :
( ~ class_Rings_Olinordered__idom(X5481)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2315,plain,
! [X5483] :
( ~ class_Rings_Olinordered__idom(X5483)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2316,plain,
! [X5492] :
( ~ class_Rings_Olinordered__idom(X5492)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2317,plain,
! [X5503] :
( ~ class_Rings_Olinordered__idom(X5503)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2318,plain,
! [X5480] :
( ~ class_Rings_Olinordered__idom(X5480)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2319,plain,
! [X5515] :
( ~ class_Rings_Ocomm__semiring__0(X5515)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2320,plain,
! [X5500] :
( ~ class_Rings_Ocomm__semiring__0(X5500)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2321,plain,
! [X5482] :
( ~ class_Rings_Oidom(X5482)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2322,plain,
! [X5497] :
( ~ class_Rings_Olinordered__idom(X5497)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5497)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2323,plain,
! [X5484] :
( ~ class_Rings_Olinordered__idom(X5484)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2324,plain,
! [X5472] :
( ~ class_Rings_Olinordered__idom(X5472)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2325,plain,
! [X5490] :
( ~ class_Rings_Ocomm__semiring__1(X5490)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2326,plain,
! [X5509] :
( ~ class_Rings_Ocomm__semiring__0(X5509)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2327,plain,
! [X5479] :
( ~ class_Rings_Oidom(X5479)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2328,plain,
! [X5468] :
( ~ class_Rings_Oidom(X5468)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5468)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2329,plain,
! [X5502] :
( ~ class_Rings_Ocomm__semiring__1(X5502)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2330,plain,
! [X5494] :
( ~ class_Rings_Oidom(X5494)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5494)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2331,plain,
! [X5511] :
( ~ class_Rings_Ocomm__semiring__0(X5511)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2332,plain,
! [X5522] :
( ~ class_Rings_Ocomm__semiring__1(X5522)
| class_Power_Opower(tc_Polynomial_Opoly(X5522)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2333,plain,
! [X5498] :
( ~ class_Rings_Ocomm__semiring__1(X5498)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2334,plain,
! [X5506] :
( ~ class_Rings_Ocomm__semiring__1(X5506)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5506)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2335,plain,
! [X5488] :
( ~ class_Rings_Olinordered__idom(X5488)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).
cnf(i_0_2336,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(split_conjunct,[status(thm)],[fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096]),
[final] ).
cnf(i_0_2337,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
inference(split_conjunct,[status(thm)],[fact_th11]),
[final] ).
cnf(i_0_2338,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),
inference(split_conjunct,[status(thm)],[fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096]),
[final] ).
cnf(i_0_2339,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(split_conjunct,[status(thm)],[fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096]),
[final] ).
cnf(i_0_2340,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(split_conjunct,[status(thm)],[fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096]),
[final] ).
cnf(i_0_2341,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(split_conjunct,[status(thm)],[fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096]),
[final] ).
cnf(i_0_2342,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(split_conjunct,[status(thm)],[i_0_1330]),
[final] ).
cnf(i_0_2343,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,esk27_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_1331]),
[final] ).
cnf(i_0_2344,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_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1332]),
[final] ).
cnf(i_0_2345,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1333]),
[final] ).
cnf(i_0_2346,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X2)),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_1334]),
[final] ).
cnf(i_0_2347,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
inference(split_conjunct,[status(thm)],[i_0_1332]),
[final] ).
cnf(i_0_2348,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),esk22_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk23_0,esk24_0)),X1))),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_2349,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X1))),
inference(split_conjunct,[status(thm)],[i_0_1336]),
[final] ).
cnf(i_0_2350,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk17_0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1337]),
[final] ).
cnf(i_0_2351,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096]),
[final] ).
cnf(i_0_2352,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),X1)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[i_0_1338]),
[final] ).
cnf(i_0_2353,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096]),
[final] ).
cnf(i_0_2354,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk25_4(X3,X2,X4,X1)),hAPP(X3,esk25_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1339]),
[final] ).
cnf(i_0_2355,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(split_conjunct,[status(thm)],[fact_inv0]),
[final] ).
cnf(i_0_2356,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_2357,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(split_conjunct,[status(thm)],[fact_t_I3_J]),
[final] ).
cnf(i_0_2358,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X4)),X5)),hAPP(hAPP(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_1341]),
[final] ).
cnf(i_0_2359,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_1342]),
[final] ).
cnf(i_0_2360,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk18_0) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),esk19_0),
inference(split_conjunct,[status(thm)],[i_0_1343]),
[final] ).
cnf(i_0_2361,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Osynthetic__div(X1,X3,X2)),c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = X3
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1344]),
[final] ).
cnf(i_0_2362,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1345]),
[final] ).
cnf(i_0_2363,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1346]),
[final] ).
cnf(i_0_2364,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1347]),
[final] ).
cnf(i_0_2365,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5),X2),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X4)),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1348]),
[final] ).
cnf(i_0_2366,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1349]),
[final] ).
cnf(i_0_2367,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1350]),
[final] ).
cnf(i_0_2368,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1351]),
[final] ).
cnf(i_0_2369,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2370,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(split_conjunct,[status(thm)],[i_0_1353]),
[final] ).
cnf(i_0_2371,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X2,X3)),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1354]),
[final] ).
cnf(i_0_2372,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1345]),
[final] ).
cnf(i_0_2373,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1346]),
[final] ).
cnf(i_0_2374,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1347]),
[final] ).
cnf(i_0_2375,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1348]),
[final] ).
cnf(i_0_2376,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1349]),
[final] ).
cnf(i_0_2377,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1350]),
[final] ).
cnf(i_0_2378,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1351]),
[final] ).
cnf(i_0_2379,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2380,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_1355]),
[final] ).
cnf(i_0_2381,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk7_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1356]),
[final] ).
cnf(i_0_2382,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_1357]),
[final] ).
cnf(i_0_2383,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)),esk33_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_1358]),
[final] ).
cnf(i_0_2384,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(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_1359]),
[final] ).
cnf(i_0_2385,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1360]),
[final] ).
cnf(i_0_2386,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1361]),
[final] ).
cnf(i_0_2387,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,c_Groups_Oone__class_Oone(X1),X2)),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1362]),
[final] ).
cnf(i_0_2388,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),esk20_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1363]),
[final] ).
cnf(i_0_2389,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1364]),
[final] ).
cnf(i_0_2390,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2391,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))),
inference(split_conjunct,[status(thm)],[i_0_1366]),
[final] ).
cnf(i_0_2392,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1367]),
[final] ).
cnf(i_0_2393,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5),X6))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1368]),
[final] ).
cnf(i_0_2394,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))),esk30_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_2395,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1370]),
[final] ).
cnf(i_0_2396,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_2397,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1372]),
[final] ).
cnf(i_0_2398,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3),X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1373]),
[final] ).
cnf(i_0_2399,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4),X5)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1374]),
[final] ).
cnf(i_0_2400,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X5) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(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_1375]),
[final] ).
cnf(i_0_2401,plain,
( c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5),X1) = c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5),X6)
| X1 != c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(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_1376]),
[final] ).
cnf(i_0_2402,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_1377]),
[final] ).
cnf(i_0_2403,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X5)),hAPP(hAPP(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_1378]),
[final] ).
cnf(i_0_2404,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),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_1379]),
[final] ).
cnf(i_0_2405,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1364]),
[final] ).
cnf(i_0_2406,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2407,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4)),X2),X3) = X5
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1373]),
[final] ).
cnf(i_0_2408,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1)),X2),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1374]),
[final] ).
cnf(i_0_2409,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4) = X6
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1375]),
[final] ).
cnf(i_0_2410,plain,
( X4 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X5,X2)),X3),X6)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1376]),
[final] ).
cnf(i_0_2411,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1380]),
[final] ).
cnf(i_0_2412,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096]),
[final] ).
cnf(i_0_2413,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,esk27_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_1331]),
[final] ).
cnf(i_0_2414,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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(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_1381]),
[final] ).
cnf(i_0_2415,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Groups_Oplus__class_Oplus(X1,X2,X3))),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1382]),
[final] ).
cnf(i_0_2416,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)
| ~ class_Rings_Olinordered__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1383]),
[final] ).
cnf(i_0_2417,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4)),X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1384]),
[final] ).
cnf(i_0_2418,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk38_3(X2,X4,X1))))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X4,X3))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1385]),
[final] ).
cnf(i_0_2419,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),X2),X4),
inference(split_conjunct,[status(thm)],[i_0_1386]),
[final] ).
cnf(i_0_2420,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)),X4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1387]),
[final] ).
cnf(i_0_2421,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1388]),
[final] ).
cnf(i_0_2422,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1389]),
[final] ).
cnf(i_0_2423,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_2424,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_2425,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]),
[final] ).
cnf(i_0_2426,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_r01]),
[final] ).
cnf(i_0_2427,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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2)),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ 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,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1392]),
[final] ).
cnf(i_0_2428,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2429,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2430,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1395]),
[final] ).
cnf(i_0_2431,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1396]),
[final] ).
cnf(i_0_2432,plain,
( X1 = X2
| X3 = X4
| c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4)) != c_Groups_Oplus__class_Oplus(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1397]),
[final] ).
cnf(i_0_2433,plain,
( X2 = X4
| X3 = X5
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_2434,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_1399]),
[final] ).
cnf(i_0_2435,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(split_conjunct,[status(thm)],[fact_th02]),
[final] ).
cnf(i_0_2436,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_OpCons(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1400]),
[final] ).
cnf(i_0_2437,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1401]),
[final] ).
cnf(i_0_2438,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,esk37_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1385]),
[final] ).
cnf(i_0_2439,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1402]),
[final] ).
cnf(i_0_2440,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1403]),
[final] ).
cnf(i_0_2441,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_1404]),
[final] ).
cnf(i_0_2442,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_1405]),
[final] ).
cnf(i_0_2443,plain,
( c_Polynomial_Opcompose(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),c_Polynomial_Opcompose(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1406]),
[final] ).
cnf(i_0_2444,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2445,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1408]),
[final] ).
cnf(i_0_2446,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_1409]),
[final] ).
cnf(i_0_2447,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_1410]),
[final] ).
cnf(i_0_2448,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1411]),
[final] ).
cnf(i_0_2449,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk9_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2450,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk8_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2451,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2452,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,esk9_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2453,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,esk8_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2454,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)),c_Polynomial_Omonom(X1,X4,X5)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_2455,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1416]),
[final] ).
cnf(i_0_2456,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_1417]),
[final] ).
cnf(i_0_2457,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_1418]),
[final] ).
cnf(i_0_2458,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk24_0),esk22_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_2459,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[fact_kas_I3_J]),
[final] ).
cnf(i_0_2460,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_1419]),
[final] ).
cnf(i_0_2461,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2462,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_1399]),
[final] ).
cnf(i_0_2463,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_1399]),
[final] ).
cnf(i_0_2464,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_1421]),
[final] ).
cnf(i_0_2465,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_1422]),
[final] ).
cnf(i_0_2466,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2467,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2468,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1425]),
[final] ).
cnf(i_0_2469,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1426]),
[final] ).
cnf(i_0_2470,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2471,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1428]),
[final] ).
cnf(i_0_2472,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(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_1429]),
[final] ).
cnf(i_0_2473,plain,
( hBOOL(hAPP(X1,esk37_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Osemiring__0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1385]),
[final] ).
cnf(i_0_2474,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3))) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2475,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_2476,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1432]),
[final] ).
cnf(i_0_2477,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_2478,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1388]),
[final] ).
cnf(i_0_2479,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1388]),
[final] ).
cnf(i_0_2480,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2481,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2482,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2483,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2484,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1437]),
[final] ).
cnf(i_0_2485,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1438]),
[final] ).
cnf(i_0_2486,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2487,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1440]),
[final] ).
cnf(i_0_2488,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1441]),
[final] ).
cnf(i_0_2489,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1442]),
[final] ).
cnf(i_0_2490,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1443]),
[final] ).
cnf(i_0_2491,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1444]),
[final] ).
cnf(i_0_2492,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1445]),
[final] ).
cnf(i_0_2493,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2494,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2495,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2496,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1449]),
[final] ).
cnf(i_0_2497,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1450]),
[final] ).
cnf(i_0_2498,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1451]),
[final] ).
cnf(i_0_2499,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1452]),
[final] ).
cnf(i_0_2500,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X5)) = c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1453]),
[final] ).
cnf(i_0_2501,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]),
[final] ).
cnf(i_0_2502,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_1455]),
[final] ).
cnf(i_0_2503,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_1456]),
[final] ).
cnf(i_0_2504,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_1457]),
[final] ).
cnf(i_0_2505,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1458]),
[final] ).
cnf(i_0_2506,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1459]),
[final] ).
cnf(i_0_2507,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1460]),
[final] ).
cnf(i_0_2508,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2509,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2510,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),esk28_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2511,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(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_1464]),
[final] ).
cnf(i_0_2512,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),esk29_2(X2,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_2513,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1466]),
[final] ).
cnf(i_0_2514,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1467]),
[final] ).
cnf(i_0_2515,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_2516,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1469]),
[final] ).
cnf(i_0_2517,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1470]),
[final] ).
cnf(i_0_2518,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]),
[final] ).
cnf(i_0_2519,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1472]),
[final] ).
cnf(i_0_2520,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2521,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2522,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2523,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2524,plain,
( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1397]),
[final] ).
cnf(i_0_2525,plain,
( c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_2526,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2527,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2528,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1473]),
[final] ).
cnf(i_0_2529,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1474]),
[final] ).
cnf(i_0_2530,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1475]),
[final] ).
cnf(i_0_2531,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_1421]),
[final] ).
cnf(i_0_2532,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_1422]),
[final] ).
cnf(i_0_2533,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_1476]),
[final] ).
cnf(i_0_2534,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_1477]),
[final] ).
cnf(i_0_2535,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_1478]),
[final] ).
cnf(i_0_2536,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_1479]),
[final] ).
cnf(i_0_2537,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X5 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X4
| c_Groups_Oplus__class_Oplus(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)) != c_Groups_Oplus__class_Oplus(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1480]),
[final] ).
cnf(i_0_2538,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_2540,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2541,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2542,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1485]),
[final] ).
cnf(i_0_2543,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_2544,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1487]),
[final] ).
cnf(i_0_2545,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_2546,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_1489]),
[final] ).
cnf(i_0_2547,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_1490]),
[final] ).
cnf(i_0_2548,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_1491]),
[final] ).
cnf(i_0_2549,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_1492]),
[final] ).
cnf(i_0_2550,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_1493]),
[final] ).
cnf(i_0_2551,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4) = c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2552,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_1495]),
[final] ).
cnf(i_0_2553,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_1496]),
[final] ).
cnf(i_0_2554,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_1412]),
[final] ).
cnf(i_0_2555,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_1413]),
[final] ).
cnf(i_0_2556,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_1412]),
[final] ).
cnf(i_0_2557,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_1413]),
[final] ).
cnf(i_0_2558,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_1497]),
[final] ).
cnf(i_0_2559,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_1497]),
[final] ).
cnf(i_0_2560,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1498]),
[final] ).
cnf(i_0_2561,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1499]),
[final] ).
cnf(i_0_2562,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2563,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2564,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2)),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1502]),
[final] ).
cnf(i_0_2565,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1503]),
[final] ).
cnf(i_0_2566,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_1504]),
[final] ).
cnf(i_0_2567,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_1505]),
[final] ).
cnf(i_0_2568,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_1506]),
[final] ).
cnf(i_0_2569,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_1507]),
[final] ).
cnf(i_0_2570,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_1508]),
[final] ).
cnf(i_0_2571,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_1509]),
[final] ).
cnf(i_0_2572,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_1510]),
[final] ).
cnf(i_0_2573,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_1511]),
[final] ).
cnf(i_0_2574,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_1512]),
[final] ).
cnf(i_0_2575,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2576,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2577,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk6_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1515]),
[final] ).
cnf(i_0_2578,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w]),
[final] ).
cnf(i_0_2579,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_1417]),
[final] ).
cnf(i_0_2580,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2581,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X3)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1517]),
[final] ).
cnf(i_0_2582,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_1518]),
[final] ).
cnf(i_0_2583,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_1519]),
[final] ).
cnf(i_0_2584,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_2585,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
inference(split_conjunct,[status(thm)],[fact_lgqr]),
[final] ).
cnf(i_0_2586,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk9_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_1412]),
[final] ).
cnf(i_0_2587,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk8_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_1413]),
[final] ).
cnf(i_0_2588,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2589,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1522]),
[final] ).
cnf(i_0_2590,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1523]),
[final] ).
cnf(i_0_2591,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_2592,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2593,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_2594,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_1527]),
[final] ).
cnf(i_0_2595,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk9_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_1412]),
[final] ).
cnf(i_0_2596,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk8_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_1413]),
[final] ).
cnf(i_0_2597,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1528]),
[final] ).
cnf(i_0_2598,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2599,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),c_RealVector_Onorm__class_Onorm(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2600,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2601,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2602,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__comm__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2603,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_2604,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2605,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2606,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2607,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2608,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2609,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2610,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1445]),
[final] ).
cnf(i_0_2611,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2612,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2613,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2614,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2615,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1540]),
[final] ).
cnf(i_0_2616,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2617,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2618,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2619,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_1542]),
[final] ).
cnf(i_0_2620,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_1543]),
[final] ).
cnf(i_0_2621,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_1544]),
[final] ).
cnf(i_0_2622,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_1545]),
[final] ).
cnf(i_0_2623,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_1546]),
[final] ).
cnf(i_0_2624,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1547]),
[final] ).
cnf(i_0_2625,plain,
( c_Orderings_Oord__class_Oless__eq(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2626,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2627,plain,
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1451]),
[final] ).
cnf(i_0_2628,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2629,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2630,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2631,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2632,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2633,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2634,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_2635,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1553]),
[final] ).
cnf(i_0_2636,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1554]),
[final] ).
cnf(i_0_2637,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2638,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2639,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_1557]),
[final] ).
cnf(i_0_2640,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_1558]),
[final] ).
cnf(i_0_2641,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_1559]),
[final] ).
cnf(i_0_2642,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_1560]),
[final] ).
cnf(i_0_2643,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_1561]),
[final] ).
cnf(i_0_2644,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(split_conjunct,[status(thm)],[fact_tw]),
[final] ).
cnf(i_0_2645,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2646,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2647,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_2648,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_2649,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1565]),
[final] ).
cnf(i_0_2650,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1566]),
[final] ).
cnf(i_0_2651,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_2652,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1568]),
[final] ).
cnf(i_0_2653,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2654,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2655,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2656,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1572]),
[final] ).
cnf(i_0_2657,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2658,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2659,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2660,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2661,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2662,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2663,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_1577]),
[final] ).
cnf(i_0_2664,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_1578]),
[final] ).
cnf(i_0_2665,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2666,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2667,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk32_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_1581]),
[final] ).
cnf(i_0_2668,plain,
( c_Polynomial_Osynthetic__div(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X3),X4),c_Polynomial_Osynthetic__div(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2669,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2670,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2671,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_2672,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2673,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1485]),
[final] ).
cnf(i_0_2674,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2675,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2676,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2677,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2678,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_2679,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2680,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2681,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_2682,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2683,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_1590]),
[final] ).
cnf(i_0_2684,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_1591]),
[final] ).
cnf(i_0_2685,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_1590]),
[final] ).
cnf(i_0_2686,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_1591]),
[final] ).
cnf(i_0_2687,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1592]),
[final] ).
cnf(i_0_2688,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_1593]),
[final] ).
cnf(i_0_2689,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_1594]),
[final] ).
cnf(i_0_2690,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_1595]),
[final] ).
cnf(i_0_2691,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_1596]),
[final] ).
cnf(i_0_2692,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_1597]),
[final] ).
cnf(i_0_2693,plain,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X5)) != c_Polynomial_OpCons(X2,X1,X5)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2694,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_2695,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2696,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2697,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2698,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2699,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2700,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2701,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2702,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2703,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2704,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2705,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1603]),
[final] ).
cnf(i_0_2706,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2707,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1605]),
[final] ).
cnf(i_0_2708,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_2709,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1607]),
[final] ).
cnf(i_0_2710,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2711,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_1609]),
[final] ).
cnf(i_0_2712,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2713,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2714,plain,
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_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2715,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_1612]),
[final] ).
cnf(i_0_2716,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_1613]),
[final] ).
cnf(i_0_2717,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_1614]),
[final] ).
cnf(i_0_2718,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_1615]),
[final] ).
cnf(i_0_2719,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_1616]),
[final] ).
cnf(i_0_2720,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_1617]),
[final] ).
cnf(i_0_2721,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_1618]),
[final] ).
cnf(i_0_2722,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_1619]),
[final] ).
cnf(i_0_2723,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_1620]),
[final] ).
cnf(i_0_2724,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2725,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2726,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2727,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2728,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2729,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2730,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2731,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2732,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2733,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2734,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2735,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2736,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2737,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2738,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2739,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2740,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2742,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2743,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2744,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2745,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2746,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2747,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_1638]),
[final] ).
cnf(i_0_2748,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_1504]),
[final] ).
cnf(i_0_2749,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_1639]),
[final] ).
cnf(i_0_2750,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_1506]),
[final] ).
cnf(i_0_2751,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_1640]),
[final] ).
cnf(i_0_2752,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_1508]),
[final] ).
cnf(i_0_2753,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_1641]),
[final] ).
cnf(i_0_2754,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_1510]),
[final] ).
cnf(i_0_2755,plain,
( 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_s____),X1)),esk11_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_2756,plain,
( 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_s____),X1)),esk10_0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2757,plain,
( 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_s____),X1)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_2758,plain,
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_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X1))),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_2759,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1646]),
[final] ).
cnf(i_0_2760,plain,
( c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2761,plain,
( c_SEQ_Odecseq(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk35_2(X2,X1)),hAPP(X2,esk34_2(X2,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_2762,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_1648]),
[final] ).
cnf(i_0_2763,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_1649]),
[final] ).
cnf(i_0_2764,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_1650]),
[final] ).
cnf(i_0_2765,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_1651]),
[final] ).
cnf(i_0_2766,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_1652]),
[final] ).
cnf(i_0_2767,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_1653]),
[final] ).
cnf(i_0_2768,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2769,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_1655]),
[final] ).
cnf(i_0_2770,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_1656]),
[final] ).
cnf(i_0_2771,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_1657]),
[final] ).
cnf(i_0_2772,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_1658]),
[final] ).
cnf(i_0_2773,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_1518]),
[final] ).
cnf(i_0_2774,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_1659]),
[final] ).
cnf(i_0_2775,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_1660]),
[final] ).
cnf(i_0_2776,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_1661]),
[final] ).
cnf(i_0_2777,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_1519]),
[final] ).
cnf(i_0_2778,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2779,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_2780,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)),esk36_1(X1)))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1664]),
[final] ).
cnf(i_0_2781,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)),esk26_1(X1)))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_2782,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X2)),esk21_1(X1)))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_2783,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_1667]),
[final] ).
cnf(i_0_2784,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_2785,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),X3,X4)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X3),X4)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2786,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2787,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X4)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2788,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_1672]),
[final] ).
cnf(i_0_2789,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_1673]),
[final] ).
cnf(i_0_2790,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_1674]),
[final] ).
cnf(i_0_2791,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_1675]),
[final] ).
cnf(i_0_2792,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2793,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_1677]),
[final] ).
cnf(i_0_2794,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_1678]),
[final] ).
cnf(i_0_2795,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_1679]),
[final] ).
cnf(i_0_2796,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_1680]),
[final] ).
cnf(i_0_2797,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_1681]),
[final] ).
cnf(i_0_2798,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_1682]),
[final] ).
cnf(i_0_2799,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_1683]),
[final] ).
cnf(i_0_2800,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_1684]),
[final] ).
cnf(i_0_2801,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_1685]),
[final] ).
cnf(i_0_2802,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_1686]),
[final] ).
cnf(i_0_2803,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_1687]),
[final] ).
cnf(i_0_2804,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_1688]),
[final] ).
cnf(i_0_2805,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_1689]),
[final] ).
cnf(i_0_2806,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_1690]),
[final] ).
cnf(i_0_2807,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_1691]),
[final] ).
cnf(i_0_2808,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2809,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_1693]),
[final] ).
cnf(i_0_2810,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2811,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_1695]),
[final] ).
cnf(i_0_2812,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_1696]),
[final] ).
cnf(i_0_2813,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_1697]),
[final] ).
cnf(i_0_2814,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Omonom(X1,X3,X4)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2815,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1699]),
[final] ).
cnf(i_0_2816,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_1700]),
[final] ).
cnf(i_0_2817,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_2818,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2819,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_2820,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X3)),X2) = c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_2821,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_2822,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_1706]),
[final] ).
cnf(i_0_2823,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_1706]),
[final] ).
cnf(i_0_2824,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_1707]),
[final] ).
cnf(i_0_2825,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_1707]),
[final] ).
cnf(i_0_2826,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
inference(split_conjunct,[status(thm)],[fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096]),
[final] ).
cnf(i_0_2827,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2828,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2829,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2830,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2831,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_2832,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_1577]),
[final] ).
cnf(i_0_2833,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_1578]),
[final] ).
cnf(i_0_2834,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_1711]),
[final] ).
cnf(i_0_2835,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_1712]),
[final] ).
cnf(i_0_2836,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_1713]),
[final] ).
cnf(i_0_2837,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_1714]),
[final] ).
cnf(i_0_2838,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_1715]),
[final] ).
cnf(i_0_2839,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_1716]),
[final] ).
cnf(i_0_2840,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_1717]),
[final] ).
cnf(i_0_2841,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_1718]),
[final] ).
cnf(i_0_2842,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_1719]),
[final] ).
cnf(i_0_2843,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_1720]),
[final] ).
cnf(i_0_2844,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_1721]),
[final] ).
cnf(i_0_2845,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_1722]),
[final] ).
cnf(i_0_2846,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2847,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_2848,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_1725]),
[final] ).
cnf(i_0_2849,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_1726]),
[final] ).
cnf(i_0_2850,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_1727]),
[final] ).
cnf(i_0_2851,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_1728]),
[final] ).
cnf(i_0_2852,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_1729]),
[final] ).
cnf(i_0_2853,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_1730]),
[final] ).
cnf(i_0_2854,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_1731]),
[final] ).
cnf(i_0_2855,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_1732]),
[final] ).
cnf(i_0_2856,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_1733]),
[final] ).
cnf(i_0_2857,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_1734]),
[final] ).
cnf(i_0_2858,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_1734]),
[final] ).
cnf(i_0_2859,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_1735]),
[final] ).
cnf(i_0_2860,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_1736]),
[final] ).
cnf(i_0_2861,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_1737]),
[final] ).
cnf(i_0_2862,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_1738]),
[final] ).
cnf(i_0_2863,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_1739]),
[final] ).
cnf(i_0_2864,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_1739]),
[final] ).
cnf(i_0_2865,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2866,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_1741]),
[final] ).
cnf(i_0_2867,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X3),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_2868,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_1743]),
[final] ).
cnf(i_0_2869,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_1744]),
[final] ).
cnf(i_0_2870,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X4),X3)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2871,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_2872,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_2873,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2874,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2875,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2876,plain,
( c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2877,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2878,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2879,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_1747]),
[final] ).
cnf(i_0_2880,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2881,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_2882,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_2883,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2884,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_1752]),
[final] ).
cnf(i_0_2885,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_1690]),
[final] ).
cnf(i_0_2886,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_1691]),
[final] ).
cnf(i_0_2887,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_1688]),
[final] ).
cnf(i_0_2888,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_1689]),
[final] ).
cnf(i_0_2889,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X3,X2)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2890,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X3,X2)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_2891,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_2892,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2893,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2894,plain,
( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2895,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_1739]),
[final] ).
cnf(i_0_2896,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_2897,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_2898,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,X1))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk14_1(X1)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X1),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_2899,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_2900,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_1679]),
[final] ).
cnf(i_0_2901,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_1680]),
[final] ).
cnf(i_0_2902,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_1681]),
[final] ).
cnf(i_0_2903,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_1677]),
[final] ).
cnf(i_0_2904,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_1678]),
[final] ).
cnf(i_0_2905,plain,
( X3 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_2906,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_1761]),
[final] ).
cnf(i_0_2907,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_1762]),
[final] ).
cnf(i_0_2908,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_1763]),
[final] ).
cnf(i_0_2909,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_2910,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_2911,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[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_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[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(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_2914,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_1769]),
[final] ).
cnf(i_0_2915,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_1770]),
[final] ).
cnf(i_0_2916,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X3)),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_2917,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_2918,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_1744]),
[final] ).
cnf(i_0_2919,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_1696]),
[final] ).
cnf(i_0_2920,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_1697]),
[final] ).
cnf(i_0_2921,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_1773]),
[final] ).
cnf(i_0_2922,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(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_1774]),
[final] ).
cnf(i_0_2923,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_1763]),
[final] ).
cnf(i_0_2924,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_1761]),
[final] ).
cnf(i_0_2925,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_2926,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_1776]),
[final] ).
cnf(i_0_2927,plain,
( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_2928,plain,
( c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_2929,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_2930,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_2931,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_2932,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3)) = c_Polynomial_OpCons(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_2933,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_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_1358]),
[final] ).
cnf(i_0_2934,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1783]),
[final] ).
cnf(i_0_2935,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_2936,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_1785]),
[final] ).
cnf(i_0_2937,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_1786]),
[final] ).
cnf(i_0_2938,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_1620]),
[final] ).
cnf(i_0_2939,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_1620]),
[final] ).
cnf(i_0_2940,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2941,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_2942,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_1788]),
[final] ).
cnf(i_0_2943,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_1720]),
[final] ).
cnf(i_0_2944,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_1722]),
[final] ).
cnf(i_0_2945,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_1721]),
[final] ).
cnf(i_0_2946,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_1719]),
[final] ).
cnf(i_0_2947,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_1789]),
[final] ).
cnf(i_0_2948,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_1790]),
[final] ).
cnf(i_0_2949,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_1725]),
[final] ).
cnf(i_0_2950,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_1726]),
[final] ).
cnf(i_0_2951,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_1727]),
[final] ).
cnf(i_0_2952,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2953,plain,
( c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_2954,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_1791]),
[final] ).
cnf(i_0_2955,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_1792]),
[final] ).
cnf(i_0_2956,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_1793]),
[final] ).
cnf(i_0_2957,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2958,plain,
( c_RealVector_Oof__real(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_RealVector_Oof__real(X1,X2)),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_2959,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_1795]),
[final] ).
cnf(i_0_2960,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_1796]),
[final] ).
cnf(i_0_2961,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_1339]),
[final] ).
cnf(i_0_2962,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_1797]),
[final] ).
cnf(i_0_2963,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_1798]),
[final] ).
cnf(i_0_2964,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_1799]),
[final] ).
cnf(i_0_2965,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_1800]),
[final] ).
cnf(i_0_2966,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_1801]),
[final] ).
cnf(i_0_2967,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_1802]),
[final] ).
cnf(i_0_2968,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_1803]),
[final] ).
cnf(i_0_2969,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_1804]),
[final] ).
cnf(i_0_2970,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_1805]),
[final] ).
cnf(i_0_2971,plain,
( X2 = X3
| c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2972,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_2973,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_2974,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_2975,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1),X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_2976,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_2977,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_2978,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_2979,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_2980,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_2981,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_1812]),
[final] ).
cnf(i_0_2982,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_1813]),
[final] ).
cnf(i_0_2983,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_1814]),
[final] ).
cnf(i_0_2984,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_1815]),
[final] ).
cnf(i_0_2985,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_1816]),
[final] ).
cnf(i_0_2986,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_1817]),
[final] ).
cnf(i_0_2987,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_1818]),
[final] ).
cnf(i_0_2988,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_1819]),
[final] ).
cnf(i_0_2989,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_1820]),
[final] ).
cnf(i_0_2990,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_1821]),
[final] ).
cnf(i_0_2991,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_1822]),
[final] ).
cnf(i_0_2992,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_1823]),
[final] ).
cnf(i_0_2993,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_2994,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_2995,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_2996,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_1827]),
[final] ).
cnf(i_0_2997,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_1828]),
[final] ).
cnf(i_0_2998,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_1829]),
[final] ).
cnf(i_0_2999,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1830]),
[final] ).
cnf(i_0_3000,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3001,plain,
( c_Groups_Oabs__class_Oabs(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oabs__class_Oabs(X1,X2)),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3002,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_3003,plain,
( c_Rings_Oinverse__class_Oinverse(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3004,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X3)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3005,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3006,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_1836]),
[final] ).
cnf(i_0_3007,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_1836]),
[final] ).
cnf(i_0_3008,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_wm1]),
[final] ).
cnf(i_0_3009,plain,
( c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2)),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3010,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_1838]),
[final] ).
cnf(i_0_3011,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_1839]),
[final] ).
cnf(i_0_3012,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_1840]),
[final] ).
cnf(i_0_3013,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_1841]),
[final] ).
cnf(i_0_3014,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_1647]),
[final] ).
cnf(i_0_3015,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3016,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X2)),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3017,plain,
( c_RealVector_Oof__real(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_RealVector_Oof__real(X1,X2)),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3018,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_1845]),
[final] ).
cnf(i_0_3019,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_1744]),
[final] ).
cnf(i_0_3020,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_1846]),
[final] ).
cnf(i_0_3021,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_1732]),
[final] ).
cnf(i_0_3022,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_1847]),
[final] ).
cnf(i_0_3023,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_1847]),
[final] ).
cnf(i_0_3024,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_1733]),
[final] ).
cnf(i_0_3025,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_1848]),
[final] ).
cnf(i_0_3026,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_1848]),
[final] ).
cnf(i_0_3027,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_1849]),
[final] ).
cnf(i_0_3028,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_1849]),
[final] ).
cnf(i_0_3029,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_1850]),
[final] ).
cnf(i_0_3030,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_1850]),
[final] ).
cnf(i_0_3031,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_1851]),
[final] ).
cnf(i_0_3032,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_1852]),
[final] ).
cnf(i_0_3033,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3034,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3035,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3036,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_1856]),
[final] ).
cnf(i_0_3037,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_1857]),
[final] ).
cnf(i_0_3038,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_1858]),
[final] ).
cnf(i_0_3039,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_1859]),
[final] ).
cnf(i_0_3040,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_1860]),
[final] ).
cnf(i_0_3041,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_1861]),
[final] ).
cnf(i_0_3042,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_1862]),
[final] ).
cnf(i_0_3043,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_1863]),
[final] ).
cnf(i_0_3044,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_1864]),
[final] ).
cnf(i_0_3045,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_1865]),
[final] ).
cnf(i_0_3046,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_3047,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_1866]),
[final] ).
cnf(i_0_3048,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3049,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_1867]),
[final] ).
cnf(i_0_3050,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_1868]),
[final] ).
cnf(i_0_3051,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_1869]),
[final] ).
cnf(i_0_3052,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[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_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_1871]),
[final] ).
cnf(i_0_3055,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_3056,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_1872]),
[final] ).
cnf(i_0_3057,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3058,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3)) = c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3059,plain,
( c_Groups_Ouminus__class_Ouminus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3060,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X1,X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_3061,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_1876]),
[final] ).
cnf(i_0_3062,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_1827]),
[final] ).
cnf(i_0_3063,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_1877]),
[final] ).
cnf(i_0_3064,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_1828]),
[final] ).
cnf(i_0_3065,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_1829]),
[final] ).
cnf(i_0_3066,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_1878]),
[final] ).
cnf(i_0_3067,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_1879]),
[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_Oabs__class_Oabs(tc_RealDef_Oreal,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3069,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_1880]),
[final] ).
cnf(i_0_3070,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_1881]),
[final] ).
cnf(i_0_3071,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_1882]),
[final] ).
cnf(i_0_3072,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_1883]),
[final] ).
cnf(i_0_3073,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_1884]),
[final] ).
cnf(i_0_3074,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X2) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3075,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),X2) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3076,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3077,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3078,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_1889]),
[final] ).
cnf(i_0_3079,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_1862]),
[final] ).
cnf(i_0_3080,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3081,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_1863]),
[final] ).
cnf(i_0_3082,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3083,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_1867]),
[final] ).
cnf(i_0_3084,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3085,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_1868]),
[final] ).
cnf(i_0_3086,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_1869]),
[final] ).
cnf(i_0_3087,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_1890]),
[final] ).
cnf(i_0_3088,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Oinverse(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3089,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_1864]),
[final] ).
cnf(i_0_3090,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_1865]),
[final] ).
cnf(i_0_3091,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_1866]),
[final] ).
cnf(i_0_3092,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_1891]),
[final] ).
cnf(i_0_3093,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_1870]),
[final] ).
cnf(i_0_3094,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_1871]),
[final] ).
cnf(i_0_3095,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3096,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oabs__class_Oabs(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3097,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3098,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3099,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3100,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_1732]),
[final] ).
cnf(i_0_3101,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_1897]),
[final] ).
cnf(i_0_3102,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_1733]),
[final] ).
cnf(i_0_3103,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3104,plain,
( X2 = X3
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3105,plain,
( c_Polynomial_Opos__poly(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3106,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_1901]),
[final] ).
cnf(i_0_3107,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_1901]),
[final] ).
cnf(i_0_3108,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_1881]),
[final] ).
cnf(i_0_3109,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_1882]),
[final] ).
cnf(i_0_3110,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_1883]),
[final] ).
cnf(i_0_3111,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_1884]),
[final] ).
cnf(i_0_3112,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),X2)
| X1 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3113,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_1903]),
[final] ).
cnf(i_0_3114,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_1860]),
[final] ).
cnf(i_0_3115,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_1861]),
[final] ).
cnf(i_0_3116,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_1904]),
[final] ).
cnf(i_0_3117,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_1905]),
[final] ).
cnf(i_0_3118,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_1906]),
[final] ).
cnf(i_0_3119,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_1907]),
[final] ).
cnf(i_0_3120,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_1908]),
[final] ).
cnf(i_0_3121,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_1909]),
[final] ).
cnf(i_0_3122,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_1910]),
[final] ).
cnf(i_0_3123,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X1,X4) != c_Polynomial_OpCons(X3,X2,X5)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3124,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X4,X1) != c_Polynomial_OpCons(X3,X5,X2)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3125,plain,
( X2 = X4
| c_Polynomial_Omonom(X1,X2,X3) != c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_3126,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_1913]),
[final] ).
cnf(i_0_3127,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_1914]),
[final] ).
cnf(i_0_3128,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_1915]),
[final] ).
cnf(i_0_3129,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_1916]),
[final] ).
cnf(i_0_3130,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_1917]),
[final] ).
cnf(i_0_3131,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3132,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
inference(split_conjunct,[status(thm)],[fact_k1n]),
[final] ).
cnf(i_0_3133,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_1919]),
[final] ).
cnf(i_0_3134,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_1920]),
[final] ).
cnf(i_0_3135,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_1921]),
[final] ).
cnf(i_0_3136,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_1922]),
[final] ).
cnf(i_0_3137,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_1923]),
[final] ).
cnf(i_0_3138,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_1872]),
[final] ).
cnf(i_0_3139,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_1924]),
[final] ).
cnf(i_0_3140,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_1925]),
[final] ).
cnf(i_0_3141,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_1926]),
[final] ).
cnf(i_0_3142,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_1927]),
[final] ).
cnf(i_0_3143,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_1928]),
[final] ).
cnf(i_0_3144,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_1929]),
[final] ).
cnf(i_0_3145,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_1930]),
[final] ).
cnf(i_0_3146,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_1931]),
[final] ).
cnf(i_0_3147,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_1932]),
[final] ).
cnf(i_0_3148,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,esk32_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_1581]),
[final] ).
cnf(i_0_3149,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3150,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3151,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_1933]),
[final] ).
cnf(i_0_3152,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_1752]),
[final] ).
cnf(i_0_3153,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_1934]),
[final] ).
cnf(i_0_3154,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3155,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_1936]),
[final] ).
cnf(i_0_3156,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_1937]),
[final] ).
cnf(i_0_3157,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_1938]),
[final] ).
cnf(i_0_3158,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_1939]),
[final] ).
cnf(i_0_3159,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_1940]),
[final] ).
cnf(i_0_3160,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3161,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3162,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_1942]),
[final] ).
cnf(i_0_3163,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_1943]),
[final] ).
cnf(i_0_3164,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk31_0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3165,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk15_0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3166,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X1)),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3167,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_1909]),
[final] ).
cnf(i_0_3168,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_1719]),
[final] ).
cnf(i_0_3169,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3170,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1948]),
[final] ).
cnf(i_0_3171,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk5_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3172,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk4_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3173,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_1951]),
[final] ).
cnf(i_0_3174,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_1952]),
[final] ).
cnf(i_0_3175,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_1953]),
[final] ).
cnf(i_0_3176,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_1954]),
[final] ).
cnf(i_0_3177,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_1955]),
[final] ).
cnf(i_0_3178,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_1956]),
[final] ).
cnf(i_0_3179,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_1933]),
[final] ).
cnf(i_0_3180,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_1957]),
[final] ).
cnf(i_0_3181,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_1958]),
[final] ).
cnf(i_0_3182,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_3183,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3184,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_1959]),
[final] ).
cnf(i_0_3185,plain,
( c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X3,X2))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3186,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_1957]),
[final] ).
cnf(i_0_3187,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3188,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(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_1960]),
[final] ).
cnf(i_0_3189,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_1958]),
[final] ).
cnf(i_0_3190,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3191,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3192,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3193,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3194,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3195,plain,
( c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3196,plain,
( c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3197,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_1968]),
[final] ).
cnf(i_0_3198,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_1969]),
[final] ).
cnf(i_0_3199,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_1970]),
[final] ).
cnf(i_0_3200,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_1971]),
[final] ).
cnf(i_0_3201,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_1972]),
[final] ).
cnf(i_0_3202,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_1973]),
[final] ).
cnf(i_0_3203,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_1974]),
[final] ).
cnf(i_0_3204,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_1903]),
[final] ).
cnf(i_0_3205,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_1975]),
[final] ).
cnf(i_0_3206,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3207,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_3208,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3209,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_1977]),
[final] ).
cnf(i_0_3210,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_1978]),
[final] ).
cnf(i_0_3211,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_1979]),
[final] ).
cnf(i_0_3212,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_1968]),
[final] ).
cnf(i_0_3213,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_1969]),
[final] ).
cnf(i_0_3214,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_1872]),
[final] ).
cnf(i_0_3215,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_1980]),
[final] ).
cnf(i_0_3216,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3217,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Rings_Odvd(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3218,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_1982]),
[final] ).
cnf(i_0_3219,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_1983]),
[final] ).
cnf(i_0_3220,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_1983]),
[final] ).
cnf(i_0_3221,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_1984]),
[final] ).
cnf(i_0_3222,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_1985]),
[final] ).
cnf(i_0_3223,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_1986]),
[final] ).
cnf(i_0_3224,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3225,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_1988]),
[final] ).
cnf(i_0_3226,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_1989]),
[final] ).
cnf(i_0_3227,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_1990]),
[final] ).
cnf(i_0_3228,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_1991]),
[final] ).
cnf(i_0_3229,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_1992]),
[final] ).
cnf(i_0_3230,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_1993]),
[final] ).
cnf(i_0_3231,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_1994]),
[final] ).
cnf(i_0_3232,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_1995]),
[final] ).
cnf(i_0_3233,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_1996]),
[final] ).
cnf(i_0_3234,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_1997]),
[final] ).
cnf(i_0_3235,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_1998]),
[final] ).
cnf(i_0_3236,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_1999]),
[final] ).
cnf(i_0_3237,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_1993]),
[final] ).
cnf(i_0_3238,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_2000]),
[final] ).
cnf(i_0_3239,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3240,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_2002]),
[final] ).
cnf(i_0_3241,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_1949]),
[final] ).
cnf(i_0_3242,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_1950]),
[final] ).
cnf(i_0_3243,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Oabs__class_Oabs(X1,X2)) = X2
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3244,plain,
( c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3245,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_2005]),
[final] ).
cnf(i_0_3246,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_2006]),
[final] ).
cnf(i_0_3247,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_1994]),
[final] ).
cnf(i_0_3248,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_2007]),
[final] ).
cnf(i_0_3249,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_1995]),
[final] ).
cnf(i_0_3250,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_1996]),
[final] ).
cnf(i_0_3251,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_2008]),
[final] ).
cnf(i_0_3252,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_2009]),
[final] ).
cnf(i_0_3253,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_1998]),
[final] ).
cnf(i_0_3254,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_1999]),
[final] ).
cnf(i_0_3255,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),
inference(split_conjunct,[status(thm)],[fact__0960_A_060_At_A_094_Ak_096]),
[final] ).
cnf(i_0_3256,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_2010]),
[final] ).
cnf(i_0_3257,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3258,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_2011]),
[final] ).
cnf(i_0_3259,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_2012]),
[final] ).
cnf(i_0_3260,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_2013]),
[final] ).
cnf(i_0_3261,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_3262,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_2015]),
[final] ).
cnf(i_0_3263,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_2016]),
[final] ).
cnf(i_0_3264,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_2017]),
[final] ).
cnf(i_0_3265,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_2018]),
[final] ).
cnf(i_0_3266,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_2019]),
[final] ).
cnf(i_0_3267,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_2020]),
[final] ).
cnf(i_0_3268,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_2021]),
[final] ).
cnf(i_0_3269,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3270,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk34_2(X1,X2),esk35_2(X1,X2))
| c_SEQ_Odecseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_3271,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_2023]),
[final] ).
cnf(i_0_3272,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Osmult(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3273,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_2025]),
[final] ).
cnf(i_0_3274,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_2026]),
[final] ).
cnf(i_0_3275,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3276,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3277,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3278,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_2006]),
[final] ).
cnf(i_0_3279,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_2029]),
[final] ).
cnf(i_0_3280,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_2030]),
[final] ).
cnf(i_0_3281,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3282,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3283,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_1974]),
[final] ).
cnf(i_0_3284,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X2,X3,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3285,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_2034]),
[final] ).
cnf(i_0_3286,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_1923]),
[final] ).
cnf(i_0_3287,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_2035]),
[final] ).
cnf(i_0_3288,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_2036]),
[final] ).
cnf(i_0_3289,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_2037]),
[final] ).
cnf(i_0_3290,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_2038]),
[final] ).
cnf(i_0_3291,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_2039]),
[final] ).
cnf(i_0_3292,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1)
| hAPP(X1,esk12_1(X1)) != hAPP(X1,esk13_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3293,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_2041]),
[final] ).
cnf(i_0_3294,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_2042]),
[final] ).
cnf(i_0_3295,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_2043]),
[final] ).
cnf(i_0_3296,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_2044]),
[final] ).
cnf(i_0_3297,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_1921]),
[final] ).
cnf(i_0_3298,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_2045]),
[final] ).
cnf(i_0_3299,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_1920]),
[final] ).
cnf(i_0_3300,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_2046]),
[final] ).
cnf(i_0_3301,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_2047]),
[final] ).
cnf(i_0_3302,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_2048]),
[final] ).
cnf(i_0_3303,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_2049]),
[final] ).
cnf(i_0_3304,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_2050]),
[final] ).
cnf(i_0_3305,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_2051]),
[final] ).
cnf(i_0_3306,plain,
( hAPP(X3,X4) = hAPP(X3,X5)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3307,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3308,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3309,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_2053]),
[final] ).
cnf(i_0_3310,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_2054]),
[final] ).
cnf(i_0_3311,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_2055]),
[final] ).
cnf(i_0_3312,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_2056]),
[final] ).
cnf(i_0_3313,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_2057]),
[final] ).
cnf(i_0_3314,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_2058]),
[final] ).
cnf(i_0_3315,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3316,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3317,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3318,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3319,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3320,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3321,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3322,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_2066]),
[final] ).
cnf(i_0_3323,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_2067]),
[final] ).
cnf(i_0_3324,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_2068]),
[final] ).
cnf(i_0_3325,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_1930]),
[final] ).
cnf(i_0_3326,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_2023]),
[final] ).
cnf(i_0_3327,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_1934]),
[final] ).
cnf(i_0_3328,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_2069]),
[final] ).
cnf(i_0_3329,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_2070]),
[final] ).
cnf(i_0_3330,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_2071]),
[final] ).
cnf(i_0_3331,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3332,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3333,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3334,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_2075]),
[final] ).
cnf(i_0_3335,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_2076]),
[final] ).
cnf(i_0_3336,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_2077]),
[final] ).
cnf(i_0_3337,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_2078]),
[final] ).
cnf(i_0_3338,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_2079]),
[final] ).
cnf(i_0_3339,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_kn]),
[final] ).
cnf(i_0_3340,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_1979]),
[final] ).
cnf(i_0_3341,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_2080]),
[final] ).
cnf(i_0_3342,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_2081]),
[final] ).
cnf(i_0_3343,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3344,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_2083]),
[final] ).
cnf(i_0_3345,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_2084]),
[final] ).
cnf(i_0_3346,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_1959]),
[final] ).
cnf(i_0_3347,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3348,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_2086]),
[final] ).
cnf(i_0_3349,plain,
( c_Polynomial_OpCons(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3350,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3351,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3352,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3353,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3354,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_1992]),
[final] ).
cnf(i_0_3355,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3356,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ouminus__class_Ouminus(X2,c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3357,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3358,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3359,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2088]),
[final] ).
cnf(i_0_3360,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3361,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3362,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3363,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3364,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_2030]),
[final] ).
cnf(i_0_3365,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3366,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3367,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_2093]),
[final] ).
cnf(i_0_3368,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_2094]),
[final] ).
cnf(i_0_3369,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3370,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_1984]),
[final] ).
cnf(i_0_3371,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_2096]),
[final] ).
cnf(i_0_3372,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_2097]),
[final] ).
cnf(i_0_3373,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3374,plain,
( 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)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3375,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_2100]),
[final] ).
cnf(i_0_3376,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_2101]),
[final] ).
cnf(i_0_3377,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_2102]),
[final] ).
cnf(i_0_3378,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3379,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3380,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3381,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_2106]),
[final] ).
cnf(i_0_3382,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_2107]),
[final] ).
cnf(i_0_3383,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_2108]),
[final] ).
cnf(i_0_3384,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3385,plain,
( c_RealVector_Oof__real(X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__div__algebra(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3386,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_2111]),
[final] ).
cnf(i_0_3387,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_2111]),
[final] ).
cnf(i_0_3388,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_2112]),
[final] ).
cnf(i_0_3389,plain,
( c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3390,plain,
( c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3391,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3392,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk16_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3393,plain,
( c_Polynomial_Osmult(X2,X3,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3394,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_2117]),
[final] ).
cnf(i_0_3395,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_2050]),
[final] ).
cnf(i_0_3396,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_2051]),
[final] ).
cnf(i_0_3397,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_2118]),
[final] ).
cnf(i_0_3398,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_3399,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_3400,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3401,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_2120]),
[final] ).
cnf(i_0_3402,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_2121]),
[final] ).
cnf(i_0_3403,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_2122]),
[final] ).
cnf(i_0_3404,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_2123]),
[final] ).
cnf(i_0_3405,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_2124]),
[final] ).
cnf(i_0_3406,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X1,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X2)) = c_Rings_Oinverse__class_Oinverse(X1,c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3407,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_2126]),
[final] ).
cnf(i_0_3408,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_2127]),
[final] ).
cnf(i_0_3409,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_2128]),
[final] ).
cnf(i_0_3410,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3411,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3412,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3413,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3414,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3415,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3416,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3417,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_2131]),
[final] ).
cnf(i_0_3418,plain,
( 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__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3419,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_2133]),
[final] ).
cnf(i_0_3420,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_2134]),
[final] ).
cnf(i_0_3421,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_2135]),
[final] ).
cnf(i_0_3422,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_2136]),
[final] ).
cnf(i_0_3423,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3424,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X2)
| c_Polynomial_Opos__poly(X1,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_3425,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_2021]),
[final] ).
cnf(i_0_3426,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_2020]),
[final] ).
cnf(i_0_3427,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3428,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ouminus__class_Ouminus(X1,c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3429,plain,
( c_Groups_Osgn__class_Osgn(X1,c_RealVector_Oof__real(X1,X2)) = c_RealVector_Oof__real(X1,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X2))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3430,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3431,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3432,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_2011]),
[final] ).
cnf(i_0_3433,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_2025]),
[final] ).
cnf(i_0_3434,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3435,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_2144]),
[final] ).
cnf(i_0_3436,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3437,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3438,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3439,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3440,plain,
( c_Polynomial_Omonom(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3441,plain,
( c_Polynomial_Osmult(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3442,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_2147]),
[final] ).
cnf(i_0_3443,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_2148]),
[final] ).
cnf(i_0_3444,plain,
( c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3445,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3446,plain,
( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3447,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_2083]),
[final] ).
cnf(i_0_3448,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk26_1(X1))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_3449,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk21_1(X1))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_3450,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3451,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3452,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3453,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3454,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3455,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_2078]),
[final] ).
cnf(i_0_3456,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_2079]),
[final] ).
cnf(i_0_3457,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_2157]),
[final] ).
cnf(i_0_3458,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_2158]),
[final] ).
cnf(i_0_3459,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_3460,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_3461,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3462,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3463,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3464,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3465,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X3),X1,X2)
| X1 != X2
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_3466,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_2084]),
[final] ).
cnf(i_0_3467,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_2054]),
[final] ).
cnf(i_0_3468,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_2055]),
[final] ).
cnf(i_0_3469,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_2056]),
[final] ).
cnf(i_0_3470,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Nat__Transfer_Otsub(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3471,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3472,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3473,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3474,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3475,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk30_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_3476,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_3477,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_2080]),
[final] ).
cnf(i_0_3478,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_2081]),
[final] ).
cnf(i_0_3479,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_1930]),
[final] ).
cnf(i_0_3480,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pqc0]),
[final] ).
cnf(i_0_3481,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3482,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_2167]),
[final] ).
cnf(i_0_3483,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_2168]),
[final] ).
cnf(i_0_3484,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_2169]),
[final] ).
cnf(i_0_3485,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_2170]),
[final] ).
cnf(i_0_3486,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_2171]),
[final] ).
cnf(i_0_3487,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_2172]),
[final] ).
cnf(i_0_3488,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_2173]),
[final] ).
cnf(i_0_3489,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3490,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_2111]),
[final] ).
cnf(i_0_3491,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3492,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3493,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_3494,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3495,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3496,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_2180]),
[final] ).
cnf(i_0_3497,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3498,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3499,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3500,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3501,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_2182]),
[final] ).
cnf(i_0_3502,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3503,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3504,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_2185]),
[final] ).
cnf(i_0_3505,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_2186]),
[final] ).
cnf(i_0_3506,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_2102]),
[final] ).
cnf(i_0_3507,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_a00]),
[final] ).
cnf(i_0_3508,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_3509,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_2188]),
[final] ).
cnf(i_0_3510,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_2189]),
[final] ).
cnf(i_0_3511,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_2190]),
[final] ).
cnf(i_0_3512,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_2191]),
[final] ).
cnf(i_0_3513,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_2192]),
[final] ).
cnf(i_0_3514,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3515,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3516,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3517,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3518,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_2096]),
[final] ).
cnf(i_0_3519,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_2195]),
[final] ).
cnf(i_0_3520,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_2196]),
[final] ).
cnf(i_0_3521,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3522,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_3523,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_3524,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_3525,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3526,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_2199]),
[final] ).
cnf(i_0_3527,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_2200]),
[final] ).
cnf(i_0_3528,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_i__mult__eq2]),
[final] ).
cnf(i_0_3529,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_complex__of__real__minus__one]),
[final] ).
cnf(i_0_3530,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_2201]),
[final] ).
cnf(i_0_3531,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_2202]),
[final] ).
cnf(i_0_3532,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_2203]),
[final] ).
cnf(i_0_3533,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_2204]),
[final] ).
cnf(i_0_3534,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_2205]),
[final] ).
cnf(i_0_3535,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3536,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3537,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3538,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3539,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_2207]),
[final] ).
cnf(i_0_3540,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_2208]),
[final] ).
cnf(i_0_3541,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_2209]),
[final] ).
cnf(i_0_3542,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_1933]),
[final] ).
cnf(i_0_3543,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_2210]),
[final] ).
cnf(i_0_3544,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_2200]),
[final] ).
cnf(i_0_3545,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_pc0]),
[final] ).
cnf(i_0_3546,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_3547,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk11_0),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_3548,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk10_0),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3549,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_3550,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(split_conjunct,[status(thm)],[fact_m_I1_J]),
[final] ).
cnf(i_0_3551,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
inference(split_conjunct,[status(thm)],[fact_t_I1_J]),
[final] ).
cnf(i_0_3552,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_3553,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact_t_I2_J]),
[final] ).
cnf(i_0_3554,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_3555,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3556,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3557,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_3558,plain,
( X2 = X3
| c_RealVector_Oof__real(X1,X2) != c_RealVector_Oof__real(X1,X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_3559,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_2213]),
[final] ).
cnf(i_0_3560,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_2214]),
[final] ).
cnf(i_0_3561,plain,
( X2 = X3
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3562,plain,
( X2 = X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Rings_Oinverse__class_Oinverse(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_3563,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_2217]),
[final] ).
cnf(i_0_3564,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_3565,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2219]),
[final] ).
cnf(i_0_3566,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_3567,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3568,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3569,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3570,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_3571,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2225]),
[final] ).
cnf(i_0_3572,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_3573,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_2227]),
[final] ).
cnf(i_0_3574,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_2228]),
[final] ).
cnf(i_0_3575,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_3576,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_2230]),
[final] ).
cnf(i_0_3577,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_2231]),
[final] ).
cnf(i_0_3578,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_2231]),
[final] ).
cnf(i_0_3579,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_2232]),
[final] ).
cnf(i_0_3580,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_2232]),
[final] ).
cnf(i_0_3581,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_2233]),
[final] ).
cnf(i_0_3582,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_2233]),
[final] ).
cnf(i_0_3583,plain,
( X1 = X2
| c_RealDef_Oreal(tc_Nat_Onat,X1) != c_RealDef_Oreal(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3584,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_2235]),
[final] ).
cnf(i_0_3585,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_2236]),
[final] ).
cnf(i_0_3586,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_2237]),
[final] ).
cnf(i_0_3587,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_2238]),
[final] ).
cnf(i_0_3588,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_2239]),
[final] ).
cnf(i_0_3589,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_2240]),
[final] ).
cnf(i_0_3590,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_2241]),
[final] ).
cnf(i_0_3591,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_2242]),
[final] ).
cnf(i_0_3592,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_2243]),
[final] ).
cnf(i_0_3593,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_3594,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_2245]),
[final] ).
cnf(i_0_3595,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3596,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3597,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3598,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3599,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3600,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3601,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_2252]),
[final] ).
cnf(i_0_3602,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_2253]),
[final] ).
cnf(i_0_3603,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_2254]),
[final] ).
cnf(i_0_3604,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3605,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_2023]),
[final] ).
cnf(i_0_3606,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_2236]),
[final] ).
cnf(i_0_3607,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_2237]),
[final] ).
cnf(i_0_3608,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_2238]),
[final] ).
cnf(i_0_3609,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_2239]),
[final] ).
cnf(i_0_3610,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_2242]),
[final] ).
cnf(i_0_3611,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_2243]),
[final] ).
cnf(i_0_3612,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_2235]),
[final] ).
cnf(i_0_3613,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_2245]),
[final] ).
cnf(i_0_3614,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_2256]),
[final] ).
cnf(i_0_3615,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_2257]),
[final] ).
cnf(i_0_3616,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_2258]),
[final] ).
cnf(i_0_3617,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_2259]),
[final] ).
cnf(i_0_3618,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_2260]),
[final] ).
cnf(i_0_3619,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_2261]),
[final] ).
cnf(i_0_3620,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_2262]),
[final] ).
cnf(i_0_3621,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_2263]),
[final] ).
cnf(i_0_3622,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_2264]),
[final] ).
cnf(i_0_3623,plain,
( c_RealVector_Oof__real(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_3624,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_2253]),
[final] ).
cnf(i_0_3625,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_2254]),
[final] ).
cnf(i_0_3626,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_2265]),
[final] ).
cnf(i_0_3627,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_2266]),
[final] ).
cnf(i_0_3628,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3629,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3630,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3631,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3632,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_2271]),
[final] ).
cnf(i_0_3633,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_2272]),
[final] ).
cnf(i_0_3634,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk31_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3635,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk15_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3636,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[fact_q_I1_J]),
[final] ).
cnf(i_0_3637,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
inference(split_conjunct,[status(thm)],[fact_inverse__i]),
[final] ).
cnf(i_0_3638,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_2271]),
[final] ).
cnf(i_0_3639,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_2273]),
[final] ).
cnf(i_0_3640,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_2274]),
[final] ).
cnf(i_0_3641,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_3642,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_3643,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_3644,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_3645,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_2275]),
[final] ).
cnf(i_0_3646,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_3647,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3648,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_3649,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3650,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_3651,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_3652,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2282]),
[final] ).
cnf(i_0_3653,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3654,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3655,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3656,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3657,plain,
( class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_3658,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_3659,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3660,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_3661,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3662,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_3663,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3664,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_3665,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_3666,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3667,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3668,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3669,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_2299]),
[final] ).
cnf(i_0_3670,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3671,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3672,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3673,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3674,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3675,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_2305]),
[final] ).
cnf(i_0_3676,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3677,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3678,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3679,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3680,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3681,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3682,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3683,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3684,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3685,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3686,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_3687,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3688,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3689,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3690,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3691,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3692,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3693,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3694,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3695,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3696,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3697,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3698,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3699,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3700,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3701,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3702,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3703,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3704,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_3705,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_3706,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_3707,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_3708,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_3709,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_3710,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_3711,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_3712,plain,
esk23_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_3713,plain,
esk22_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_3714,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_3715,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_3716,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_kas_I1_J]),
[final] ).
cnf(i_0_3717,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w0]),
[final] ).
cnf(i_0_3718,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_kas_I2_J]),
[final] ).
cnf(i_0_3719,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_3720,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_3721,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_3722,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_3723,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_3724,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_3725,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]),
[final] ).
cnf(i_0_3726,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]),
[final] ).
cnf(i_0_3727,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
[final] ).
cnf(i_0_3728,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]),
[final] ).
cnf(i_0_3729,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_3730,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_3731,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
[final] ).
cnf(i_0_3732,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
[final] ).
cnf(i_0_3733,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_3734,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_3735,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_3736,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]),
[final] ).
cnf(i_0_3737,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]),
[final] ).
cnf(i_0_3738,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_3739,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_3740,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_3741,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_3742,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_3743,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_3744,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_3745,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_3746,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_3747,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_3748,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_3749,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_3750,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_3751,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_3752,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_3753,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_3754,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3755,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3756,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3757,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_3758,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_3759,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_3760,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_3761,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_3762,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_3763,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_3764,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
[final] ).
cnf(i_0_3765,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]),
[final] ).
cnf(i_0_3766,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_3767,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_3768,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_3769,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_3770,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_3771,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_3772,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_3773,plain,
class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__div__algebra]),
[final] ).
cnf(i_0_3774,plain,
class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__div__algebra]),
[final] ).
cnf(i_0_3775,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_3776,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_3777,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_3778,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_3779,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_3780,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_3781,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_3782,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_3783,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_3784,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_3785,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_3786,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]),
[final] ).
cnf(i_0_3787,plain,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__algebra__1]),
[final] ).
cnf(i_0_3788,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_3789,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_3790,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_3791,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3792,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3793,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3794,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_3795,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_3796,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_3797,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_3798,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_3799,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_3800,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_3801,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_3802,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_3803,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_3804,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_3805,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3806,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3807,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3808,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3809,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_3810,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_3811,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_3812,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_3813,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_3814,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_3815,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_3816,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_3817,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_3818,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_3819,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_3820,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_3821,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_3822,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_3823,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_3824,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_3825,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_3826,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_3827,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_3828,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_3829,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3830,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3831,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3832,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3833,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_3834,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_3835,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_3836,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_3837,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_3838,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_3839,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_3840,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_3841,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_3842,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3843,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3844,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3845,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_3846,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_3847,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_3848,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_3849,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_3850,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_3851,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3852,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3853,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_3854,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_3855,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_3856,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_3857,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_3858,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3859,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3860,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3861,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3862,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3863,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_3864,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_3865,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_3866,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_3867,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_3868,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_3869,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_3870,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_3871,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_3872,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3873,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3874,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3875,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3876,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_3877,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_3878,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_3879,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3880,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3881,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_3882,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_3883,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_3884,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
[final] ).
cnf(i_0_3885,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_3886,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_3887,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_3888,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_3889,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_3890,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_3891,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3892,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3893,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3894,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3895,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3896,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3897,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3898,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_3899,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_3900,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_3901,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_3902,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3903,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3904,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_3905,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_3906,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_3907,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_3908,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_3909,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_3910,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_3911,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_3912,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_3913,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_3914,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_3915,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_3916,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_3917,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_3918,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_3919,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_3920,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_3921,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_3922,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_3923,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_3924,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_3925,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_3926,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3927,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3928,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3929,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3930,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_3931,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_3932,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_3933,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_3934,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_3935,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_3936,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3937,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3938,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3939,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_3940,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_3941,axiom,
X1 = X1 ).
cnf(i_0_3942,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3943,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3944,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3945,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3946,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3947,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3948,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3949,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3950,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3951,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3952,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3953,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3954,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3955,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3956,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3957,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3958,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3959,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3960,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3961,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3962,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3963,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3964,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3965,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3966,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3967,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3968,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3969,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3970,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3971,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3972,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3973,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3974,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3975,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X4) ) ).
cnf(i_0_3976,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X4) ) ).
cnf(i_0_3977,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X2) ) ).
cnf(i_0_3978,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3979,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3980,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3981,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3982,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3983,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3984,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3985,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3986,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3987,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3988,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3989,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3990,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3991,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3992,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3993,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3994,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3995,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_3996,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_3997,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_3998,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_3999,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4000,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4001,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4002,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4003,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4004,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4005,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4006,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4007,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4008,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4009,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4010,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4011,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4012,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4013,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4014,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4015,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4016,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4017,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4018,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4019,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4020,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4021,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4022,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4023,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4024,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4025,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4026,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4027,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4028,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4029,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4030,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4031,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4032,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4033,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4034,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4035,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4036,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4037,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4038,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4039,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4040,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4041,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4042,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4043,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4044,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4045,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4046,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4047,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4048,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4049,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4050,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4051,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4052,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4053,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4054,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4055,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4056,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4057,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4058,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4059,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4060,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4061,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4062,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4063,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4064,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4065,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4066,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4067,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4068,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4069,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4070,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4071,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4072,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4073,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4074,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4075,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4076,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4077,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4078,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4079,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4080,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4081,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4082,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4083,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4084,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X3,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X4) ) ).
cnf(i_0_4085,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X1,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X2,X4) ) ).
cnf(i_0_4086,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X2) ) ).
cnf(i_0_4087,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4088,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4089,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4090,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4091,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4092,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_3941_001,axiom,
X1 = X1 ).
cnf(i_0_3942_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3943_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3944_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3945_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3946_006,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3947_007,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3948_008,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3949_009,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3950_010,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3951_011,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3952_012,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3953_013,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3954_014,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3955_015,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3956_016,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3957_017,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3958_018,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3959_019,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3960_020,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3961_021,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3962_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3963_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3964_024,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3965_025,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3966_026,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3967_027,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3968_028,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3969_029,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3970_030,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3971_031,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3972_032,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3973_033,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3974_034,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3975_035,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X4) ) ).
cnf(i_0_3976_036,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X4) ) ).
cnf(i_0_3977_037,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X2) ) ).
cnf(i_0_3978_038,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3979_039,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3980_040,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3981_041,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3982_042,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3983_043,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3984_044,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3985_045,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3986_046,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3987_047,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3988_048,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3989_049,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3990_050,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3991_051,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3992_052,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3993_053,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3994_054,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3995_055,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_3996_056,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_3997_057,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_3998_058,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_3999_059,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4000_060,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4001_061,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4002_062,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4003_063,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4004_064,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4005_065,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4006_066,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4007_067,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4008_068,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4009_069,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4010_070,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4011_071,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4012_072,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4013_073,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4014_074,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4015_075,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4016_076,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4017_077,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4018_078,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4019_079,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4020_080,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4021_081,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4022_082,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4023_083,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4024_084,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4025_085,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4026_086,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4027_087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4028_088,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4029_089,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4030_090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4031_091,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4032_092,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4033_093,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4034_094,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4035_095,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4036_096,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4037_097,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4038_098,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4039_099,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4040_100,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4041_101,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4042_102,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4043_103,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4044_104,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4045_105,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4046_106,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4047_107,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4048_108,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4049_109,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4050_110,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4051_111,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4052_112,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4053_113,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4054_114,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4055_115,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4056_116,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4057_117,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4058_118,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4059_119,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4060_120,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4061_121,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4062_122,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4063_123,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4064_124,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4065_125,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4066_126,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4067_127,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4068_128,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4069_129,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4070_130,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4071_131,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4072_132,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4073_133,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4074_134,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4075_135,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4076_136,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4077_137,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4078_138,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4079_139,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4080_140,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4081_141,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4082_142,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4083_143,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4084_144,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X3,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X4) ) ).
cnf(i_0_4085_145,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X1,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X2,X4) ) ).
cnf(i_0_4086_146,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X2) ) ).
cnf(i_0_4087_147,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4088_148,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4089_149,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4090_150,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4091_151,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4092_152,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4093,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_inference,[],[2392]) ).
cnf(i_0_4094,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1)) ),
inference(equality_inference,[],[2393]) ).
cnf(i_0_4095,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) ),
inference(equality_inference,[],[2398]) ).
cnf(i_0_4096,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X4) ),
inference(equality_inference,[],[2399]) ).
cnf(i_0_4097,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X5)),X3),X4)) ),
inference(equality_inference,[],[2400]) ).
cnf(i_0_4098,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X4,X2)),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X5) ),
inference(equality_inference,[],[2401]) ).
cnf(i_0_4099,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3) = X3 ),
inference(equality_inference,[],[2407]) ).
cnf(i_0_4100,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X3),X2) ),
inference(equality_inference,[],[2408]) ).
cnf(i_0_4101,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X2,X2)),X3),X4) = X4 ),
inference(equality_inference,[],[2409]) ).
cnf(i_0_4102,plain,
( ~ class_Rings_Oring(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ominus__class_Ominus(X1,X3,X3)),X4),X2) ),
inference(equality_inference,[],[2410]) ).
cnf(i_0_4103,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2433]) ).
cnf(i_0_4104,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(equality_inference,[],[2525]) ).
cnf(i_0_4105,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,[],[2557]) ).
cnf(i_0_4106,plain,
( X1 = X1
| ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(equality_inference,[],[2591]) ).
cnf(i_0_4107,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)) ),
inference(equality_inference,[],[2704]) ).
cnf(i_0_4108,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,[],[2788]) ).
cnf(i_0_4109,plain,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[2870]) ).
cnf(i_0_4110,plain,
( ~ class_Fields_Ofield(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(equality_inference,[],[2875]) ).
cnf(i_0_4111,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(equality_inference,[],[2894]) ).
cnf(i_0_4112,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[2905]) ).
cnf(i_0_4113,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[2952]) ).
cnf(i_0_4114,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) ),
inference(equality_inference,[],[2953]) ).
cnf(i_0_4115,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_inference,[],[2976]) ).
cnf(i_0_4116,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[2977]) ).
cnf(i_0_4117,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,[],[3006]) ).
cnf(i_0_4118,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,[],[3007]) ).
cnf(i_0_4119,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[3104]) ).
cnf(i_0_4120,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3123]) ).
cnf(i_0_4121,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3124]) ).
cnf(i_0_4122,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3125]) ).
cnf(i_0_4123,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3127]) ).
cnf(i_0_4124,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3128]) ).
cnf(i_0_4125,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3130]) ).
cnf(i_0_4126,plain,
X1 = X1,
inference(equality_inference,[],[3162]) ).
cnf(i_0_4127,plain,
X1 = X1,
inference(equality_inference,[],[3163]) ).
cnf(i_0_4128,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,[],[3168]) ).
cnf(i_0_4129,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3183]) ).
cnf(i_0_4130,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,[],[3184]) ).
cnf(i_0_4131,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3190]) ).
cnf(i_0_4132,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3191]) ).
cnf(i_0_4133,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3193]) ).
cnf(i_0_4134,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3194]) ).
cnf(i_0_4135,plain,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(equality_inference,[],[3217]) ).
cnf(i_0_4136,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,[],[3221]) ).
cnf(i_0_4137,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3242]) ).
cnf(i_0_4138,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,X2)),c_Groups_Ouminus__class_Ouminus(X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) ),
inference(equality_inference,[],[3257]) ).
cnf(i_0_4139,plain,
X1 = X1,
inference(equality_inference,[],[3269]) ).
cnf(i_0_4140,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,[],[3283]) ).
cnf(i_0_4141,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,[],[3340]) ).
cnf(i_0_4142,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),
inference(equality_inference,[],[3352]) ).
cnf(i_0_4143,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3353]) ).
cnf(i_0_4144,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,[],[3354]) ).
cnf(i_0_4145,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3355]) ).
cnf(i_0_4146,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))),c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3356]) ).
cnf(i_0_4147,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3360]) ).
cnf(i_0_4148,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3361]) ).
cnf(i_0_4149,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3362]) ).
cnf(i_0_4150,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3363]) ).
cnf(i_0_4151,plain,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3393]) ).
cnf(i_0_4152,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3394]) ).
cnf(i_0_4153,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,[],[3395]) ).
cnf(i_0_4154,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,[],[3396]) ).
cnf(i_0_4155,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3410]) ).
cnf(i_0_4156,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3413]) ).
cnf(i_0_4157,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3415]) ).
cnf(i_0_4158,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3416]) ).
cnf(i_0_4159,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,[],[3425]) ).
cnf(i_0_4160,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,[],[3426]) ).
cnf(i_0_4161,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,[],[3433]) ).
cnf(i_0_4162,plain,
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3440]) ).
cnf(i_0_4163,plain,
( ~ class_Rings_Oidom(X1)
| c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3441]) ).
cnf(i_0_4164,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,[],[3447]) ).
cnf(i_0_4165,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,[],[3455]) ).
cnf(i_0_4166,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,[],[3456]) ).
cnf(i_0_4167,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3462]) ).
cnf(i_0_4168,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3463]) ).
cnf(i_0_4169,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3464]) ).
cnf(i_0_4170,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X2) ),
inference(equality_inference,[],[3465]) ).
cnf(i_0_4171,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,[],[3466]) ).
cnf(i_0_4172,plain,
( ~ class_Power_Opower(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3476]) ).
cnf(i_0_4173,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3477]) ).
cnf(i_0_4174,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3478]) ).
cnf(i_0_4175,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,[],[3479]) ).
cnf(i_0_4176,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3498]) ).
cnf(i_0_4177,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3499]) ).
cnf(i_0_4178,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3500]) ).
cnf(i_0_4179,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,[],[3501]) ).
cnf(i_0_4180,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X2 ),
inference(equality_inference,[],[3513]) ).
cnf(i_0_4181,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,[],[3527]) ).
cnf(i_0_4182,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3537]) ).
cnf(i_0_4183,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3538]) ).
cnf(i_0_4184,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,[],[3542]) ).
cnf(i_0_4185,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3555]) ).
cnf(i_0_4186,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3556]) ).
cnf(i_0_4187,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(equality_inference,[],[3557]) ).
cnf(i_0_4188,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = X2 ),
inference(equality_inference,[],[3558]) ).
cnf(i_0_4189,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[3559]) ).
cnf(i_0_4190,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3560]) ).
cnf(i_0_4191,plain,
( X1 = X1
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(equality_inference,[],[3562]) ).
cnf(i_0_4192,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(equality_inference,[],[3578]) ).
cnf(i_0_4193,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(equality_inference,[],[3580]) ).
cnf(i_0_4194,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,[],[3582]) ).
cnf(i_0_4195,plain,
X1 = X1,
inference(equality_inference,[],[3583]) ).
cnf(i_0_4196,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,[],[3605]) ).
cnf(i_0_4197,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,[],[3606]) ).
cnf(i_0_4198,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,[],[3607]) ).
cnf(i_0_4199,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,[],[3608]) ).
cnf(i_0_4200,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,[],[3609]) ).
cnf(i_0_4201,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,[],[3610]) ).
cnf(i_0_4202,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,[],[3611]) ).
cnf(i_0_4203,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,[],[3612]) ).
cnf(i_0_4204,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,[],[3613]) ).
cnf(i_0_4205,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3623]) ).
cnf(i_0_4206,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,[],[3624]) ).
cnf(i_0_4207,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,[],[3625]) ).
cnf(i_0_4208,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,[],[3638]) ).
cnf(i_0_4209,plain,
$false,
inference(scs_inference,[],[i_0_2342,i_0_3847,i_0_2353,i_0_3255,i_0_2608]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW262+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n007.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:30:08 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.84/5.79 % Version : CSE_E---1.7
% 0.84/5.79 % Problem : theBenchmark.p
% 0.84/5.79 % SZS status Theorem for theBenchmark.p
% 0.84/5.79 % SZS output start CNFRefutation
% See solution above
% 6.23/5.93 % Total time : 5.446s
%------------------------------------------------------------------------------