%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW263+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:30:51 PM UTC 2026
% Result : Theorem 0.79s 5.79s
% Output : CNFRefutation 6.19s
% 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,
~ ! [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,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/sandbox/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,
! [X10,X12,X6] :
( class_Rings_Olinordered__ring(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X10)),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_nat__diff__split__asm,axiom,
! [X19,X20,X45] :
( hBOOL(hAPP(X45,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
& ~ hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X58] :
( X20 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X58)
& ~ hBOOL(hAPP(X45,X58)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X12] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_add__leE,axiom,
! [X4,X38,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X38),X4)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X6,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X67),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_less_Ohyps,axiom,
! [X72] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X72),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,X72))
=> ? [X53] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X72),X53) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less_Ohyps) ).
fof(fact_not__square__less__zero,axiom,
! [X5,X6] :
( class_Rings_Olinordered__ring(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X5),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_not__add__less1,axiom,
! [X39,X22] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X39),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X22,X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X22),X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X13] :
( ~ 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),X13),X13))
<=> X13 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_add__diff__inverse,axiom,
! [X4,X21] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X15,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X5,X23,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X5)
=> ~ c_Orderings_Oord__class_Oless(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_linorder__not__le,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> c_Orderings_Oord__class_Oless(X6,X15,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X12,X10,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> ~ c_Orderings_Oord__class_Oless(X6,X12,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless(X6,X15,X13)
| X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__not__sym,axiom,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__asym_H,axiom,
! [X23,X5,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ~ c_Orderings_Oord__class_Oless(X6,X23,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__asym,axiom,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_sgn__poly__def,axiom,
! [X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( ( X12 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X12)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X12)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_abs__poly__def,axiom,
! [X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X12) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X6),X12) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__poly__def) ).
fof(fact_tsub__def,axiom,
! [X12,X10] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X12)
=> c_Nat__Transfer_Otsub(X12,X10) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X10) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X12)
=> c_Nat__Transfer_Otsub(X12,X10) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_abs__not__less__zero,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_norm__not__less__zero,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_abs__if,axiom,
! [X5,X6] :
( class_Groups_Oabs__if(X6)
=> ( ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__if) ).
fof(fact_sgn__if,axiom,
! [X12,X6] :
( class_Groups_Osgn__if(X6)
=> ( ( X12 = c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Ozero__class_Ozero(X6) )
& ( X12 != c_Groups_Ozero__class_Ozero(X6)
=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Oone__class_Oone(X6) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X13,X15,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X15,X13)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__cases,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ( X12 != X10
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X10,X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__le__cases,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_leI,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [X12,X10,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> c_Orderings_Oord__class_Oless(X6,X12,X10) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(fact_real__abs__def,axiom,
! [X11] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__abs__def) ).
fof(fact_abs__real__def,axiom,
! [X5] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__def) ).
fof(fact_not__one__le__zero,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X10,X12] :
( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X12,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X12,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_not__less0,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_not__pos__poly__0,axiom,
! [X6] :
( class_Rings_Olinordered__idom(X6)
=> ~ c_Polynomial_Opos__poly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_lemmaCauchy,axiom,
! [X80,X81,X6,X67] :
( ( class_RealVector_Oreal__normed__vector(X67)
& class_Orderings_Oord(X6) )
=> ( ! [X43] :
( c_Orderings_Oord__class_Oless__eq(X6,X81,X43)
=> 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,X43))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X43] :
( c_Orderings_Oord__class_Oless__eq(X6,X81,X43)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X67,hAPP(X80,X43)),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/sandbox/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_mrmq__eq,axiom,
! [X64] :
( 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____)),X64)),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____),X64)),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/sandbox/benchmark/theBenchmark.p',fact_mrmq__eq) ).
fof(fact_decr__lemma,axiom,
! [X16,X12,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,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,X12,X16)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [X12,X16,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,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,X12,X16)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24))) ),
file('/export/starexec/sandbox/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,
? [X44,X77] :
( X77 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X44 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X73] :
( 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,X73),X44),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____))
& ! [X53] : 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____)),X53) = 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),X53),X44)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X77,X73)),X53))) ) ),
file('/export/starexec/sandbox/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,
! [X53] : 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____)),X53) = 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),X53),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X53))),
file('/export/starexec/sandbox/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))
=> ? [X50] : 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____)),X50)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/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,
! [X53] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X53) = 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____)),X53)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_qr) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X6,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X23,X5,X10,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X12,X5)),c_Groups_Ominus__class_Ominus(X6,X10,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X12,X5)),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ominus__class_Ominus(X6,X10,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [X21,X40,X10,X12] : 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,X12,X10),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X40),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X40))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X21))))),
file('/export/starexec/sandbox/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/sandbox/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,
! [X55,X25,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_OpCons(X6,c_Groups_Ouminus__class_Ouminus(X6,X25),c_Polynomial_OpCons(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))))),c_Polynomial_Osynthetic__div(X6,X55,X25)),c_Polynomial_OpCons(X6,hAPP(c_Polynomial_Opoly(X6,X55),X25),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_le__add__iff1,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51))
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X20,X19)),X52),X26),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X20,X19)),X52),X26),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51))
<=> c_Orderings_Oord__class_Oless__eq(X6,X26,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X19,X20)),X52),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51))
<=> c_Orderings_Oord__class_Oless(X6,X26,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X19,X20)),X52),X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_nat__le__add__iff1,axiom,
! [X18,X34,X59,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( 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),X57),X59),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18))
<=> 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,X57,X56)),X59),X34),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X18,X34,X59,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( 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),X57),X59),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18))
<=> 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,X57,X56)),X59),X34),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [X18,X34,X59,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( 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),X57),X59),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,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,X56,X57)),X59),X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X18,X34,X59,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( 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),X57),X59),X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,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,X56,X57)),X59),X18)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_th01) ).
fof(fact_order__1,axiom,
! [X55,X5,X6] :
( class_Rings_Oidom(X6)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X6),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X6)),c_Polynomial_OpCons(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Polynomial_OpCons(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))))),c_Polynomial_Oorder(X6,X5,X55)),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__1) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X24,X25,X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Oplus__class_Oplus(X6,X25,X24))),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X5,X25)),c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X23,X24)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_reduce__poly__simple,axiom,
! [X4,X23] :
( X23 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X53] : 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),X53),X4)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [X24,X25,X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Oplus__class_Oplus(X6,X25,X24))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X25)),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X23,X24)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_poly__cont,axiom,
! [X55,X16,X29] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X29)
=> ? [X58] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X58)
& ! [X50] :
( ( 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,X50,X16)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X50,X16)),X58) )
=> 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,X55),X50),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X55),X16))),X29) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__cont) ).
fof(fact_Deriv_Oinverse__diff__inverse,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23)) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),c_Groups_Ominus__class_Ominus(X6,X5,X23))),c_Rings_Oinverse__class_Oinverse(X6,X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X4,X21,X28,X22,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,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),X28),X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X28),X4)) = 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,X39)),X28),X21),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X4,X21,X28,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> 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),X28),X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X28),X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,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,X39,X22)),X28),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_poly__replicate__append,axiom,
! [X12,X55,X4,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_Omonom(X6,c_Groups_Oone__class_Oone(X6),X4)),X55)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4)),hAPP(c_Polynomial_Opoly(X6,X55),X12)) ),
file('/export/starexec/sandbox/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,
? [X53] : 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))))),X53) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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_I3_J,axiom,
! [X86,X87,X51,X6] :
( ( class_Rings_Ocomm__ring(X6)
& class_Rings_Odvd(X6) )
=> ( c_Rings_Odvd__class_Odvd(X6,X51,X87)
=> ! [X3,X44] :
( c_Rings_Odvd__class_Odvd(X6,X51,c_Groups_Oplus__class_Oplus(X6,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X6,X51,c_Groups_Oplus__class_Oplus(X6,c_Groups_Ominus__class_Ominus(X6,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X44),X87)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X86,X87,X51,X6] :
( ( class_Rings_Ocomm__ring(X6)
& class_Rings_Odvd(X6) )
=> ( c_Rings_Odvd__class_Odvd(X6,X51,X87)
=> ! [X3,X44] :
( c_Rings_Odvd__class_Odvd(X6,X51,c_Groups_Oplus__class_Oplus(X6,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X6,X51,c_Groups_Oplus__class_Oplus(X6,c_Groups_Ominus__class_Ominus(X6,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X44),X87)),X86)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_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/sandbox/benchmark/theBenchmark.p',fact_rnc) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X74,X75,X33,X11,X54,X23] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X54),X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X75),X74)
=> ( 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),X33),X75),X74),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X74)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X75,X54) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X74,X75,X33,X11,X54,X23] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X54),X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X75),X74)
=> ( 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),X33),X75),X74))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X33,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X75) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_mult_Opos__bounded,axiom,
! [X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> ? [X69] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X69)
& ! [X77,X82] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),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(X6,X77)),c_RealVector_Onorm__class_Onorm(X6,X82))),X69)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_inverse__add,axiom,
! [X23,X5,X6] :
( class_Fields_Ofield(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)),c_Rings_Oinverse__class_Oinverse(X6,X5))),c_Rings_Oinverse__class_Oinverse(X6,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__add) ).
fof(fact_unique__quotient__lemma,axiom,
! [X11,X54,X74,X75,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),X75),X74),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X54),X11))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X74)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X23)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X75,X54) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X11,X54,X74,X75,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),X75),X74),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23),X54),X11))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X11)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X74)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X75) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X18,X34,X59,X57,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X57)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X59),X34) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18)
<=> 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,X57,X56)),X59),X34) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X18,X34,X59,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X59),X34) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X56),X59),X18)
<=> X34 = 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,X56,X57)),X59),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oring(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51)
<=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X20,X19)),X52),X26) = X51 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X51,X19,X26,X52,X20,X6] :
( class_Rings_Oring(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X52),X26) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X52),X51)
<=> X26 = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X19,X20)),X52),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_unimodular__reduce__norm,axiom,
! [X16] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16) = 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,X16,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,X16,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,X16,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,X16,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).
fof(fact_mult__diff__mult,axiom,
! [X23,X5,X10,X12,X6] :
( class_Rings_Oring(X6)
=> c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),c_Groups_Ominus__class_Ominus(X6,X10,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X12,X5)),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X4,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> 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,X4)),X12),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,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_combine__common__factor,axiom,
! [X25,X23,X29,X5,X6] :
( class_Rings_Osemiring(X6)
=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X29),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X29),X25)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)),X29),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_division__ring__inverse__diff,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),c_Groups_Ominus__class_Ominus(X6,X23,X5))),c_Rings_Oinverse__class_Oinverse(X6,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
fof(fact_division__ring__inverse__add,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),c_Groups_Oplus__class_Oplus(X6,X5,X23))),c_Rings_Oinverse__class_Oinverse(X6,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
fof(fact_convex__bound__le,axiom,
! [X27,X28,X10,X5,X12,X6] :
( class_Rings_Olinordered__semiring__1(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X28)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X27)
=> ( c_Groups_Oplus__class_Oplus(X6,X28,X27) = c_Groups_Oone__class_Oone(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X28),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X27),X10)),X5) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X27,X28,X10,X5,X12,X6] :
( class_Rings_Olinordered__semiring__1__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X5)
=> ( c_Orderings_Oord__class_Oless(X6,X10,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X28)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X27)
=> ( c_Groups_Oplus__class_Oplus(X6,X28,X27) = c_Groups_Oone__class_Oone(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X28),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X27),X10)),X5) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_unity__coeff__ex,axiom,
! [X41,X45,X6] :
( ( class_Rings_Odvd(X6)
& class_Rings_Osemiring__0(X6) )
=> ( ? [X3] : hBOOL(hAPP(X45,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X41),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X6,X41,c_Groups_Oplus__class_Oplus(X6,X3,c_Groups_Ozero__class_Ozero(X6)))
& hBOOL(hAPP(X45,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_left__add__mult__distrib,axiom,
! [X38,X39,X28,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X28),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X28),X38)) = 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,X39)),X28),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_real__mult__inverse__cancel,axiom,
! [X28,X10,X36,X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X28))
=> 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,X12)),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X36)),X28)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X15,X13,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X15),X15)))
<=> ( X13 != c_Groups_Ozero__class_Ozero(X6)
| X15 != c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X60,X61,X63,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),X60)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X15,X13,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X15),X15)),c_Groups_Ozero__class_Ozero(X6))
<=> ( X13 = c_Groups_Ozero__class_Ozero(X6)
& X15 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_ath,axiom,
! [X46,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,X46)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X46,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),X46)),X12),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ath) ).
fof(fact_mult__pCons__left,axiom,
! [X54,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_OpCons(X6,X5,X55)),X54) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X54),c_Polynomial_OpCons(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(fact_offset__poly__pCons,axiom,
! [X85,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,c_Polynomial_OpCons(X6,X5,X55),X85) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X85,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X55,X85)),c_Polynomial_OpCons(X6,X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X55,X85))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_real__mult__inverse__cancel2,axiom,
! [X28,X10,X36,X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X36),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X28))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X28),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X36))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).
fof(fact_realpow__minus__mult,axiom,
! [X12,X4,X6] :
( class_Groups_Omonoid__mult(X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X12) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_crossproduct__noteq,axiom,
! [X51,X26,X19,X20,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( ( X20 != X19
& X26 != X51 )
<=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X51)) != c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X37,X13,X15,X64,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X64),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X37)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X64),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X15))
<=> ( X64 = X13
| X15 = X37 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_abs__diff__less__iff,axiom,
! [X65,X20,X13,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X13,X20)),X65)
<=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ominus__class_Ominus(X6,X20,X65),X13)
& c_Orderings_Oord__class_Oless(X6,X13,c_Groups_Oplus__class_Oplus(X6,X20,X65)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_mult__pCons__right,axiom,
! [X54,X5,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),c_Polynomial_OpCons(X6,X5,X54)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55),c_Polynomial_OpCons(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_power__minus,axiom,
! [X4,X5,X6] :
( class_Rings_Oring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6))),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_q__neg__lemma,axiom,
! [X74,X75,X33] :
( 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),X33),X75),X74),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),X74)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X75,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X74,X75,X33] :
( 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),X33),X75),X74))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X33)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23))),c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_norm__triangle__ineq3,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X23))),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_pcompose__pCons,axiom,
! [X54,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Opcompose(X6,c_Polynomial_OpCons(X6,X5,X55),X54) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X54),c_Polynomial_Opcompose(X6,X55,X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X60,X61,X63,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X61)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X63),X60)) ),
file('/export/starexec/sandbox/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,
! [X60,X61,X63,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X63),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [X5,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,X5)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X23)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X16,X17] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X17),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X17,X16)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_mult__poly__add__left,axiom,
! [X11,X54,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,X54)),X11) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X54),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_nat__diff__split,axiom,
! [X19,X20,X45] :
( hBOOL(hAPP(X45,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
=> hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X58] :
( X20 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X58)
=> hBOOL(hAPP(X45,X58)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_abs__mult__less,axiom,
! [X24,X23,X25,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X5),X25)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X23),X24)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X5)),c_Groups_Oabs__class_Oabs(X6,X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_mult__monom,axiom,
! [X4,X23,X21,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_Omonom(X6,X5,X21)),c_Polynomial_Omonom(X6,X23,X4)) = c_Polynomial_Omonom(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(fact_power__Suc__less,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_odd__less__0,axiom,
! [X37] :
( 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),X37),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X9,X10,X11,X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),X11)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X10),X9)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oplus__class_Oplus(X6,X12,X10)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_poly__mult,axiom,
! [X12,X54,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(c_Polynomial_Opoly(X6,X55),X12)),hAPP(c_Polynomial_Opoly(X6,X54),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_mult__eq__if,axiom,
! [X4,X21] :
( ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_le__diff__iff,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X42),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X42))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X42),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X42))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_mult__mono_H,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Oordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Oordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X25,X24)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X24)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_norm__mult__less,axiom,
! [X9,X10,X11,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),X11)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X10),X9)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_synthetic__div__correct,axiom,
! [X25,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,c_Polynomial_Osmult(X6,X25,c_Polynomial_Osynthetic__div(X6,X55,X25))) = c_Polynomial_OpCons(X6,hAPP(c_Polynomial_Opoly(X6,X55),X25),c_Polynomial_Osynthetic__div(X6,X55,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X54,X10,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)),X54) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X54)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X10),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_power__mult__distrib,axiom,
! [X4,X23,X5,X6] :
( class_Groups_Ocomm__monoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X23),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X10,X12,X6] :
( class_Rings_Olinordered__ring(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X12,X6] :
( class_Rings_Oring__1(X6)
=> c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X12),c_Groups_Oone__class_Oone(X6)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X12,c_Groups_Oone__class_Oone(X6))),c_Groups_Ominus__class_Ominus(X6,X12,c_Groups_Oone__class_Oone(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_poly__pCons,axiom,
! [X12,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_OpCons(X6,X5,X55)),X12) = c_Groups_Oplus__class_Oplus(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),hAPP(c_Polynomial_Opoly(X6,X55),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_power__less__power__Suc,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X23,X25,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X23,X5,X25,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X26)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X23,X25,X5,X6] :
( class_Rings_Olinordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X23,X25,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X23,X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X23),X4))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X23,X5,X25,X6] :
( class_Rings_Olinordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X23,X5,X25,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X26)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> c_Orderings_Oord__class_Oless(X6,X20,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X26,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> c_Orderings_Oord__class_Oless__eq(X6,X19,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X26,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> c_Orderings_Oord__class_Oless(X6,X19,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_power__increasing__iff,axiom,
! [X15,X13,X19,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X19)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X19),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X19),X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X4,X21,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X15,X13,X19,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X19)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X19),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X19),X15))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X4,X21,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_diff__pCons,axiom,
! [X54,X23,X55,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X5,X55),c_Polynomial_OpCons(X6,X23,X54)) = c_Polynomial_OpCons(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X55,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(fact_add__pCons,axiom,
! [X54,X23,X55,X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X5,X55),c_Polynomial_OpCons(X6,X23,X54)) = c_Polynomial_OpCons(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(fact_poly__power,axiom,
! [X12,X4,X55,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X6)),X55),X4)),X12) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(c_Polynomial_Opoly(X6,X55),X12)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_le__mult__natfloor,axiom,
! [X23,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5)
=> ( 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(X5)),c_RComplete_Onatfloor(X23)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X23))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X24,X23,X25,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23),c_Groups_Ominus__class_Ominus(X6,X25,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X24,X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Oplus__class_Oplus(X6,X25,X24)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_power__decreasing,axiom,
! [X5,X14,X4,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X5,X14,X4,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X14)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X14),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__strict__mono,axiom,
! [X4,X23,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X23),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X26)
& c_Orderings_Oord__class_Oless(X6,X20,X19) )
| ( c_Orderings_Oord__class_Oless(X6,X26,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless(X6,X19,X20) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X19,X26,X20,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X26))
<=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X26)
& c_Orderings_Oord__class_Oless(X6,X20,X19) )
| ( c_Orderings_Oord__class_Oless(X6,X26,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless(X6,X19,X20) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X10,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> ? [X69] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X69)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X3),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X3)),X69)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X12)),c_RealVector_Onorm__class_Onorm(X6,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> ? [X69] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X69)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X3)),X69)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X23,X21,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mult_Odiff__left,axiom,
! [X23,X31,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X5,X31)),X23) = c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X31),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [X30,X10,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ominus__class_Ominus(X6,X12,X10)),X30) = c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)),X25) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)),X25) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult_Oadd__left,axiom,
! [X23,X31,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X31)),X23) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X31),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_mult__left_Oadd,axiom,
! [X30,X10,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X12,X10)),X30) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X30),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X54,X55,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X55)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X54)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X4,X21,X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X21)),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X61,X63,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X61)),X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ominus__class_Ominus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23)),c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ominus__class_Ominus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23)),c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X23,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23)),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X24,X25,X23,X5,X11,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X11 != c_Groups_Ozero__class_Ozero(X6)
=> ( ( X5 = X23
& X25 != X24 )
=> c_Groups_Oplus__class_Oplus(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X11),X25)) != c_Groups_Oplus__class_Oplus(X6,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X11),X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_mult__le__cancel2,axiom,
! [X18,X42,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X42))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_mult__le__cancel1,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X15,X13,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X15,X13,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X37),X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X4,X21,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),X21),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X4))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_real__mult__less__iff1,axiom,
! [X15,X13,X37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X37)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X37))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_natceiling__eq,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X12) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X23)),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__diff__ineq,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X23)),c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5),c_RealVector_Onorm__class_Onorm(X6,X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_norm__triangle__ineq,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oplus__class_Oplus(X6,X12,X10)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),c_RealVector_Onorm__class_Onorm(X6,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_mult__smult__left,axiom,
! [X54,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_Osmult(X6,X5,X55)),X54) = c_Polynomial_Osmult(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_poly__diff,axiom,
! [X12,X54,X55,X6] :
( class_Rings_Ocomm__ring(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X55,X54)),X12) = c_Groups_Ominus__class_Ominus(X6,hAPP(c_Polynomial_Opoly(X6,X55),X12),hAPP(c_Polynomial_Opoly(X6,X54),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__add,axiom,
! [X12,X54,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,X54)),X12) = c_Groups_Oplus__class_Oplus(X6,hAPP(c_Polynomial_Opoly(X6,X55),X12),hAPP(c_Polynomial_Opoly(X6,X54),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_le__diff__conv2,axiom,
! [X57,X56,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X56)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X42))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X42),X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X17,X48,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X49,X48)),X17) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X17,X48,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X48)),X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X38,X4,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)),X38) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X38,X4,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)),X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X17,X48,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X49,X48)),X17) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X49),X17),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X48),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_norm__power__ineq,axiom,
! [X4,X12,X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X12)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__le__cancel__right,axiom,
! [X19,X26,X20,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X20,X26),c_Groups_Oplus__class_Oplus(X6,X19,X26))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X23,X25,X5,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X25))
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X19,X20,X26,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X26,X20),c_Groups_Oplus__class_Oplus(X6,X26,X19))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X23,X5,X25,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X25,X5),c_Groups_Oplus__class_Oplus(X6,X25,X23))
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__cancel__right,axiom,
! [X19,X26,X20,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X20,X26),c_Groups_Oplus__class_Oplus(X6,X19,X26))
<=> c_Orderings_Oord__class_Oless(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X23,X25,X5,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X25))
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X19,X20,X26,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X26,X20),c_Groups_Oplus__class_Oplus(X6,X26,X19))
<=> c_Orderings_Oord__class_Oless(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X23,X5,X25,X6] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X25,X5),c_Groups_Oplus__class_Oplus(X6,X25,X23))
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X4,X21,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X4)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X38),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X19,X20,X26,X6] :
( class_Rings_Oidom(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X26),X19))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X6)
| c_Rings_Odvd__class_Odvd(X6,X20,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X19,X26,X20,X6] :
( class_Rings_Oidom(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X26))
<=> ( X26 = c_Groups_Ozero__class_Ozero(X6)
| c_Rings_Odvd__class_Odvd(X6,X20,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_power__gt1__lemma,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4))) ) ),
file('/export/starexec/sandbox/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,
~ ! [X50] : 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),X50),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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,
! [X16,X10,X12] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X5,X55,X25,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X25,X55),c_Polynomial_OpCons(X6,X5,X55)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> X55 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X34),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_self__quotient__aux2,axiom,
! [X54,X11,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ( X5 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X54))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [X54,X11,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ( X5 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X54))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X54) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_smult__diff__right,axiom,
! [X54,X55,X5,X6] :
( class_Rings_Ocomm__ring(X6)
=> c_Polynomial_Osmult(X6,X5,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X55,X54)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55),c_Polynomial_Osmult(X6,X5,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(fact_smult__add__right,axiom,
! [X54,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,X54)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55),c_Polynomial_Osmult(X6,X5,X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X23,X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),X23),X4)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
=> X5 = X23 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X21,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X21),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oone__class_Oone(X6))),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X5,X21,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oone__class_Oone(X6))),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_natfloor__eq,axiom,
! [X12,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X12) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_mult__right__le__one__le,axiom,
! [X10,X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X10,X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X10)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X12),X12) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X10,X12,X25,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),c_RealVector_Onorm__class_Onorm(X6,X10)))
=> X12 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__right__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Oordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Oordered__comm__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Oordered__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_power__mono,axiom,
! [X4,X23,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X23),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Olinordered__comm__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__right__mono__neg,axiom,
! [X25,X5,X23,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X25,X5,X23,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X25,X5,X23,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X5)
=> ( c_Orderings_Oord__class_Oless(X6,X25,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X25,X5,X23,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X5)
=> ( c_Orderings_Oord__class_Oless(X6,X25,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X25),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X21,X4,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X21),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,X24)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X25,X24)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X25,X24)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X24,X25,X23,X5,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X25,X24)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_power__increasing,axiom,
! [X5,X14,X4,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X5,X14,X4,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X14)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_abs__eq__mult,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__ring__abs(X6)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
| c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6)) )
& ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
| c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6)) ) )
=> c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X5)),c_Groups_Oabs__class_Oabs(X6,X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_diff__monom,axiom,
! [X23,X4,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_Omonom(X6,X5,X4),c_Polynomial_Omonom(X6,X23,X4)) = c_Polynomial_Omonom(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(fact_add__monom,axiom,
! [X23,X4,X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Omonom(X6,X5,X4),c_Polynomial_Omonom(X6,X23,X4)) = c_Polynomial_Omonom(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__monom) ).
fof(fact_smult__diff__left,axiom,
! [X55,X23,X5,X6] :
( class_Rings_Ocomm__ring(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23),X55) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55),c_Polynomial_Osmult(X6,X23,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(fact_smult__add__left,axiom,
! [X55,X23,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X55) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55),c_Polynomial_Osmult(X6,X23,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(fact_realpow__num__eq__if,axiom,
! [X21,X4,X6] :
( class_Power_Opower(X6)
=> ( ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X21),X4) = c_Groups_Oone__class_Oone(X6) )
& ( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X21),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X21),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_smult__pCons,axiom,
! [X55,X23,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_OpCons(X6,X23,X55)) = c_Polynomial_OpCons(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Polynomial_Osmult(X6,X5,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(fact_add__le__mono,axiom,
! [X40,X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X16,X70,X17,X71] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,X16)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X71,X70),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X25,X23,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X25),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X40,X4,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X40,X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X15,X13,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X15),X15)) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X13 = c_Groups_Ozero__class_Ozero(X6)
& X15 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [X10,X12,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,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,X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10)))
=> X12 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_mult_Odiff__right,axiom,
! [X33,X23,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ominus__class_Ominus(X6,X23,X33)) = c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [X10,X12,X32,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),c_Groups_Ominus__class_Ominus(X6,X12,X10)) = c_Groups_Ominus__class_Ominus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X16,X10,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),c_Groups_Oplus__class_Oplus(X6,X10,X16)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult_Oadd__right,axiom,
! [X33,X23,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oplus__class_Oplus(X6,X23,X33)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_mult__right_Oadd,axiom,
! [X10,X12,X32,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),c_Groups_Oplus__class_Oplus(X6,X12,X10)) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult__less__cancel1,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X18,X42,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X42))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X5,X23,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X5))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X61,X63,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X63)),X61) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X63),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oab__semigroup__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_power__commutes,axiom,
! [X4,X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X60,X61,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X61)),X60) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_nat__less__real__le,axiom,
! [X34,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X34)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X34,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X34)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X34),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_poly__monom,axiom,
! [X12,X4,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_Omonom(X6,X5,X4)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_synthetic__div__unique,axiom,
! [X11,X54,X25,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,c_Polynomial_Osmult(X6,X25,X54)) = c_Polynomial_OpCons(X6,X11,X54)
=> ( X11 = hAPP(c_Polynomial_Opoly(X6,X55),X25)
& X54 = c_Polynomial_Osynthetic__div(X6,X55,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_reals__Archimedean6,axiom,
! [X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
=> ? [X43] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X11)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_RealDef_Oreal(tc_Nat_Onat,X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_synthetic__div__pCons,axiom,
! [X25,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osynthetic__div(X6,c_Polynomial_OpCons(X6,X5,X55),X25) = c_Polynomial_OpCons(X6,hAPP(c_Polynomial_Opoly(X6,X55),X25),c_Polynomial_Osynthetic__div(X6,X55,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_power__mult,axiom,
! [X4,X21,X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X21)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X54,X55,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X55)),X54) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X39)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X38)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X10,X12,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_power__eq__if,axiom,
! [X55,X21] :
( ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X55),X21) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X55),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X55),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_le__diff__conv,axiom,
! [X57,X42,X56] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X42),X57)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X42,X56,X57] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X42))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X42),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X40,X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X40)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_diff__add__assoc2,axiom,
! [X22,X39,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X22),X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__assoc2,axiom,
! [X22,X39,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38),X22) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X22),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X22,X39,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X39),X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X22,X39,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X38),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X22,X39,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X39)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X39),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_mult__smult__right,axiom,
! [X54,X5,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),c_Polynomial_Osmult(X6,X5,X54)) = c_Polynomial_Osmult(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_poly__smult,axiom,
! [X12,X55,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_Osmult(X6,X5,X55)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(c_Polynomial_Opoly(X6,X55),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_mult__le__0__iff,axiom,
! [X19,X20,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X19),c_Groups_Ozero__class_Ozero(X6))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20)
& c_Orderings_Oord__class_Oless__eq(X6,X19,c_Groups_Ozero__class_Ozero(X6)) )
| ( c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X19,X20,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X19))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20)
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X19) )
| ( c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless__eq(X6,X19,c_Groups_Ozero__class_Ozero(X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X18,X13] :
( 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,X13)),X18))
<=> ( X13 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X48,X49,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X49,X48)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X48,X49,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X48)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X4,X21,X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X4,X21,X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_poly__pcompose,axiom,
! [X12,X54,X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_Opcompose(X6,X55,X54)),X12) = hAPP(c_Polynomial_Opoly(X6,X55),hAPP(c_Polynomial_Opoly(X6,X54),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X21,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X21,X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Oone__class_Oone(X6))),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_Bseq__inverse__lemma,axiom,
! [X12,X11,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,c_RealVector_Onorm__class_Onorm(X6,X12))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_Rings_Oinverse__class_Oinverse(X6,X12)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X15,X13] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X13 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_cq0,axiom,
! [X50] : 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____),X50))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cq0) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__pos__nonneg,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X5,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__gr__0,axiom,
! [X18,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_zmult__assoc,axiom,
! [X47,X48,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),X48)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X38,X4,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4)),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X47,X48,X49] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X49),X48)),X47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X48),X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_zpower__zpower,axiom,
! [X16,X10,X12] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),X10)),X16) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__cancel__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__cancel__semiring(X6)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
& c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6)) )
| ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23) ) )
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__cancel__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__cancel__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X5),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__neg__pos,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X5),c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_split__mult__pos__le,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__ring(X6)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23) )
| ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
& c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6)) ) )
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__cancel__semiring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_less__1__mult,axiom,
! [X4,X21,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X21)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X4)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X21),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_mult__pos__pos,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__semiring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X23,X5,X6] :
( class_Rings_Oordered__ring(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__neg__neg,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__ring__strict(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_add__right__mono,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X25,X5),c_Groups_Oplus__class_Oplus(X6,X25,X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),c_Groups_Oplus__class_Oplus(X6,X23,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X25,X5),c_Groups_Oplus__class_Oplus(X6,X25,X23)) ) ),
file('/export/starexec/sandbox/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)
=> ~ ! [X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X53),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____),X53)),X66) ) ),
file('/export/starexec/sandbox/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)
& ! [X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X53),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____),X53)),X66) ) ),
file('/export/starexec/sandbox/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,
! [X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X53),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____),X53)),v_m____) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m_I2_J) ).
fof(fact_c,axiom,
! [X50] : 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____),X50))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_c) ).
fof(fact_one__less__power,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_dvd__power__same,axiom,
! [X4,X10,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X12,X10)
=> c_Rings_Odvd__class_Odvd(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X10),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_decseq__def,axiom,
! [X80,X6] :
( class_Orderings_Oorder(X6)
=> ( c_SEQ_Odecseq(X6,X80)
<=> ! [X66,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X43)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(X80,X43),hAPP(X80,X66)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__def) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X4,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X16),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X16,c_RealDef_Oreal(tc_Nat_Onat,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_add__increasing,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X25)
=> c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Oplus__class_Oplus(X6,X5,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X5,X23,X25,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X25)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X5)
=> c_Orderings_Oord__class_Oless__eq(X6,X23,c_Groups_Oplus__class_Oplus(X6,X5,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X25)
=> c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Oplus__class_Oplus(X6,X5,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X25)
=> c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Oplus__class_Oplus(X6,X5,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X25)
=> c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Oplus__class_Oplus(X6,X5,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_real__minus__mult__self__le,axiom,
! [X12,X28] : 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),X28),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_zadd__left__mono,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X22),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X38,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X40,X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X40),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X40,X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X16,X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X12),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X39)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X38),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X39,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_abs__power__minus,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),X4)) = c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus) ).
fof(fact_dvd__diff,axiom,
! [X16,X10,X12,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X12,X10)
=> ( c_Rings_Odvd__class_Odvd(X6,X12,X16)
=> c_Rings_Odvd__class_Odvd(X6,X12,c_Groups_Ominus__class_Ominus(X6,X10,X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X5,X23)
=> ( c_Rings_Odvd__class_Odvd(X6,X5,X25)
=> c_Rings_Odvd__class_Odvd(X6,X5,c_Groups_Oplus__class_Oplus(X6,X23,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_of__real_Obounded,axiom,
! [X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> ? [X69] :
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Obounded) ).
fof(fact_of__real_Ononneg__bounded,axiom,
! [X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> ? [X69] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X69)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X69)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Ononneg__bounded) ).
fof(fact_of__real_Opos__bounded,axiom,
! [X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> ? [X69] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X69)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X69)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Opos__bounded) ).
fof(fact_abs__add__abs,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Oplus__class_Oplus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23))) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Oabs__class_Oabs(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_smult__dvd__iff,axiom,
! [X76,X72,X20,X6] :
( class_Fields_Ofield(X6)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X20,X72),X76)
<=> ( ( X20 = c_Groups_Ozero__class_Ozero(X6)
=> X76 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) )
& ( X20 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X6),X72,X76) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(fact_eq__diff__iff,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X34)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X18)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X42) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X42)
<=> X34 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__less,axiom,
! [X21,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_natfloor__subtract,axiom,
! [X12,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),X12)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X5))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_natceiling__subtract,axiom,
! [X12,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),X12)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X5))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X20,X20))
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,X20,X20))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oplus__class_Oplus(X6,X20,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X20,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,X20,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X25) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X25) = c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oplus__class_Oplus(X6,X23,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Oab__semigroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X25) = c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oplus__class_Oplus(X6,X23,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X24,X25,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oplus__class_Oplus(X6,X25,X24)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X25),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X24,X25,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oplus__class_Oplus(X6,X25,X24)) = c_Groups_Oplus__class_Oplus(X6,X25,c_Groups_Oplus__class_Oplus(X6,X5,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_real__0__le__add__iff,axiom,
! [X15,X13] :
( 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,X13,X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__0__less__add__iff,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X15))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_inverse__le__imp__le,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
fof(fact_inverse__less__imp__less,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23))
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
fof(fact_inverse__le__imp__le__neg,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23))
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
fof(fact_inverse__less__imp__less__neg,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Rings_Oinverse__class_Oinverse(X6,X23))
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X20,X19)
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ominus__class_Ominus(X6,X20,X19),c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X20,X19)
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ominus__class_Ominus(X6,X20,X19),c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_smult__monom,axiom,
! [X4,X23,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_Omonom(X6,X23,X4)) = c_Polynomial_Omonom(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(fact_smult__smult,axiom,
! [X55,X23,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_Osmult(X6,X23,X55)) = c_Polynomial_Osmult(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X10,X12] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X18,X34] :
( 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),X34),X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X34)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_real__mult__order,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_abs__mult__pos,axiom,
! [X10,X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X10)),X12) = c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_le__cube,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X21))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X51,X26,X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Groups_Ominus__class_Ominus(X6,X20,X19) = c_Groups_Ominus__class_Ominus(X6,X26,X51)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X20,X19)
<=> c_Orderings_Oord__class_Oless__eq(X6,X26,X51) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X51,X26,X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Groups_Ominus__class_Ominus(X6,X20,X19) = c_Groups_Ominus__class_Ominus(X6,X26,X51)
=> ( c_Orderings_Oord__class_Oless(X6,X20,X19)
<=> c_Orderings_Oord__class_Oless(X6,X26,X51) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_mult__le__mono1,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X60,X61,X62,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),X60)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X62),X60)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X4,X21,X38] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X21),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X4)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X4,X38,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X38),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X38)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X38,X39,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X39),X38) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X38),X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X38,X39,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X39),X38) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X47,X48,X49] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,X48),X47) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X38,X4,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4),X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X38)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X16,X10,X12] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X16)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X16,X10,X12] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X37,X64] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X37)
| X64 = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X37,X64] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X64,c_Groups_Oone__class_Oone(tc_Int_Oint)),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X37,X64] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X64,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X37,X64] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X64,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X37,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_real__le__eq__diff,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X15)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_less__bin__lemma,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,X41)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X42,X41),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zero__less__diff,axiom,
! [X34,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X34))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X4,X21,X40,X38] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X38,X40)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X40) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X4)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_natfloor__add,axiom,
! [X5,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X5))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_natceiling__add,axiom,
! [X5,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X5))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_abs__leI,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,X5),X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__le__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,X20),X19)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X20,X19)
& c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__less__iff,axiom,
! [X19,X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X20),X19)
<=> ( c_Orderings_Oord__class_Oless(X6,X20,X19)
& c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_add__leD1,axiom,
! [X4,X38,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X38),X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X4,X38,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X38),X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X39),X38)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_real__of__nat__diff,axiom,
! [X21,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X21)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_RealDef_Oreal(tc_Nat_Onat,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X15,X13,X6] :
( class_Groups_Oordered__comm__monoid__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X13)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X15)
=> ( c_Groups_Oplus__class_Oplus(X6,X13,X15) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X13 = c_Groups_Ozero__class_Ozero(X6)
& X15 = c_Groups_Ozero__class_Ozero(X6) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_le__imp__inverse__le,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X23),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
fof(fact_less__imp__inverse__less,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X23),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
fof(fact_le__imp__inverse__le__neg,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X23),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
fof(fact_less__imp__inverse__less__neg,axiom,
! [X23,X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ( c_Orderings_Oord__class_Oless(X6,X23,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X23),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X18,X13] :
( 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),X13),X18))
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X18,X13] :
( 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),X13),X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13)
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_minus__apply,axiom,
! [X13,X83,X84,X67,X6] :
( class_Groups_Ominus(X6)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X67,X6),X84,X83),X13) = c_Groups_Ominus__class_Ominus(X6,hAPP(X84,X13),hAPP(X83,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_one__le__inverse__iff,axiom,
! [X13,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Rings_Oinverse__class_Oinverse(X6,X13))
<=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X13)
& c_Orderings_Oord__class_Oless__eq(X6,X13,c_Groups_Oone__class_Oone(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
fof(fact_one__le__inverse,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__inverse) ).
fof(fact_one__less__inverse__iff,axiom,
! [X13,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Rings_Oinverse__class_Oinverse(X6,X13))
<=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X13)
& c_Orderings_Oord__class_Oless(X6,X13,c_Groups_Oone__class_Oone(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
fof(fact_one__less__inverse,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Oone__class_Oone(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__inverse) ).
fof(fact_abs__le__interval__iff,axiom,
! [X65,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13),X65)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X65),X13)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_less__eq__poly__def,axiom,
! [X15,X13,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X6),X13,X15)
<=> ( X13 = X15
| c_Polynomial_Opos__poly(X6,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X15,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_less__poly__def,axiom,
! [X15,X13,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),X13,X15)
<=> c_Polynomial_Opos__poly(X6,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X15,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(fact_zero__le__power__abs,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Oabs__class_Oabs(X6,X5)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_pos__poly__pCons,axiom,
! [X72,X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Polynomial_Opos__poly(X6,c_Polynomial_OpCons(X6,X20,X72))
<=> ( c_Polynomial_Opos__poly(X6,X72)
| ( X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
& c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_power__inject__exp,axiom,
! [X18,X34,X20,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X20)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X6),X20),X34) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),X20),X18)
<=> X34 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_natceiling__le__eq,axiom,
! [X20,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X13),X20)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_RealDef_Oreal(tc_Nat_Onat,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_less__natfloor,axiom,
! [X4,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X4))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X12),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_le__natfloor__eq,axiom,
! [X20,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_RComplete_Onatfloor(X13))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X20),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_one__le__power,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_inverse__le__1__iff,axiom,
! [X13,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X13),c_Groups_Oone__class_Oone(X6))
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,c_Groups_Ozero__class_Ozero(X6))
| c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
fof(fact_inverse__less__1__iff,axiom,
! [X13,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X13),c_Groups_Oone__class_Oone(X6))
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,c_Groups_Ozero__class_Ozero(X6))
| c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
fof(fact_natfloor__add__one,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_natceiling__add__one,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_nonzero__inverse__mult__distrib,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X23)),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
fof(fact_odd__nonzero,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16),X16) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X12,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X20,X78,X79,X6] : hAPP(hAPP(c_Power_Opower_Opower(X6,X79,X78),X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_le__imp__0__less,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16)
=> 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),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_sgn__times,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Osgn__class_Osgn(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Osgn__class_Osgn(X6,X5)),c_Groups_Osgn__class_Osgn(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).
fof(fact_sgn__mult,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> c_Groups_Osgn__class_Osgn(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Osgn__class_Osgn(X6,X12)),c_Groups_Osgn__class_Osgn(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__mult) ).
fof(fact_abs__mult,axiom,
! [X23,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X5)),c_Groups_Oabs__class_Oabs(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_inverse__mult__distrib,axiom,
! [X23,X5,X6] :
( class_Fields_Ofield__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),c_Rings_Oinverse__class_Oinverse(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
fof(fact_minus__pCons,axiom,
! [X55,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Polynomial_OpCons(X6,X5,X55)) = c_Polynomial_OpCons(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [X55,X5,X67] :
( class_Groups_Oab__group__add(X67)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X67),c_Polynomial_OpCons(X67,X5,X55)) = c_Polynomial_OpCons(X67,c_Groups_Ouminus__class_Ouminus(X67,X5),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X67),X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_abs__minus__commute,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)) = c_Groups_Oabs__class_Oabs(X6,c_Groups_Ominus__class_Ominus(X6,X23,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_norm__minus__commute,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)) = c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ominus__class_Ominus(X6,X23,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_norm__mult,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X12)),c_RealVector_Onorm__class_Onorm(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X16,X17] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oone__class_Oone(tc_Int_Oint)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X21,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X21)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4),X4) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X4,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X4)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X22)) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X21,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X21)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_of__real__mult,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_RealVector_Oof__real(X6,X12)),c_RealVector_Oof__real(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__mult) ).
fof(fact_le__funE,axiom,
! [X13,X1,X2,X6,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X13),hAPP(X1,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X13,X1,X2,X6,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X67,hAPP(X2,X13),hAPP(X1,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_less__imp__diff__less,axiom,
! [X4,X38,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X39,X38)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X4),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X16,X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X21,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X10,X16,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X16)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X21,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X16,X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X21,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X10,X16,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X16)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X21,X39,X22] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X39)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_of__real_Odiff,axiom,
! [X10,X12,X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> c_RealVector_Oof__real(X6,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,X10)) = c_Groups_Ominus__class_Ominus(X6,c_RealVector_Oof__real(X6,X12),c_RealVector_Oof__real(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Odiff) ).
fof(fact_of__real_Oadd,axiom,
! [X10,X12,X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> c_RealVector_Oof__real(X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X10)) = c_Groups_Oplus__class_Oplus(X6,c_RealVector_Oof__real(X6,X12),c_RealVector_Oof__real(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Oadd) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X4,X12] : 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,X12)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X18,X34,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18)
<=> X34 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X4,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> 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),X12),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_dvd__trans,axiom,
! [X25,X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X5,X23)
=> ( c_Rings_Odvd__class_Odvd(X6,X23,X25)
=> c_Rings_Odvd__class_Odvd(X6,X5,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_order__trans,axiom,
! [X16,X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X16)
=> c_Orderings_Oord__class_Oless__eq(X6,X12,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X16,X12,X10,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X16,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_order__less__le__trans,axiom,
! [X16,X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X16)
=> c_Orderings_Oord__class_Oless(X6,X12,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X16,X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless(X6,X10,X16)
=> c_Orderings_Oord__class_Oless(X6,X12,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__trans,axiom,
! [X16,X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless(X6,X10,X16)
=> c_Orderings_Oord__class_Oless(X6,X12,X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [X16,X12,X10,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X10,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X16,X10)
=> c_Orderings_Oord__class_Oless(X6,X16,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I8_J,axiom,
! [X16,X12,X10,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X10)
=> c_Orderings_Oord__class_Oless(X6,X16,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I10_J,axiom,
! [X16,X12,X10,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X10,X12)
=> ( c_Orderings_Oord__class_Oless(X6,X16,X10)
=> c_Orderings_Oord__class_Oless(X6,X16,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X23,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Ouminus__class_Ouminus(X6,X23)) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_minus__add__distrib,axiom,
! [X23,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Ouminus__class_Ouminus(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23)) = c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X23),c_Groups_Ouminus__class_Ouminus(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X12] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X12)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_nonzero__power__inverse,axiom,
! [X4,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
fof(fact_of__real__diff,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,X10)) = c_Groups_Ominus__class_Ominus(X6,c_RealVector_Oof__real(X6,X12),c_RealVector_Oof__real(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__diff) ).
fof(fact_of__real__add,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X10)) = c_Groups_Oplus__class_Oplus(X6,c_RealVector_Oof__real(X6,X12),c_RealVector_Oof__real(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__add) ).
fof(fact_compl__le__compl__iff,axiom,
! [X15,X13,X6] :
( class_Lattices_Oboolean__algebra(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X13),c_Groups_Ouminus__class_Ouminus(X6,X15))
<=> c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X20,X19,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X19),c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_neg__less__iff__less,axiom,
! [X20,X19,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X19),c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless(X6,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_mult_Ominus__left,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),X23) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__left_Ominus,axiom,
! [X10,X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,X12)),X10) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_power__abs,axiom,
! [X4,X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Oabs__class_Oabs(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Oabs__class_Oabs(X6,X5)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_minus__mult__left,axiom,
! [X23,X5,X6] :
( class_Rings_Oring(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_power__inverse,axiom,
! [X4,X5,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inverse) ).
fof(fact_smult__minus__right,axiom,
! [X55,X5,X6] :
( class_Rings_Ocomm__ring(X6)
=> c_Polynomial_Osmult(X6,X5,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X55)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X42,X56,X57] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X57) = X42
<=> X56 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_norm__power,axiom,
! [X4,X12,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> c_RealVector_Onorm__class_Onorm(X6,hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X12)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_add__minus__cancel,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X23)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_zle__trans,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_real__le__trans,axiom,
! [X38,X39,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_pos__poly__mult,axiom,
! [X54,X55,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Polynomial_Opos__poly(X6,X55)
=> ( c_Polynomial_Opos__poly(X6,X54)
=> c_Polynomial_Opos__poly(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_real__of__nat__mult,axiom,
! [X4,X21] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X21)),c_RealDef_Oreal(tc_Nat_Onat,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_of__real__power,axiom,
! [X4,X12,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X12),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_RealVector_Oof__real(X6,X12)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__power) ).
fof(fact_poly__minus,axiom,
! [X12,X55,X6] :
( class_Rings_Ocomm__ring(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X55)),X12) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(c_Polynomial_Opoly(X6,X55),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_abs__le__D2,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,X5),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D2) ).
fof(fact_minus__le__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X19)
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X19),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_minus__less__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X19)
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X19),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_le__minus__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ouminus__class_Ouminus(X6,X19))
<=> c_Orderings_Oord__class_Oless__eq(X6,X19,c_Groups_Ouminus__class_Ouminus(X6,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ouminus__class_Ouminus(X6,X19))
<=> c_Orderings_Oord__class_Oless(X6,X19,c_Groups_Ouminus__class_Ouminus(X6,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_real__of__nat__add,axiom,
! [X4,X21] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X21),c_RealDef_Oreal(tc_Nat_Onat,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X17,X16] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X17)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X16),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_minus__monom,axiom,
! [X4,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Polynomial_Omonom(X6,X5,X4)) = c_Polynomial_Omonom(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(fact_smult__minus__left,axiom,
! [X55,X5,X6] :
( class_Rings_Ocomm__ring(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X55) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(fact_mult__left__idem,axiom,
! [X23,X5,X6] :
( class_Lattices_Oab__semigroup__idem__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X12] : 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,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_inverse__positive__imp__positive,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X5))
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
fof(fact_inverse__negative__imp__negative,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Groups_Ozero__class_Ozero(X6))
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X34,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_RealDef_Oreal(tc_Nat_Onat,X34))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X34,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_RealDef_Oreal(tc_Nat_Onat,X34))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
! [X20,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X20))
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X20,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X20))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(fact_sgn__greater,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Osgn__class_Osgn(X6,X20))
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).
fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
! [X20,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Rings_Oinverse__class_Oinverse(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
fof(fact_inverse__negative__iff__negative,axiom,
! [X20,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
fof(fact_sgn__less,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Osgn__class_Osgn(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_mult_Ominus__right,axiom,
! [X23,X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ouminus__class_Ouminus(X6,X23)) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_mult__right_Ominus,axiom,
! [X12,X32,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),c_Groups_Ouminus__class_Ouminus(X6,X12)) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X32),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_minus__mult__right,axiom,
! [X23,X5,X6] :
( class_Rings_Oring(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ouminus__class_Ouminus(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_compl__mono,axiom,
! [X10,X12,X6] :
( class_Lattices_Oboolean__algebra(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X10),c_Groups_Ouminus__class_Ouminus(X6,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X23),c_Groups_Ouminus__class_Ouminus(X6,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_zero__less__two,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oplus__class_Oplus(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Oone__class_Oone(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X12] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_minus__add__cancel,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Oplus__class_Oplus(X6,X5,X23)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_minus__le__self__iff,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X20)
<=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__less__nonneg,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ouminus__class_Ouminus(X6,X20),X20)
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_le__minus__self__iff,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless__eq(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ouminus__class_Ouminus(X6,X20))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_zmult__zminus,axiom,
! [X17,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X16)),X17) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_complex__of__real__power,axiom,
! [X4,X12] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X12)),X4) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X12),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(fact_power__real__of__nat,axiom,
! [X4,X21] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X21)),X4) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__power,axiom,
! [X4,X21] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X21)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_nat__less__cases,axiom,
! [X45,X18,X34] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18)
=> hBOOL(hAPP(hAPP(X45,X18),X34)) )
=> ( ( X34 = X18
=> hBOOL(hAPP(hAPP(X45,X18),X34)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X34)
=> hBOOL(hAPP(hAPP(X45,X18),X34)) )
=> hBOOL(hAPP(hAPP(X45,X18),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_negative__imp__inverse__negative,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Orderings_Oord__class_Oless(X6,c_Rings_Oinverse__class_Oinverse(X6,X5),c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X5,X55,X25,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> ( c_Polynomial_Osmult(X6,X25,X55) = c_Polynomial_OpCons(X6,X5,X55)
=> X55 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(fact_abs__mult__self,axiom,
! [X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oabs__class_Oabs(X6,X5)),c_Groups_Oabs__class_Oabs(X6,X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_minus__mult__minus,axiom,
! [X23,X5,X6] :
( class_Rings_Oring(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),c_Groups_Ouminus__class_Ouminus(X6,X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X23,X5,X6] :
( class_Rings_Oring(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,X5)),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ouminus__class_Ouminus(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__dvd__iff,axiom,
! [X15,X13,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,c_Groups_Ouminus__class_Ouminus(X6,X13),X15)
<=> c_Rings_Odvd__class_Odvd(X6,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_abs__dvd__iff,axiom,
! [X42,X34,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,c_Groups_Oabs__class_Oabs(X6,X34),X42)
<=> c_Rings_Odvd__class_Odvd(X6,X34,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_abs__le__D1,axiom,
! [X23,X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,X5),X23)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_dvd__minus__iff,axiom,
! [X15,X13,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X13,c_Groups_Ouminus__class_Ouminus(X6,X15))
<=> c_Rings_Odvd__class_Odvd(X6,X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__abs__iff,axiom,
! [X42,X34,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,X34,c_Groups_Oabs__class_Oabs(X6,X42))
<=> c_Rings_Odvd__class_Odvd(X6,X34,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_square__eq__iff,axiom,
! [X19,X20,X6] :
( class_Rings_Oidom(X6)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X19),X19)
<=> ( X20 = X19
| X20 = c_Groups_Ouminus__class_Ouminus(X6,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_pos__poly__add,axiom,
! [X54,X55,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Polynomial_Opos__poly(X6,X55)
=> ( c_Polynomial_Opos__poly(X6,X54)
=> c_Polynomial_Opos__poly(X6,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X51,X26,X19,X20,X6] :
( class_Groups_Oab__group__add(X6)
=> ( c_Groups_Ominus__class_Ominus(X6,X20,X19) = c_Groups_Ominus__class_Ominus(X6,X26,X51)
=> ( X20 = X19
<=> X26 = X51 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_natfloor__power,axiom,
! [X4,X12] :
( X12 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X12))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X12),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X12)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_minus__diff__eq,axiom,
! [X23,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23)) = c_Groups_Ominus__class_Ominus(X6,X23,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_xt1_I5_J,axiom,
! [X12,X10,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> X12 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X10,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> X12 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X13,X15,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X15,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X15,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( X13 = X15
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
& c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_less__add__one,axiom,
! [X5,X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oone__class_Oone(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_pCons__eq__iff,axiom,
! [X76,X19,X72,X20,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_OpCons(X6,X20,X72) = c_Polynomial_OpCons(X6,X19,X76)
<=> ( X20 = X19
& X72 = X76 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_monom__eq__iff,axiom,
! [X19,X18,X20,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_Omonom(X6,X20,X18) = c_Polynomial_Omonom(X6,X19,X18)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_add__right__cancel,axiom,
! [X26,X20,X19,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X19,X20) = c_Groups_Oplus__class_Oplus(X6,X26,X20)
<=> X19 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X25,X5,X23,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X23,X5) = c_Groups_Oplus__class_Oplus(X6,X25,X5)
=> X23 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Ocancel__ab__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X5,X23) = c_Groups_Oplus__class_Oplus(X6,X5,X25)
=> X23 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X26,X19,X20,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X20,X19) = c_Groups_Oplus__class_Oplus(X6,X20,X26)
<=> X19 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X25,X23,X5,X6] :
( class_Groups_Ocancel__semigroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X5,X23) = c_Groups_Oplus__class_Oplus(X6,X5,X25)
=> X23 = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X4,X21] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X4)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X21) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_natceiling__le,axiom,
! [X5,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,X5))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X5,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X12),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,c_RComplete_Onatfloor(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_order__root,axiom,
! [X20,X72,X6] :
( class_Rings_Oidom(X6)
=> ( hAPP(c_Polynomial_Opoly(X6,X72),X20) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
| c_Polynomial_Oorder(X6,X20,X72) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diffs0__imp__equal,axiom,
! [X4,X21] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X21 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_real__natfloor__le,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X12)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_zero__le__square,axiom,
! [X5,X6] :
( class_Rings_Olinordered__ring(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_zle__antisym,axiom,
! [X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16)
=> X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X21)
=> X21 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16)
=> X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Oplus__class_Oplus(X6,X5,X23),X23) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ominus__class_Ominus(X6,X5,X23),X23) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X18,X34] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34),X18) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X34 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X18 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [X18,X42,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X42) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X42)
<=> X34 = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X18,X34,X42] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X34) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X18)
<=> X34 = X18 ),
file('/export/starexec/sandbox/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,
~ ! [X73] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X73) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
=> ~ ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X73),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox/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,
? [X73] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X73) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X73),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_q_I2_J) ).
fof(fact_dvd__triv__left,axiom,
! [X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Rings_Odvd__class_Odvd(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_le__iff__add,axiom,
! [X18,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18)
<=> ? [X44] : X18 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
<=> ? [X43] : X41 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_diff__add__0,axiom,
! [X21,X4] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X21)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__add__inverse,axiom,
! [X21,X4] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X21),X4) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X4,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4),X4) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__le__self,axiom,
! [X4,X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X21,X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X21,X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X13))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X13),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_zero__less__abs__iff,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oabs__class_Oabs(X6,X20))
<=> X20 != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/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,
! [X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ? [X8] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X8,X7) ) ),
file('/export/starexec/sandbox/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,
! [X18,X42,X34] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X42) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X42)
<=> ( X34 = X18
| X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__right__cancel,axiom,
! [X19,X20,X26] :
( X26 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X20),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X19),X26)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X18,X34,X42] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18)
<=> ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X34 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X18,X34,X42] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X18)
<=> ( X34 = X18
| X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_real__mult__left__cancel,axiom,
! [X19,X20,X26] :
( X26 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X19)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_tsub__eq,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X12)
=> c_Nat__Transfer_Otsub(X12,X10) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_order__less__le,axiom,
! [X15,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
& X13 != X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X15,X13,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless(X6,X13,X15)
| X13 = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__neq__le__trans,axiom,
! [X23,X5,X6] :
( class_Orderings_Oorder(X6)
=> ( X5 != X23
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X10,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
| X12 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X23,X5,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,X23)
=> ( X5 != X23
=> c_Orderings_Oord__class_Oless(X6,X5,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X5,X23,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X5)
=> ( X5 != X23
=> c_Orderings_Oord__class_Oless(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X23,X5,X6] :
( class_Orderings_Oorder(X6)
=> ( X5 != X23
=> ( c_Orderings_Oord__class_Oless__eq(X6,X23,X5)
=> c_Orderings_Oord__class_Oless(X6,X23,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X12,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6))),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_natfloor__mono,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X12),c_RComplete_Onatfloor(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natceiling__mono,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X12),c_RComplete_Onatceiling(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_abs__le__zero__iff,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oabs__class_Oabs(X6,X20),c_Groups_Ozero__class_Ozero(X6))
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_order__less__imp__le,axiom,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X12,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_abs__minus__le__zero,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oabs__class_Oabs(X6,X5)),c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X37)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X13,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X13))
<=> X13 != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X12] : 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,X12)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_le__square,axiom,
! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_diff__minus__eq__add,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,c_Groups_Ouminus__class_Ouminus(X6,X23)) = c_Groups_Oplus__class_Oplus(X6,X5,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X10,X12,X6] :
( class_Rings_Ocomm__ring__1(X6)
=> c_Groups_Ominus__class_Ominus(X6,X12,X10) = c_Groups_Oplus__class_Oplus(X6,X12,c_Groups_Ouminus__class_Ouminus(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_ab__diff__minus,axiom,
! [X23,X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,X23) = c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ouminus__class_Ouminus(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,X23) = c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ouminus__class_Ouminus(X6,X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_norm__le__zero__iff,axiom,
! [X13,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X18,X34] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X34,X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X64,X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,X64)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X37,X64)
& X37 != X64 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X18,X34] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18)
& X34 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X18,X34] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X18)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18)
| X34 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> ( X21 != X4
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__eq__real__def,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X15)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X15)
| X13 = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [X15,X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X15)
& X13 != X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_complex__i__mult__minus,axiom,
! [X12] : 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),X12)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(fact_uminus__apply,axiom,
! [X13,X84,X67,X6] :
( class_Groups_Ouminus(X6)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X67,X6),X84),X13) = c_Groups_Ouminus__class_Ouminus(X6,hAPP(X84,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_mult__sgn__abs,axiom,
! [X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Osgn__class_Osgn(X6,X12)),c_Groups_Oabs__class_Oabs(X6,X12)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_monom__0,axiom,
! [X5,X6] :
( class_Groups_Ozero(X6)
=> c_Polynomial_Omonom(X6,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__0) ).
fof(fact_sgn__neg,axiom,
! [X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Osgn__class_Osgn(X6,X5) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).
fof(fact_sgn__1__neg,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Groups_Osgn__class_Osgn(X6,X20) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6))
<=> c_Orderings_Oord__class_Oless(X6,X20,c_Groups_Ozero__class_Ozero(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__imp__le__nat,axiom,
! [X4,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X4,X21] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
| X21 = X4 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_abs__of__nonpos,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__of__neg,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__neg) ).
fof(fact_mult__poly__0__left,axiom,
! [X54,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))),X54) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X17,X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X17)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X16,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X17,X16] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X16,X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_complex__diff__def,axiom,
! [X10,X12] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X12,X10) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X12,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(fact_minus__real__def,axiom,
! [X10,X12] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X12,X10) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__diff__def,axiom,
! [X9,X11] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X11,X9) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X11,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(fact_zabs__less__one__iff,axiom,
! [X37] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X37),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> X37 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_smult__eq__0__iff,axiom,
! [X72,X20,X6] :
( class_Rings_Oidom(X6)
=> ( c_Polynomial_Osmult(X6,X20,X72) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
<=> ( X20 = c_Groups_Ozero__class_Ozero(X6)
| X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [X20,X13] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X13 = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X18,X20,X6] :
( ( class_Power_Opower(X6)
& class_Rings_Omult__zero(X6)
& class_Rings_Ono__zero__divisors(X6)
& class_Rings_Ozero__neq__one(X6) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X6),X20),X18) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X20 = c_Groups_Ozero__class_Ozero(X6)
& X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [X13,X6] :
( class_Rings_Oring__1__no__zero__divisors(X6)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X13),X13) = c_Groups_Oone__class_Oone(X6)
<=> ( X13 = c_Groups_Oone__class_Oone(X6)
| X13 = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_sgn__pos,axiom,
! [X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Groups_Osgn__class_Osgn(X6,X5) = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Groups_Osgn__class_Osgn(X6,X20) = c_Groups_Oone__class_Oone(X6)
<=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_field__inverse,axiom,
! [X5,X6] :
( class_Fields_Ofield(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),X5) = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse) ).
fof(fact_left__inverse,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),X5) = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__inverse) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X72,X20,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_OpCons(X6,X20,X72) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
<=> ( X20 = c_Groups_Ozero__class_Ozero(X6)
& X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X88,X72,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X72,X88) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
<=> X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( X13 != X15
<=> ( c_Orderings_Oord__class_Oless(X6,X13,X15)
| c_Orderings_Oord__class_Oless(X6,X15,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
| X12 = X10
| c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_constant__def,axiom,
! [X2,X67,X6] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X6,X67,X2)
<=> ! [X3,X68] : hAPP(X2,X3) = hAPP(X2,X68) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).
fof(fact_abs__of__nonneg,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Groups_Oabs__class_Oabs(X6,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> c_Groups_Oabs__class_Oabs(X6,X5) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_linorder__linear,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
| c_Orderings_Oord__class_Oless__eq(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
| c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X25,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,X25) = c_Groups_Oplus__class_Oplus(X6,X25,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_minus__unique,axiom,
! [X23,X5,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X5,X23) = c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,X5) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X19,X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( X20 = c_Groups_Ouminus__class_Ouminus(X6,X19)
<=> c_Groups_Oplus__class_Oplus(X6,X20,X19) = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X15,X13,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X13,X15) = c_Groups_Ozero__class_Ozero(X6)
<=> X15 = c_Groups_Ouminus__class_Ouminus(X6,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_monom__eq__0__iff,axiom,
! [X18,X20,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_Omonom(X6,X20,X18) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),c_Groups_Oabs__class_Oabs(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
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/sandbox/benchmark/theBenchmark.p',fact_qnc) ).
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/sandbox/benchmark/theBenchmark.p',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_mult__poly__0__right,axiom,
! [X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X55),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X23,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X23),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_inverse__unique,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) = c_Groups_Oone__class_Oone(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,X5) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__unique) ).
fof(fact_zless__linear,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X10)
| X12 = X10
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X18,X34] :
( X34 != X18
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X34) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_dvd__0__left,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> X5 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_zle__linear,axiom,
! [X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X17)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X4,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_real__le__linear,axiom,
! [X17,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X17)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_mult__eq__0__iff,axiom,
! [X19,X20,X6] :
( class_Rings_Oring__no__zero__divisors(X6)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X20),X19) = c_Groups_Ozero__class_Ozero(X6)
<=> ( X20 = c_Groups_Ozero__class_Ozero(X6)
| X19 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [X23,X5,X6] :
( class_Rings_Ono__zero__divisors(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) != c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [X23,X5,X6] :
( class_Rings_Ono__zero__divisors(X6)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X23) = c_Groups_Ozero__class_Ozero(X6)
=> ( X5 = c_Groups_Ozero__class_Ozero(X6)
| X23 = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_dvd__if__abs__eq,axiom,
! [X38,X40,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Groups_Oabs__class_Oabs(X6,X40) = c_Groups_Oabs__class_Oabs(X6,X38)
=> c_Rings_Odvd__class_Odvd(X6,X40,X38) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [X54,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X54) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_zadd__commute,axiom,
! [X17,X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X4,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Groups_Oplus__class_Oplus(X6,X20,X20) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Groups_Ozero__class_Ozero(X6) = c_Groups_Oplus__class_Oplus(X6,X20,X20)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X19,X20,X6] :
( class_Groups_Oab__group__add(X6)
=> ( X20 = X19
<=> c_Groups_Ominus__class_Ominus(X6,X20,X19) = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X19,X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Ominus__class_Ominus(X6,X20,X19) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_field__power__not__zero,axiom,
! [X4,X5,X6] :
( class_Rings_Oring__1__no__zero__divisors(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4) != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X15,X13] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [X20,X19,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X19 = c_Groups_Oplus__class_Oplus(X6,X19,X20)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_abs__sgn,axiom,
! [X38,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Oabs__class_Oabs(X6,X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X38),c_Groups_Osgn__class_Osgn(X6,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
fof(fact_poly__zero,axiom,
! [X72,X6] :
( ( class_Int_Oring__char__0(X6)
& class_Rings_Oidom(X6) )
=> ( c_Polynomial_Opoly(X6,X72) = c_Polynomial_Opoly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))
<=> X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_real__mult__inverse__left,axiom,
! [X12] :
( X12 != 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,X12)),X12) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
fof(fact_less__imp__neq,axiom,
! [X10,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> X12 != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X10,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> X12 != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X10,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> X10 != X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_pCons__0__0,axiom,
! [X6] :
( class_Groups_Ozero(X6)
=> c_Polynomial_OpCons(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_one__poly__def,axiom,
! [X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) = c_Polynomial_OpCons(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(fact_natfloor__neg,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_right__inverse,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Rings_Oinverse__class_Oinverse(X6,X5)) = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse) ).
fof(fact_neq0__conv,axiom,
! [X18] :
( X18 != 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/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_abs__ge__zero,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oabs__class_Oabs(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_norm__inverse,axiom,
! [X5,X6] :
( ( class_RealVector_Oreal__normed__div__algebra(X6)
& class_Rings_Odivision__ring__inverse__zero(X6) )
=> c_RealVector_Onorm__class_Onorm(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__inverse) ).
fof(fact_nonzero__abs__inverse,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Oabs__class_Oabs(X6,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__inverse) ).
fof(fact_nonzero__inverse__minus__eq,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = c_Groups_Ouminus__class_Ouminus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
fof(fact_le__0__eq,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X17,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X17),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X4,X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X17,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X17) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_ab__left__minus,axiom,
! [X5,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5),X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_right__minus,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ouminus__class_Ouminus(X6,X5)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_of__real_Ominus,axiom,
! [X12,X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> c_RealVector_Oof__real(X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)) = c_Groups_Ouminus__class_Ouminus(X6,c_RealVector_Oof__real(X6,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Ominus) ).
fof(fact_of__real__inverse,axiom,
! [X12,X6] :
( ( class_RealVector_Oreal__div__algebra(X6)
& class_Rings_Odivision__ring__inverse__zero(X6) )
=> c_RealVector_Oof__real(X6,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12)) = c_Rings_Oinverse__class_Oinverse(X6,c_RealVector_Oof__real(X6,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__inverse) ).
fof(fact_add__is__0,axiom,
! [X18,X34] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nonzero__norm__inverse,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__div__algebra(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).
fof(fact_offset__poly__0,axiom,
! [X85,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X85) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(fact_pcompose__0,axiom,
! [X54,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Opcompose(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X54) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(fact_synthetic__div__0,axiom,
! [X25,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osynthetic__div(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X25) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_smult__0__right,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/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)
=> ? [X53] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X53) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/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,
! [X4,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
=> X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__ge__zero,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X4,X6] :
( ( class_Power_Opower(X6)
& class_Rings_Osemiring__0(X6) )
=> ( ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Ozero__class_Ozero(X6)),X4) = c_Groups_Oone__class_Oone(X6) )
& ( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Ozero__class_Ozero(X6)),X4) = c_Groups_Ozero__class_Ozero(X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X4,X21] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X4) = X21
=> X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_real__natceiling__ge,axiom,
! [X12] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_nonzero__of__real__inverse,axiom,
! [X12,X6] :
( class_RealVector_Oreal__div__algebra(X6)
=> ( X12 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_RealVector_Oof__real(X6,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X12)) = c_Rings_Oinverse__class_Oinverse(X6,c_RealVector_Oof__real(X6,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__of__real__inverse) ).
fof(fact_poly__1,axiom,
! [X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6))),X12) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__0,axiom,
! [X12,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))),X12) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_abs__ge__self,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X5,c_Groups_Oabs__class_Oabs(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_less__not__refl2,axiom,
! [X21,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X21)
=> X21 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X46,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X46)
=> X9 != X46 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_sgn__minus,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_Groups_Ouminus__class_Ouminus(X6,X12)) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Osgn__class_Osgn(X6,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__minus) ).
fof(fact_abs__inverse,axiom,
! [X5,X6] :
( class_Fields_Olinordered__field__inverse__zero(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Oabs__class_Oabs(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__inverse) ).
fof(fact_inverse__minus__eq,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = c_Groups_Ouminus__class_Ouminus(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X54,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X54) = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [X55,X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X6),X55,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X55,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),X55,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_pos__poly__total,axiom,
! [X55,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( X55 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
| c_Polynomial_Opos__poly(X6,X55)
| c_Polynomial_Opos__poly(X6,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X55)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(fact_mult__is__0,axiom,
! [X18,X34] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_of__real__minus,axiom,
! [X12,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X12)) = c_Groups_Ouminus__class_Ouminus(X6,c_RealVector_Oof__real(X6,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__minus) ).
fof(fact_sgn__of__real,axiom,
! [X11,X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_RealVector_Oof__real(X6,X11)) = c_RealVector_Oof__real(X6,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__of__real) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X4,X21] :
( X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X4)
=> ( X4 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_diff__0,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X18,X34] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X18) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X34 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X18,X34] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X18)
<=> ( X34 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X16),X16) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_monom__eq__0,axiom,
! [X4,X6] :
( class_Groups_Ozero(X6)
=> c_Polynomial_Omonom(X6,c_Groups_Ozero__class_Ozero(X6),X4) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(fact_smult__0__left,axiom,
! [X55,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Ozero__class_Ozero(X6),X55) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_power__power__power,axiom,
! [X6] :
( class_Power_Opower(X6)
=> c_Power_Opower__class_Opower(X6) = c_Power_Opower_Opower(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Otimes__class_Otimes(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult__zero__left,axiom,
! [X5,X6] :
( class_Rings_Omult__zero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult_Ozero__left,axiom,
! [X23,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X23) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X10,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X10) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_power__one,axiom,
! [X4,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Oone__class_Oone(X6)),X4) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_zero__le__one,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oone__class_Oone(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Groups_Oone__class_Oone(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oone__class_Oone(X6)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__1,axiom,
! [X5,X6] :
( class_Groups_Ocomm__monoid__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oone__class_Oone(X6)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oone__class_Oone(X6)),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult__zero__right,axiom,
! [X5,X6] :
( class_Rings_Omult__zero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__algebra(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_smult__1__left,axiom,
! [X55,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Oone__class_Oone(X6),X55) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X5,X6] :
( class_Groups_Omonoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_diff__0__right,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X5,X6] :
( class_Groups_Omonoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X5,X6] :
( class_Groups_Ocomm__monoid__add(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_one__dvd,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Rings_Odvd__class_Odvd(X6,c_Groups_Oone__class_Oone(X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__0__right,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Rings_Odvd__class_Odvd(X6,X5,c_Groups_Ozero__class_Ozero(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_power__0,axiom,
! [X5,X6] :
( class_Power_Opower(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X5,X6] :
( class_Groups_Ocomm__monoid__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_diff__self,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ominus__class_Ominus(X6,X5,X5) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_order__eq__refl,axiom,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( X12 = X10
=> c_Orderings_Oord__class_Oless__eq(X6,X12,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_nonzero__inverse__eq__imp__eq,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X5) = c_Rings_Oinverse__class_Oinverse(X6,X23)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> ( X23 != c_Groups_Ozero__class_Ozero(X6)
=> X5 = X23 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_power__one__right,axiom,
! [X5,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__natfloor,axiom,
! [X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_zero__le__natceiling,axiom,
! [X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_dvd__refl,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Rings_Odvd__class_Odvd(X6,X5,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_order__refl,axiom,
! [X12,X6] :
( class_Orderings_Opreorder(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X12,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_sgn__sgn,axiom,
! [X5,X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_Groups_Osgn__class_Osgn(X6,X5)) = c_Groups_Osgn__class_Osgn(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(fact_abs__idempotent,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Oabs__class_Oabs(X6,X5)) = c_Groups_Oabs__class_Oabs(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__minus__cancel,axiom,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = c_Groups_Oabs__class_Oabs(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_norm__minus__cancel,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ouminus__class_Ouminus(X6,X12)) = c_RealVector_Onorm__class_Onorm(X6,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_poly__eq__iff,axiom,
! [X76,X72,X6] :
( ( class_Int_Oring__char__0(X6)
& class_Rings_Oidom(X6) )
=> ( c_Polynomial_Opoly(X6,X72) = c_Polynomial_Opoly(X6,X76)
<=> X72 = X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_mult__idem,axiom,
! [X12,X6] :
( class_Lattices_Oab__semigroup__idem__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [X5,X6] :
( class_Lattices_Oab__semigroup__idem__mult(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_gr0I,axiom,
! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_abs__norm__cancel,axiom,
! [X5,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X5)) = c_RealVector_Onorm__class_Onorm(X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_norm__of__real,axiom,
! [X11,X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_RealVector_Oof__real(X6,X11)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(fact_diff__0__eq__0,axiom,
! [X4] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_norm__sgn,axiom,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( ( X12 = c_Groups_Ozero__class_Ozero(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Osgn__class_Osgn(X6,X12)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X12 != c_Groups_Ozero__class_Ozero(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Osgn__class_Osgn(X6,X12)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__sgn) ).
fof(fact_zadd__0,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X4] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X4,X21] :
( X21 = X4
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X6] :
( class_Groups_Oab__group__add(X6)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_diff__self__eq__0,axiom,
! [X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_mult__0,axiom,
! [X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_of__real__eq__iff,axiom,
! [X15,X13,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> ( c_RealVector_Oof__real(X6,X13) = c_RealVector_Oof__real(X6,X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X15,X13,X6] :
( class_Lattices_Oboolean__algebra(X6)
=> ( c_Groups_Ouminus__class_Ouminus(X6,X13) = c_Groups_Ouminus__class_Ouminus(X6,X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X19,X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Ouminus__class_Ouminus(X6,X20) = c_Groups_Ouminus__class_Ouminus(X6,X19)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_inverse__eq__imp__eq,axiom,
! [X23,X5,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X5) = c_Rings_Oinverse__class_Oinverse(X6,X23)
=> X5 = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
fof(fact_inverse__eq__iff__eq,axiom,
! [X19,X20,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X20) = c_Rings_Oinverse__class_Oinverse(X6,X19)
<=> X20 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
fof(fact_nonzero__inverse__inverse__eq,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(fact_zmult__1,axiom,
! [X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__1,axiom,
! [X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X16) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zle__refl,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_real__le__refl,axiom,
! [X17] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_mult__0__right,axiom,
! [X21] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_double__compl,axiom,
! [X12,X6] :
( class_Lattices_Oboolean__algebra(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ouminus__class_Ouminus(X6,X12)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X5,X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ouminus__class_Ouminus(X6,X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_inverse__inverse__eq,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Rings_Oinverse__class_Oinverse(X6,X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X12] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X12)) = c_RealDef_Oreal(tc_Nat_Onat,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_minus__equation__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Ouminus__class_Ouminus(X6,X20) = X19
<=> c_Groups_Ouminus__class_Ouminus(X6,X19) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X19,X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( X20 = c_Groups_Ouminus__class_Ouminus(X6,X19)
<=> X19 = c_Groups_Ouminus__class_Ouminus(X6,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_psize__eq__0__iff,axiom,
! [X72,X6] :
( class_Groups_Ozero(X6)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X6,X72) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X72 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_real__of__nat__inject,axiom,
! [X34,X18] :
( c_RealDef_Oreal(tc_Nat_Onat,X18) = c_RealDef_Oreal(tc_Nat_Onat,X34)
<=> X18 = X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Ozero__class_Ozero(X6) = c_Groups_Ouminus__class_Ouminus(X6,X20)
<=> c_Groups_Ozero__class_Ozero(X6) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_inverse__eq__1__iff,axiom,
! [X13,X6] :
( class_Fields_Ofield__inverse__zero(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X13) = c_Groups_Oone__class_Oone(X6)
<=> X13 = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(fact_sgn__0__0,axiom,
! [X20,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( c_Groups_Osgn__class_Osgn(X6,X20) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn__zero__iff,axiom,
! [X13,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_Groups_Osgn__class_Osgn(X6,X13) = c_Groups_Ozero__class_Ozero(X6)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_abs__eq__0,axiom,
! [X20,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ( c_Groups_Oabs__class_Oabs(X6,X20) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X20,X6] :
( class_Groups_Ogroup__add(X6)
=> ( c_Groups_Ouminus__class_Ouminus(X6,X20) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_nonzero__imp__inverse__nonzero,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,X5) != c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(fact_inverse__zero__imp__zero,axiom,
! [X5,X6] :
( class_Rings_Odivision__ring(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X5) = c_Groups_Ozero__class_Ozero(X6)
=> X5 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X20,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X20) = c_Groups_Ozero__class_Ozero(X6)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X13,X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> ( c_RealVector_Oof__real(X6,X13) = c_Groups_Ozero__class_Ozero(X6)
<=> X13 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
fof(fact_norm__eq__zero,axiom,
! [X13,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ( c_RealVector_Onorm__class_Onorm(X6,X13) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X90,X89] :
( class_Groups_Ouminus(X89)
=> class_Groups_Ouminus(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X90,X89] :
( class_Groups_Ominus(X89)
=> class_Groups_Ominus(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X90,X89] :
( class_Lattices_Oboolean__algebra(X89)
=> class_Lattices_Oboolean__algebra(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X90,X89] :
( class_Orderings_Oorder(X89)
=> class_Orderings_Oorder(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X90,X89] :
( class_Orderings_Oord(X89)
=> class_Orderings_Oord(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X90,X89] :
( class_Orderings_Opreorder(X89)
=> class_Orderings_Opreorder(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_zminus__zminus,axiom,
! [X16] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X16)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_neg__equal__zero,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( c_Groups_Ouminus__class_Ouminus(X6,X20) = X20
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X20,X6] :
( class_Groups_Olinordered__ab__group__add(X6)
=> ( X20 = c_Groups_Ouminus__class_Ouminus(X6,X20)
<=> X20 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_of__real_Ozero,axiom,
! [X6] :
( ( class_RealVector_Oreal__algebra__1(X6)
& class_RealVector_Oreal__normed__vector(X6) )
=> c_RealVector_Oof__real(X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Ozero) ).
fof(fact_sgn__one,axiom,
! [X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__one) ).
fof(fact_sgn0,axiom,
! [X6] :
( class_Groups_Osgn__if(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
fof(fact_sgn__zero,axiom,
! [X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_Groups_Osgn__class_Osgn(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero) ).
fof(fact_abs__one,axiom,
! [X6] :
( class_Rings_Olinordered__idom(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_abs__zero,axiom,
! [X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> c_Groups_Oabs__class_Oabs(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_minus__zero,axiom,
! [X6] :
( class_Groups_Ogroup__add(X6)
=> c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(fact_inverse__1,axiom,
! [X6] :
( class_Rings_Odivision__ring(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__1) ).
fof(fact_field__inverse__zero,axiom,
! [X6] :
( class_Fields_Ofield__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
fof(fact_inverse__zero,axiom,
! [X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__zero) ).
fof(fact_norm__one,axiom,
! [X6] :
( class_RealVector_Oreal__normed__algebra__1(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Oone__class_Oone(X6)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_norm__zero,axiom,
! [X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> c_RealVector_Onorm__class_Onorm(X6,c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_of__real__1,axiom,
! [X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_of__real__0,axiom,
! [X6] :
( class_RealVector_Oreal__algebra__1(X6)
=> c_RealVector_Oof__real(X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__0) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X4] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X4)) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X4] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X4)) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X18] :
( c_RealDef_Oreal(tc_Nat_Onat,X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_real__norm__def,axiom,
! [X11] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X11) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_one__neq__zero,axiom,
! [X6] :
( class_Rings_Ozero__neq__one(X6)
=> c_Groups_Oone__class_Oone(X6) != c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [X6] :
( class_Rings_Ozero__neq__one(X6)
=> c_Groups_Ozero__class_Ozero(X6) != c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Oone(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X89] :
( class_Groups_Ozero(X89)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Oring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Power_Opower(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_a00) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_inverse__i) ).
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/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_INVERSE__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/sandbox/benchmark/theBenchmark.p',fact_natfloor__one) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__zero) ).
fof(fact_natceiling__one,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__one) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(fact_kas_I1_J,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_kas_I1_J) ).
fof(fact_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w0) ).
fof(fact_kas_I2_J,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__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/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__div__algebra) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(i_0_1278,plain,
~ ! [X35] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X35)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X35,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,
! [X10,X12,X6] :
( class_Rings_Olinordered__ring(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X12),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X10),X10)),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1280,plain,
! [X19,X20,X45] :
( hBOOL(hAPP(X45,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
& ~ hBOOL(hAPP(X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X58] :
( X20 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X58)
& ~ hBOOL(hAPP(X45,X58)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1281,plain,
! [X12] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X12),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X12),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(i_0_1282,plain,
! [X4,X38,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X38),X4)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X4)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X4) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1283,plain,
! [X1,X2,X6,X67] :
( class_Orderings_Oord(X67)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X67),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X67),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1284,plain,
! [X72] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X72),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,X72))
=> ? [X53] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X72),X53) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_simplification,[status(thm)],[fact_less_Ohyps]) ).
fof(i_0_1285,plain,
! [X5,X6] :
( class_Rings_Olinordered__ring(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X5),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1286,plain,
! [X39,X22] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X39),X22),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1287,plain,
! [X22,X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X22),X22),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1288,plain,
! [X13] :
( ~ 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),X13),X13))
<=> X13 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1289,plain,
! [X4,X21] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X4)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X4)) = X21 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1290,plain,
! [X15,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1291,plain,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> X13 = X15 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1292,plain,
! [X5,X23,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X23,X5)
=> ~ c_Orderings_Oord__class_Oless(X6,X5,X23) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1293,plain,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> c_Orderings_Oord__class_Oless(X6,X15,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1294,plain,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> c_Orderings_Oord__class_Oless__eq(X6,X15,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1295,plain,
! [X12,X10,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> ~ c_Orderings_Oord__class_Oless(X6,X12,X10) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1296,plain,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> ( c_Orderings_Oord__class_Oless(X6,X15,X13)
| X13 = X15 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1297,plain,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1298,plain,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1299,plain,
! [X23,X5,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X5,X23)
=> ~ c_Orderings_Oord__class_Oless(X6,X23,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1300,plain,
! [X10,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ~ c_Orderings_Oord__class_Oless(X6,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1301,plain,
! [X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( ( X12 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X12)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X12)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__poly__def]) ).
fof(i_0_1302,plain,
! [X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X6),X12) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6),X12) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6),X12,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X6),X12) = X12 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__poly__def]) ).
fof(i_0_1303,plain,
! [X12,X10] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X12)
=> c_Nat__Transfer_Otsub(X12,X10) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X12,X10) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X12)
=> c_Nat__Transfer_Otsub(X12,X10) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_1304,plain,
! [X15,X13,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X13,X15)
<=> X13 = X15 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1305,plain,
! [X5,X6] :
( class_Groups_Oordered__ab__group__add__abs(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oabs__class_Oabs(X6,X5),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_1306,plain,
! [X12,X6] :
( class_RealVector_Oreal__normed__vector(X6)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X6,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1307,plain,
! [X5,X6] :
( class_Groups_Oabs__if(X6)
=> ( ( c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = c_Groups_Ouminus__class_Ouminus(X6,X5) )
& ( ~ c_Orderings_Oord__class_Oless(X6,X5,c_Groups_Ozero__class_Ozero(X6))
=> c_Groups_Oabs__class_Oabs(X6,X5) = X5 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__if]) ).
fof(i_0_1308,plain,
! [X12,X6] :
( class_Groups_Osgn__if(X6)
=> ( ( X12 = c_Groups_Ozero__class_Ozero(X6)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Ozero__class_Ozero(X6) )
& ( X12 != c_Groups_Ozero__class_Ozero(X6)
=> ( ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Oone__class_Oone(X6) )
& ( ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X12)
=> c_Groups_Osgn__class_Osgn(X6,X12) = c_Groups_Ouminus__class_Ouminus(X6,c_Groups_Oone__class_Oone(X6)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).
fof(i_0_1309,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X4),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,
! [X13,X15,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X15,X13)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X13,X15)
<=> X13 = X15 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1311,plain,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1312,plain,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> ( X12 != X10
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1313,plain,
! [X10,X12,X6] :
( class_Rings_Olinordered__idom(X6)
=> ( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless(X6,X10,X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1314,plain,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1315,plain,
! [X10,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X10)
=> c_Orderings_Oord__class_Oless__eq(X6,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1316,plain,
! [X12,X10,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X10,X12)
=> c_Orderings_Oord__class_Oless(X6,X12,X10) ) ),
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,
! [X11] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X11) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X11,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X11) = X11 ) ),
inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).
fof(i_0_1319,plain,
! [X5] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X5) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5) = X5 ) ),
inference(fof_simplification,[status(thm)],[fact_abs__real__def]) ).
fof(i_0_1320,plain,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1321,plain,
! [X6] :
( class_Rings_Olinordered__semidom(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(X6)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1322,plain,
! [X10,X12] :
( X12 != X10
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1323,plain,
! [X12,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X12,X12) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1324,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1325,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1326,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1327,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1328,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1329,plain,
! [X6] :
( class_Rings_Olinordered__idom(X6)
=> ~ c_Polynomial_Opos__poly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
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,
! [X5134,X5135,X5136,X5137,X5139] :
( ( c_Orderings_Oord__class_Oless__eq(X5136,X5135,esk27_4(X5134,X5135,X5136,X5137))
| ~ c_Orderings_Oord__class_Oless__eq(X5136,X5135,X5139)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5137,hAPP(X5134,X5139)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5137,hAPP(X5134,X5135))))
| ~ class_RealVector_Oreal__normed__vector(X5137)
| ~ class_Orderings_Oord(X5136) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5137,c_Groups_Ominus__class_Ominus(X5137,hAPP(X5134,X5135),hAPP(X5134,esk27_4(X5134,X5135,X5136,X5137)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X5136,X5135,X5139)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5137,hAPP(X5134,X5139)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5137,hAPP(X5134,X5135))))
| ~ class_RealVector_Oreal__normed__vector(X5137)
| ~ class_Orderings_Oord(X5136) ) ),
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,
! [X4661] :
( ( ~ 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____)),X4661)),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____),X4661)),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____),X4661)),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____)),X4661)),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,
! [X4616,X4617,X4618] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4618)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4617,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,X4617,X4616)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4618)),X4616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_1334,plain,
! [X4613,X4614,X4615] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4615)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4614,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4613,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,X4613,X4614)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4615))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_1335,plain,
! [X5115] :
( esk24_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& esk23_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,esk25_0),esk23_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____)),X5115) = 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),X5115),esk23_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk24_0,esk25_0)),X5115))) ),
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,
! [X4662] : 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____)),X4662) = 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),X4662),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X4662))),
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____)),esk18_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,
! [X4660] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4660) = 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____)),X4660)),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,
! [X4916,X4917,X4918,X4919,X4920] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4918,X4919),X4917,X4916)
| c_Orderings_Oord__class_Oless__eq(X4919,hAPP(X4917,X4920),hAPP(X4916,X4920))
| ~ class_Orderings_Oord(X4919) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4919,hAPP(X4917,esk22_4(X4916,X4917,X4918,X4919)),hAPP(X4916,esk22_4(X4916,X4917,X4918,X4919)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4918,X4919),X4917,X4916)
| ~ class_Orderings_Oord(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_le__fun__def])])])])]) ).
fof(i_0_1340,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Rings_Oinverse__class_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,
! [X3800,X3801,X3802,X3803,X3804] :
( ~ class_RealVector_Oreal__normed__algebra(X3804)
| c_Groups_Ominus__class_Ominus(X3804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3804),X3803),X3802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3804),X3801),X3800)) = c_Groups_Oplus__class_Oplus(X3804,c_Groups_Oplus__class_Oplus(X3804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3804),c_Groups_Ominus__class_Ominus(X3804,X3803,X3801)),c_Groups_Ominus__class_Ominus(X3804,X3802,X3800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3804),c_Groups_Ominus__class_Ominus(X3804,X3803,X3801)),X3800)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3804),X3801),c_Groups_Ominus__class_Ominus(X3804,X3802,X3800))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1342,plain,
! [X4507,X4508,X4509,X4510] : 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,X4510,X4509),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4508),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4507)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4510,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4508))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4509,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4507))))),
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____)),esk19_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____)),esk20_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,
! [X4884,X4885,X4886] :
( ~ class_Rings_Ocomm__ring__1(X4886)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4886)),c_Polynomial_OpCons(X4886,c_Groups_Ouminus__class_Ouminus(X4886,X4885),c_Polynomial_OpCons(X4886,c_Groups_Oone__class_Oone(X4886),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4886))))),c_Polynomial_Osynthetic__div(X4886,X4884,X4885)),c_Polynomial_OpCons(X4886,hAPP(c_Polynomial_Opoly(X4886,X4884),X4885),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4886)))) = X4884 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H])]) ).
fof(i_0_1345,plain,
! [X3831,X3832,X3833,X3834,X3835,X3836] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834),X3833),c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3832),X3834),X3831))
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),c_Groups_Ominus__class_Ominus(X3836,X3835,X3832)),X3834),X3833),X3831)
| ~ class_Rings_Oordered__ring(X3836) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),c_Groups_Ominus__class_Ominus(X3836,X3835,X3832)),X3834),X3833),X3831)
| c_Orderings_Oord__class_Oless__eq(X3836,c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3835),X3834),X3833),c_Groups_Oplus__class_Oplus(X3836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3836),X3832),X3834),X3831))
| ~ class_Rings_Oordered__ring(X3836) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1346,plain,
! [X3843,X3844,X3845,X3846,X3847,X3848] :
( ( ~ c_Orderings_Oord__class_Oless(X3848,c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),X3847),X3846),X3845),c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),X3844),X3846),X3843))
| c_Orderings_Oord__class_Oless(X3848,c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),c_Groups_Ominus__class_Ominus(X3848,X3847,X3844)),X3846),X3845),X3843)
| ~ class_Rings_Oordered__ring(X3848) )
& ( ~ c_Orderings_Oord__class_Oless(X3848,c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),c_Groups_Ominus__class_Ominus(X3848,X3847,X3844)),X3846),X3845),X3843)
| c_Orderings_Oord__class_Oless(X3848,c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),X3847),X3846),X3845),c_Groups_Oplus__class_Oplus(X3848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3848),X3844),X3846),X3843))
| ~ class_Rings_Oordered__ring(X3848) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1347,plain,
! [X3837,X3838,X3839,X3840,X3841,X3842] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3842,c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),X3841),X3840),X3839),c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),X3838),X3840),X3837))
| c_Orderings_Oord__class_Oless__eq(X3842,X3839,c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),c_Groups_Ominus__class_Ominus(X3842,X3838,X3841)),X3840),X3837))
| ~ class_Rings_Oordered__ring(X3842) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3842,X3839,c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),c_Groups_Ominus__class_Ominus(X3842,X3838,X3841)),X3840),X3837))
| c_Orderings_Oord__class_Oless__eq(X3842,c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),X3841),X3840),X3839),c_Groups_Oplus__class_Oplus(X3842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3842),X3838),X3840),X3837))
| ~ class_Rings_Oordered__ring(X3842) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1348,plain,
! [X3849,X3850,X3851,X3852,X3853,X3854] :
( ( ~ c_Orderings_Oord__class_Oless(X3854,c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),X3853),X3852),X3851),c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),X3850),X3852),X3849))
| c_Orderings_Oord__class_Oless(X3854,X3851,c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),c_Groups_Ominus__class_Ominus(X3854,X3850,X3853)),X3852),X3849))
| ~ class_Rings_Oordered__ring(X3854) )
& ( ~ c_Orderings_Oord__class_Oless(X3854,X3851,c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),c_Groups_Ominus__class_Ominus(X3854,X3850,X3853)),X3852),X3849))
| c_Orderings_Oord__class_Oless(X3854,c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),X3853),X3852),X3851),c_Groups_Oplus__class_Oplus(X3854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3854),X3850),X3852),X3849))
| ~ class_Rings_Oordered__ring(X3854) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1349,plain,
! [X4228,X4229,X4230,X4231,X4232] :
( ( ~ 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),X4231),X4230),X4229),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4232),X4230),X4228))
| 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,X4231,X4232)),X4230),X4229),X4228)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4232,X4231) )
& ( ~ 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,X4231,X4232)),X4230),X4229),X4228)
| 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),X4231),X4230),X4229),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4232),X4230),X4228))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4232,X4231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1350,plain,
! [X4291,X4292,X4293,X4294,X4295] :
( ( ~ 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),X4294),X4293),X4292),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4295),X4293),X4291))
| 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,X4294,X4295)),X4293),X4292),X4291)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4295,X4294) )
& ( ~ 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,X4294,X4295)),X4293),X4292),X4291)
| 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),X4294),X4293),X4292),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4295),X4293),X4291))
| ~ 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_nat__less__add__iff1])])]) ).
fof(i_0_1351,plain,
! [X4213,X4214,X4215,X4216,X4217] :
( ( ~ 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),X4217),X4215),X4214),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4216),X4215),X4213))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4214,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,X4216,X4217)),X4215),X4213))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4217,X4216) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4214,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,X4216,X4217)),X4215),X4213))
| 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),X4217),X4215),X4214),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4216),X4215),X4213))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4217,X4216) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1352,plain,
! [X4296,X4297,X4298,X4299,X4300] :
( ( ~ 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),X4300),X4298),X4297),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4299),X4298),X4296))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4297,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,X4299,X4300)),X4298),X4296))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4300,X4299) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4297,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,X4299,X4300)),X4298),X4296))
| 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),X4300),X4298),X4297),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4299),X4298),X4296))
| ~ 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_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,
! [X5347,X5348,X5349] :
( ~ class_Rings_Oidom(X5349)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5349),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5349)),c_Polynomial_OpCons(X5349,c_Groups_Ouminus__class_Ouminus(X5349,X5348),c_Polynomial_OpCons(X5349,c_Groups_Oone__class_Oone(X5349),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5349))))),c_Polynomial_Oorder(X5349,X5348,X5347)),X5347) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__1])]) ).
fof(i_0_1355,plain,
! [X4493,X4494,X4495,X4496,X4497] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4497)
| c_Orderings_Oord__class_Oless__eq(X4497,c_Groups_Oabs__class_Oabs(X4497,c_Groups_Ominus__class_Ominus(X4497,c_Groups_Oplus__class_Oplus(X4497,X4496,X4495),c_Groups_Oplus__class_Oplus(X4497,X4494,X4493))),c_Groups_Oplus__class_Oplus(X4497,c_Groups_Oabs__class_Oabs(X4497,c_Groups_Ominus__class_Ominus(X4497,X4496,X4494)),c_Groups_Oabs__class_Oabs(X4497,c_Groups_Ominus__class_Ominus(X4497,X4495,X4493)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_1356,plain,
! [X4050,X4051] :
( X4051 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X4050 = 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),X4051),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk7_2(X4050,X4051)),X4050)))),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,
! [X3900,X3901,X3902,X3903,X3904] :
( ~ class_RealVector_Oreal__normed__vector(X3904)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3904,c_Groups_Ominus__class_Ominus(X3904,c_Groups_Oplus__class_Oplus(X3904,X3903,X3902),c_Groups_Oplus__class_Oplus(X3904,X3901,X3900))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3904,c_Groups_Ominus__class_Ominus(X3904,X3903,X3901)),c_RealVector_Onorm__class_Onorm(X3904,c_Groups_Ominus__class_Ominus(X3904,X3902,X3900)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).
fof(i_0_1358,plain,
! [X5265,X5266,X5267,X5269] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk33_3(X5265,X5266,X5267))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5267) )
& ( ~ 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,X5269,X5266)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X5269,X5266)),esk33_3(X5265,X5266,X5267))
| 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,X5265),X5269),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5265),X5266))),X5267)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5267) ) ),
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,
! [X4045,X4046,X4047] :
( ~ class_Rings_Odivision__ring(X4047)
| X4046 = c_Groups_Ozero__class_Ozero(X4047)
| X4045 = c_Groups_Ozero__class_Ozero(X4047)
| c_Groups_Ominus__class_Ominus(X4047,c_Rings_Oinverse__class_Oinverse(X4047,X4046),c_Rings_Oinverse__class_Oinverse(X4047,X4045)) = c_Groups_Ouminus__class_Ouminus(X4047,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4047),c_Rings_Oinverse__class_Oinverse(X4047,X4046)),c_Groups_Ominus__class_Ominus(X4047,X4046,X4045))),c_Rings_Oinverse__class_Oinverse(X4047,X4045))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oinverse__diff__inverse])]) ).
fof(i_0_1360,plain,
! [X4223,X4224,X4225,X4226,X4227] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4227,X4226)
| 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),X4226),X4225),X4224),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4227),X4225),X4223)) = 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,X4226,X4227)),X4225),X4224),X4223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1361,plain,
! [X4208,X4209,X4210,X4211,X4212] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4212,X4211)
| 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),X4212),X4210),X4209),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4211),X4210),X4208)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4209,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,X4211,X4212)),X4210),X4208)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1362,plain,
! [X4704,X4705,X4706,X4707] :
( ~ class_Rings_Ocomm__ring__1(X4707)
| hAPP(c_Polynomial_Opoly(X4707,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4707)),c_Polynomial_Omonom(X4707,c_Groups_Oone__class_Oone(X4707),X4706)),X4705)),X4704) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4707),hAPP(hAPP(c_Power_Opower__class_Opower(X4707),X4704),X4706)),hAPP(c_Polynomial_Opoly(X4707,X4705),X4704)) ),
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))))),esk21_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,
! [X5372,X5373,X5374,X5375,X5376,X5377] :
( ( ~ c_Rings_Odvd__class_Odvd(X5375,X5374,c_Groups_Oplus__class_Oplus(X5375,X5376,X5372))
| c_Rings_Odvd__class_Odvd(X5375,X5374,c_Groups_Oplus__class_Oplus(X5375,c_Groups_Ominus__class_Ominus(X5375,X5376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5375),X5377),X5373)),X5372))
| ~ c_Rings_Odvd__class_Odvd(X5375,X5374,X5373)
| ~ class_Rings_Ocomm__ring(X5375)
| ~ class_Rings_Odvd(X5375) )
& ( ~ c_Rings_Odvd__class_Odvd(X5375,X5374,c_Groups_Oplus__class_Oplus(X5375,c_Groups_Ominus__class_Ominus(X5375,X5376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5375),X5377),X5373)),X5372))
| c_Rings_Odvd__class_Odvd(X5375,X5374,c_Groups_Oplus__class_Oplus(X5375,X5376,X5372))
| ~ c_Rings_Odvd__class_Odvd(X5375,X5374,X5373)
| ~ class_Rings_Ocomm__ring(X5375)
| ~ class_Rings_Odvd(X5375) ) ),
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_1365,plain,
! [X5366,X5367,X5368,X5369,X5370,X5371] :
( ( ~ c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Oplus__class_Oplus(X5369,X5370,X5366))
| c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Oplus__class_Oplus(X5369,c_Groups_Ominus__class_Ominus(X5369,X5370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5369),X5371),X5367)),X5366))
| ~ c_Rings_Odvd__class_Odvd(X5369,X5368,X5367)
| ~ class_Rings_Ocomm__ring(X5369)
| ~ class_Rings_Odvd(X5369) )
& ( ~ c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Oplus__class_Oplus(X5369,c_Groups_Ominus__class_Ominus(X5369,X5370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5369),X5371),X5367)),X5366))
| c_Rings_Odvd__class_Odvd(X5369,X5368,c_Groups_Oplus__class_Oplus(X5369,X5370,X5366))
| ~ c_Rings_Odvd__class_Odvd(X5369,X5368,X5367)
| ~ class_Rings_Ocomm__ring(X5369)
| ~ class_Rings_Odvd(X5369) ) ),
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_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,
! [X4663,X4664,X4665,X4666,X4667,X4668] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4668),X4667),X4666) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4665),X4664),X4663)
| ~ 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),X4665),X4664),X4663),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4666,X4668)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4663)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4665)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4665,X4668)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4664,X4667) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1368,plain,
! [X4674,X4675,X4676,X4677,X4678,X4679] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4679),X4678),X4677) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4676),X4675),X4674)
| ~ 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),X4676),X4675),X4674))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4674,X4676)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4677)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4676)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4676,X4679)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4678,X4675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1369,plain,
! [X5144,X5146,X5147] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_1(X5144))
| ~ class_RealVector_Oreal__normed__algebra(X5144) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5144),X5146),X5147)),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(X5144,X5146)),c_RealVector_Onorm__class_Onorm(X5144,X5147))),esk29_1(X5144)))
| ~ class_RealVector_Oreal__normed__algebra(X5144) ) ),
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,
! [X3557,X3558,X3559] :
( ~ class_Fields_Ofield(X3559)
| X3558 = c_Groups_Ozero__class_Ozero(X3559)
| X3557 = c_Groups_Ozero__class_Ozero(X3559)
| c_Groups_Oplus__class_Oplus(X3559,c_Rings_Oinverse__class_Oinverse(X3559,X3558),c_Rings_Oinverse__class_Oinverse(X3559,X3557)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3559),c_Groups_Oplus__class_Oplus(X3559,X3558,X3557)),c_Rings_Oinverse__class_Oinverse(X3559,X3558))),c_Rings_Oinverse__class_Oinverse(X3559,X3557)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).
fof(i_0_1371,plain,
! [X4680,X4681,X4682,X4683,X4684] :
( ~ 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),X4684),X4683),X4682),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4684),X4681),X4680))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4682)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4682,X4684)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4680,X4684)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4683,X4681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1372,plain,
! [X4669,X4670,X4671,X4672,X4673] :
( ~ 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),X4673),X4672),X4671),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4673),X4670),X4669))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4669,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4673,X4669)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4673,X4671)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4670,X4672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
fof(i_0_1373,plain,
! [X4218,X4219,X4220,X4221,X4222] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4221),X4220),X4219) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4222),X4220),X4218)
| 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,X4221,X4222)),X4220),X4219) = X4218
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4222,X4221) )
& ( 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,X4221,X4222)),X4220),X4219) != X4218
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4221),X4220),X4219) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4222),X4220),X4218)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4222,X4221) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1374,plain,
! [X4203,X4204,X4205,X4206,X4207] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4207),X4205),X4204) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4206),X4205),X4203)
| X4204 = 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,X4206,X4207)),X4205),X4203)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4207,X4206) )
& ( X4204 != 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,X4206,X4207)),X4205),X4203)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4207),X4205),X4204) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4206),X4205),X4203)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4207,X4206) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1375,plain,
! [X3788,X3789,X3790,X3791,X3792,X3793] :
( ( c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),X3792),X3791),X3790) != c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),X3789),X3791),X3788)
| c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),c_Groups_Ominus__class_Ominus(X3793,X3792,X3789)),X3791),X3790) = X3788
| ~ class_Rings_Oring(X3793) )
& ( c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),c_Groups_Ominus__class_Ominus(X3793,X3792,X3789)),X3791),X3790) != X3788
| c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),X3792),X3791),X3790) = c_Groups_Oplus__class_Oplus(X3793,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3793),X3789),X3791),X3788)
| ~ class_Rings_Oring(X3793) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1376,plain,
! [X3794,X3795,X3796,X3797,X3798,X3799] :
( ( c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3798),X3797),X3796) != c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3795),X3797),X3794)
| X3796 = c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),c_Groups_Ominus__class_Ominus(X3799,X3795,X3798)),X3797),X3794)
| ~ class_Rings_Oring(X3799) )
& ( X3796 != c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),c_Groups_Ominus__class_Ominus(X3799,X3795,X3798)),X3797),X3794)
| c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3798),X3797),X3796) = c_Groups_Oplus__class_Oplus(X3799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3799),X3795),X3797),X3794)
| ~ class_Rings_Oring(X3799) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_1377,plain,
! [X4546] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4546) != 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,X4546,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,X4546,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,X4546,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,X4546,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,
! [X3805,X3806,X3807,X3808,X3809] :
( ~ class_Rings_Oring(X3809)
| c_Groups_Ominus__class_Ominus(X3809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3809),X3808),X3807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3809),X3806),X3805)) = c_Groups_Oplus__class_Oplus(X3809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3809),X3808),c_Groups_Ominus__class_Ominus(X3809,X3807,X3805)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3809),c_Groups_Ominus__class_Ominus(X3809,X3808,X3806)),X3805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1379,plain,
! [X5258,X5259] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5259)
| 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,X5258)),X5259),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,X5259,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
fof(i_0_1380,plain,
! [X3092,X3093,X3094,X3095,X3096] :
( ~ class_Rings_Osemiring(X3096)
| c_Groups_Oplus__class_Oplus(X3096,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3096),X3095),X3094),c_Groups_Oplus__class_Oplus(X3096,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3096),X3093),X3094),X3092)) = c_Groups_Oplus__class_Oplus(X3096,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3096),c_Groups_Oplus__class_Oplus(X3096,X3095,X3093)),X3094),X3092) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1381,plain,
! [X3857,X3858,X3859] :
( ~ class_Rings_Odivision__ring(X3859)
| X3858 = c_Groups_Ozero__class_Ozero(X3859)
| X3857 = c_Groups_Ozero__class_Ozero(X3859)
| c_Groups_Ominus__class_Ominus(X3859,c_Rings_Oinverse__class_Oinverse(X3859,X3858),c_Rings_Oinverse__class_Oinverse(X3859,X3857)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3859),c_Rings_Oinverse__class_Oinverse(X3859,X3858)),c_Groups_Ominus__class_Ominus(X3859,X3857,X3858))),c_Rings_Oinverse__class_Oinverse(X3859,X3857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__diff])]) ).
fof(i_0_1382,plain,
! [X2964,X2965,X2966] :
( ~ class_Rings_Odivision__ring(X2966)
| X2965 = c_Groups_Ozero__class_Ozero(X2966)
| X2964 = c_Groups_Ozero__class_Ozero(X2966)
| c_Groups_Oplus__class_Oplus(X2966,c_Rings_Oinverse__class_Oinverse(X2966,X2965),c_Rings_Oinverse__class_Oinverse(X2966,X2964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2966),c_Rings_Oinverse__class_Oinverse(X2966,X2965)),c_Groups_Oplus__class_Oplus(X2966,X2965,X2964))),c_Rings_Oinverse__class_Oinverse(X2966,X2964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).
fof(i_0_1383,plain,
! [X3054,X3055,X3056,X3057,X3058,X3059] :
( ~ class_Rings_Olinordered__semiring__1(X3059)
| ~ c_Orderings_Oord__class_Oless__eq(X3059,X3058,X3057)
| ~ c_Orderings_Oord__class_Oless__eq(X3059,X3056,X3057)
| ~ c_Orderings_Oord__class_Oless__eq(X3059,c_Groups_Ozero__class_Ozero(X3059),X3055)
| ~ c_Orderings_Oord__class_Oless__eq(X3059,c_Groups_Ozero__class_Ozero(X3059),X3054)
| c_Groups_Oplus__class_Oplus(X3059,X3055,X3054) != c_Groups_Oone__class_Oone(X3059)
| c_Orderings_Oord__class_Oless__eq(X3059,c_Groups_Oplus__class_Oplus(X3059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3059),X3055),X3058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3059),X3054),X3056)),X3057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1384,plain,
! [X3063,X3064,X3065,X3066,X3067,X3068] :
( ~ class_Rings_Olinordered__semiring__1__strict(X3068)
| ~ c_Orderings_Oord__class_Oless(X3068,X3067,X3066)
| ~ c_Orderings_Oord__class_Oless(X3068,X3065,X3066)
| ~ c_Orderings_Oord__class_Oless__eq(X3068,c_Groups_Ozero__class_Ozero(X3068),X3064)
| ~ c_Orderings_Oord__class_Oless__eq(X3068,c_Groups_Ozero__class_Ozero(X3068),X3063)
| c_Groups_Oplus__class_Oplus(X3068,X3064,X3063) != c_Groups_Oone__class_Oone(X3068)
| c_Orderings_Oord__class_Oless(X3068,c_Groups_Oplus__class_Oplus(X3068,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3068),X3064),X3067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3068),X3063),X3065)),X3066) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1385,plain,
! [X5382,X5383,X5384,X5385,X5387] :
( ( c_Rings_Odvd__class_Odvd(X5384,X5382,c_Groups_Oplus__class_Oplus(X5384,esk37_3(X5382,X5383,X5384),c_Groups_Ozero__class_Ozero(X5384)))
| ~ hBOOL(hAPP(X5383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5384),X5382),X5385)))
| ~ class_Rings_Odvd(X5384)
| ~ class_Rings_Osemiring__0(X5384) )
& ( hBOOL(hAPP(X5383,esk37_3(X5382,X5383,X5384)))
| ~ hBOOL(hAPP(X5383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5384),X5382),X5385)))
| ~ class_Rings_Odvd(X5384)
| ~ class_Rings_Osemiring__0(X5384) )
& ( ~ c_Rings_Odvd__class_Odvd(X5384,X5382,c_Groups_Oplus__class_Oplus(X5384,X5387,c_Groups_Ozero__class_Ozero(X5384)))
| ~ hBOOL(hAPP(X5383,X5387))
| hBOOL(hAPP(X5383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5384),X5382),esk38_3(X5382,X5383,X5384))))
| ~ class_Rings_Odvd(X5384)
| ~ class_Rings_Osemiring__0(X5384) ) ),
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,
! [X3984,X3985,X3986,X3987] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3987),X3986),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3985),X3986),X3984)) = 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,X3987,X3985)),X3986),X3984),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1387,plain,
! [X3265,X3266,X3267,X3268] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3268)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3267)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3267),X3266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3268),X3265))
| 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,X3268)),X3266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3267)),X3265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel])]) ).
fof(i_0_1388,plain,
! [X2815,X2816,X2817] :
( ( ~ c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),c_Groups_Oplus__class_Oplus(X2817,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2816),X2816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2815),X2815)))
| X2816 != c_Groups_Ozero__class_Ozero(X2817)
| X2815 != c_Groups_Ozero__class_Ozero(X2817)
| ~ class_Rings_Olinordered__ring__strict(X2817) )
& ( X2816 = c_Groups_Ozero__class_Ozero(X2817)
| c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),c_Groups_Oplus__class_Oplus(X2817,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2816),X2816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2815),X2815)))
| ~ class_Rings_Olinordered__ring__strict(X2817) )
& ( X2815 = c_Groups_Ozero__class_Ozero(X2817)
| c_Orderings_Oord__class_Oless(X2817,c_Groups_Ozero__class_Ozero(X2817),c_Groups_Oplus__class_Oplus(X2817,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2816),X2816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2817),X2815),X2815)))
| ~ class_Rings_Olinordered__ring__strict(X2817) ) ),
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,
! [X4257,X4258,X4259,X4260,X4261] :
( ~ class_Rings_Ocomm__semiring__1(X4261)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),X4260),X4259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),X4258),X4257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),X4258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4261),X4260),X4259)),X4257)) ),
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,
! [X3023,X3024,X3025] :
( ( X3024 = c_Groups_Ozero__class_Ozero(X3025)
| ~ c_Orderings_Oord__class_Oless__eq(X3025,c_Groups_Oplus__class_Oplus(X3025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3024),X3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3023),X3023)),c_Groups_Ozero__class_Ozero(X3025))
| ~ class_Rings_Olinordered__ring__strict(X3025) )
& ( X3023 = c_Groups_Ozero__class_Ozero(X3025)
| ~ c_Orderings_Oord__class_Oless__eq(X3025,c_Groups_Oplus__class_Oplus(X3025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3024),X3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3023),X3023)),c_Groups_Ozero__class_Ozero(X3025))
| ~ class_Rings_Olinordered__ring__strict(X3025) )
& ( X3024 != c_Groups_Ozero__class_Ozero(X3025)
| X3023 != c_Groups_Ozero__class_Ozero(X3025)
| c_Orderings_Oord__class_Oless__eq(X3025,c_Groups_Oplus__class_Oplus(X3025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3024),X3024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3025),X3023),X3023)),c_Groups_Ozero__class_Ozero(X3025))
| ~ class_Rings_Olinordered__ring__strict(X3025) ) ),
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,
! [X2812,X2813,X2814] :
( ~ class_Rings_Olinordered__ring(X2814)
| ~ c_Orderings_Oord__class_Oless(X2814,c_Groups_Oplus__class_Oplus(X2814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2814),X2813),X2813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2814),X2812),X2812)),c_Groups_Ozero__class_Ozero(X2814)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1279])]) ).
fof(i_0_1392,plain,
! [X4384,X4385] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4385)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4385,X4384)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4384,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),X4384)),X4385),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,
! [X4880,X4881,X4882,X4883] :
( ~ class_Rings_Ocomm__semiring__0(X4883)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4883)),c_Polynomial_OpCons(X4883,X4882,X4881)),X4880) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4883),c_Polynomial_Osmult(X4883,X4882,X4880),c_Polynomial_OpCons(X4883,c_Groups_Ozero__class_Ozero(X4883),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4883)),X4881),X4880))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__left])]) ).
fof(i_0_1394,plain,
! [X5350,X5351,X5352,X5353] :
( ~ class_Rings_Ocomm__semiring__0(X5353)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5353,c_Polynomial_OpCons(X5353,X5352,X5351),X5350) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5353),c_Polynomial_Osmult(X5353,X5350,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5353,X5351,X5350)),c_Polynomial_OpCons(X5353,X5352,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5353,X5351,X5350))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(i_0_1395,plain,
! [X3269,X3270,X3271,X3272] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3272)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3271)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3271),X3270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3272),X3269))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3270),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3269),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3271))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel2])]) ).
fof(i_0_1396,plain,
! [X4308,X4309,X4310] :
( ~ class_Groups_Omonoid__mult(X4310)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4309)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4310),hAPP(hAPP(c_Power_Opower__class_Opower(X4310),X4308),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4309,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X4308) = hAPP(hAPP(c_Power_Opower__class_Opower(X4310),X4308),X4309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
fof(i_0_1397,plain,
! [X4326,X4327,X4328,X4329,X4330] :
( ( X4329 = X4328
| X4327 = X4326
| c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4326)) != c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4327))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4330) )
& ( X4329 != X4328
| c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4326)) = c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4327))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4330) )
& ( X4327 != X4326
| c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4326)) = c_Groups_Oplus__class_Oplus(X4330,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4329),X4326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4330),X4328),X4327))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4330) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1398,plain,
! [X4339,X4340,X4341,X4342,X4343] :
( ( c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4339)) != c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4339),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4341))
| X4342 = X4340
| X4341 = X4339
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4343) )
& ( X4342 != X4340
| c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4339)) = c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4339),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4341))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4343) )
& ( X4341 != X4339
| c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4339)) = c_Groups_Oplus__class_Oplus(X4343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4342),X4339),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4343),X4340),X4341))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4343) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
fof(i_0_1399,plain,
! [X4517,X4518,X4519,X4520] :
( ( c_Orderings_Oord__class_Oless(X4520,c_Groups_Ominus__class_Ominus(X4520,X4518,X4517),X4519)
| ~ c_Orderings_Oord__class_Oless(X4520,c_Groups_Oabs__class_Oabs(X4520,c_Groups_Ominus__class_Ominus(X4520,X4519,X4518)),X4517)
| ~ class_Rings_Olinordered__idom(X4520) )
& ( c_Orderings_Oord__class_Oless(X4520,X4519,c_Groups_Oplus__class_Oplus(X4520,X4518,X4517))
| ~ c_Orderings_Oord__class_Oless(X4520,c_Groups_Oabs__class_Oabs(X4520,c_Groups_Ominus__class_Ominus(X4520,X4519,X4518)),X4517)
| ~ class_Rings_Olinordered__idom(X4520) )
& ( ~ c_Orderings_Oord__class_Oless(X4520,c_Groups_Ominus__class_Ominus(X4520,X4518,X4517),X4519)
| ~ c_Orderings_Oord__class_Oless(X4520,X4519,c_Groups_Oplus__class_Oplus(X4520,X4518,X4517))
| c_Orderings_Oord__class_Oless(X4520,c_Groups_Oabs__class_Oabs(X4520,c_Groups_Ominus__class_Ominus(X4520,X4519,X4518)),X4517)
| ~ class_Rings_Olinordered__idom(X4520) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).
fof(i_0_1400,plain,
! [X4876,X4877,X4878,X4879] :
( ~ class_Rings_Ocomm__semiring__0(X4879)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4879)),X4878),c_Polynomial_OpCons(X4879,X4877,X4876)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4879),c_Polynomial_Osmult(X4879,X4877,X4878),c_Polynomial_OpCons(X4879,c_Groups_Ozero__class_Ozero(X4879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4879)),X4878),X4876))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
fof(i_0_1401,plain,
! [X3860,X3861,X3862] :
( ~ class_Rings_Oring__1(X3862)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3862),c_Groups_Ouminus__class_Ouminus(X3862,X3861)),X3860) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3862),hAPP(hAPP(c_Power_Opower__class_Opower(X3862),c_Groups_Ouminus__class_Ouminus(X3862,c_Groups_Oone__class_Oone(X3862))),X3860)),hAPP(hAPP(c_Power_Opower__class_Opower(X3862),X3861),X3860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1402,plain,
! [X4685,X4686,X4687] :
( ~ 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),X4687),X4686),X4685),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),X4685)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4687)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4686,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,
! [X4688,X4689,X4690] :
( ~ 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),X4690),X4689),X4688))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4688,X4690)
| ~ c_Orderings_Oord__class_Oless(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) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1404,plain,
! [X4442,X4443,X4444] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4444)
| c_Orderings_Oord__class_Oless__eq(X4444,c_Groups_Oabs__class_Oabs(X4444,c_Groups_Ominus__class_Ominus(X4444,c_Groups_Oabs__class_Oabs(X4444,X4443),c_Groups_Oabs__class_Oabs(X4444,X4442))),c_Groups_Oabs__class_Oabs(X4444,c_Groups_Ominus__class_Ominus(X4444,X4443,X4442))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_1405,plain,
! [X4511,X4512,X4513] :
( ~ class_RealVector_Oreal__normed__vector(X4513)
| 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(X4513,X4512),c_RealVector_Onorm__class_Onorm(X4513,X4511))),c_RealVector_Onorm__class_Onorm(X4513,c_Groups_Ominus__class_Ominus(X4513,X4512,X4511))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).
fof(i_0_1406,plain,
! [X4887,X4888,X4889,X4890] :
( ~ class_Rings_Ocomm__semiring__0(X4890)
| c_Polynomial_Opcompose(X4890,c_Polynomial_OpCons(X4890,X4889,X4888),X4887) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4890),c_Polynomial_OpCons(X4890,X4889,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4890))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4890)),X4887),c_Polynomial_Opcompose(X4890,X4888,X4887))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__pCons])]) ).
fof(i_0_1407,plain,
! [X4262,X4263,X4264,X4265,X4266] :
( ~ class_Rings_Ocomm__semiring__1(X4266)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4265),X4264)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4263),X4262)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4265),X4263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4266),X4264),X4262)) ),
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,
! [X4252,X4253,X4254,X4255,X4256] :
( ~ class_Rings_Ocomm__semiring__1(X4256)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4255),X4254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4253),X4252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4256),X4253),X4252))) ),
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,
! [X4174,X4175] : 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,X4175,X4174)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4175)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4174)),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(i_0_1410,plain,
! [X2818,X2819] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2819),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2819,X2818)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2818))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
fof(i_0_1411,plain,
! [X4745,X4746,X4747,X4748] :
( ~ class_Rings_Ocomm__semiring__0(X4748)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4748)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4748),X4747,X4746)),X4745) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4748)),X4747),X4745),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__poly__add__left])]) ).
fof(i_0_1412,plain,
! [X4187,X4188,X4189,X4190,X4191,X4192,X4193] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4188,X4187)
| hBOOL(hAPP(X4189,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4189,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4188,X4187))) )
& ( X4188 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4187,X4190)
| hBOOL(hAPP(X4189,X4190))
| ~ hBOOL(hAPP(X4189,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4188,X4187))) )
& ( X4192 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4191,esk9_3(X4191,X4192,X4193))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4192,X4191)
| hBOOL(hAPP(X4193,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4192,X4191))) )
& ( ~ hBOOL(hAPP(X4193,esk9_3(X4191,X4192,X4193)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4192,X4191)
| hBOOL(hAPP(X4193,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4192,X4191))) )
& ( X4192 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4191,esk9_3(X4191,X4192,X4193))
| ~ hBOOL(hAPP(X4193,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4193,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4192,X4191))) )
& ( ~ hBOOL(hAPP(X4193,esk9_3(X4191,X4192,X4193)))
| ~ hBOOL(hAPP(X4193,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4193,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4192,X4191))) ) ),
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_1413,plain,
! [X4179,X4180,X4181,X4182,X4183,X4184,X4185] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4180,X4179)
| hBOOL(hAPP(X4181,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4181,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4180,X4179))) )
& ( X4180 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4179,X4182)
| hBOOL(hAPP(X4181,X4182))
| ~ hBOOL(hAPP(X4181,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4180,X4179))) )
& ( X4184 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4183,esk8_3(X4183,X4184,X4185))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4184,X4183)
| hBOOL(hAPP(X4185,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4184,X4183))) )
& ( ~ hBOOL(hAPP(X4185,esk8_3(X4183,X4184,X4185)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4184,X4183)
| hBOOL(hAPP(X4185,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4184,X4183))) )
& ( X4184 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4183,esk8_3(X4183,X4184,X4185))
| ~ hBOOL(hAPP(X4185,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4185,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4184,X4183))) )
& ( ~ hBOOL(hAPP(X4185,esk8_3(X4183,X4184,X4185)))
| ~ hBOOL(hAPP(X4185,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4185,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4184,X4183))) ) ),
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_1414,plain,
! [X4434,X4435,X4436,X4437,X4438] :
( ~ class_Rings_Olinordered__idom(X4438)
| ~ c_Orderings_Oord__class_Oless(X4438,c_Groups_Oabs__class_Oabs(X4438,X4437),X4436)
| ~ c_Orderings_Oord__class_Oless(X4438,c_Groups_Oabs__class_Oabs(X4438,X4435),X4434)
| c_Orderings_Oord__class_Oless(X4438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4438),c_Groups_Oabs__class_Oabs(X4438,X4437)),c_Groups_Oabs__class_Oabs(X4438,X4435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4438),X4436),X4434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_1415,plain,
! [X4833,X4834,X4835,X4836,X4837] :
( ~ class_Rings_Ocomm__semiring__0(X4837)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4837)),c_Polynomial_Omonom(X4837,X4836,X4835)),c_Polynomial_Omonom(X4837,X4834,X4833)) = c_Polynomial_Omonom(X4837,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4837),X4836),X4834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4835,X4833)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__monom])]) ).
fof(i_0_1416,plain,
! [X2789,X2790,X2791] :
( ~ class_Rings_Olinordered__semidom(X2791)
| ~ c_Orderings_Oord__class_Oless(X2791,c_Groups_Ozero__class_Ozero(X2791),X2790)
| ~ c_Orderings_Oord__class_Oless(X2791,X2790,c_Groups_Oone__class_Oone(X2791))
| c_Orderings_Oord__class_Oless(X2791,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2791),X2790),hAPP(hAPP(c_Power_Opower__class_Opower(X2791),X2790),X2789)),hAPP(hAPP(c_Power_Opower__class_Opower(X2791),X2790),X2789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1417,plain,
! [X4583] :
( ( ~ 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),X4583),X4583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4583,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4583,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),X4583),X4583),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,
! [X3235,X3236,X3237,X3238,X3239] :
( ~ class_RealVector_Oreal__normed__vector(X3239)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3239,X3238),X3237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3239,X3236),X3235)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3239,c_Groups_Oplus__class_Oplus(X3239,X3238,X3236)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3237,X3235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
fof(i_0_1419,plain,
! [X4753,X4754,X4755,X4756] :
( ~ class_Rings_Ocomm__semiring__0(X4756)
| hAPP(c_Polynomial_Opoly(X4756,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4756)),X4755),X4754)),X4753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4756),hAPP(c_Polynomial_Opoly(X4756,X4755),X4753)),hAPP(c_Polynomial_Opoly(X4756,X4754),X4753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1420,plain,
! [X4301,X4302] :
( ( X4302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4302),X4301) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4302),X4301) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4301,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4302,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4301)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1421,plain,
! [X4104,X4105,X4106] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4105,X4106),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4104,X4106))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4105,X4104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4106,X4104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4106,X4105) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4105,X4104)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4105,X4106),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4104,X4106))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4106,X4104)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4106,X4105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1422,plain,
! [X4136,X4137,X4138] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4137,X4138),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4136,X4138))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4137,X4136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4138,X4136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4138,X4137) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4137,X4136)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4137,X4138),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4136,X4138))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4138,X4136)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4138,X4137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1423,plain,
! [X2897,X2898,X2899,X2900,X2901] :
( ~ class_Rings_Oordered__semiring(X2901)
| ~ c_Orderings_Oord__class_Oless__eq(X2901,X2900,X2899)
| ~ c_Orderings_Oord__class_Oless__eq(X2901,X2898,X2897)
| ~ c_Orderings_Oord__class_Oless__eq(X2901,c_Groups_Ozero__class_Ozero(X2901),X2900)
| ~ c_Orderings_Oord__class_Oless__eq(X2901,c_Groups_Ozero__class_Ozero(X2901),X2898)
| c_Orderings_Oord__class_Oless__eq(X2901,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2901),X2900),X2898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2901),X2899),X2897)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1424,plain,
! [X2892,X2893,X2894,X2895,X2896] :
( ~ class_Rings_Oordered__semiring(X2896)
| ~ c_Orderings_Oord__class_Oless__eq(X2896,X2895,X2894)
| ~ c_Orderings_Oord__class_Oless__eq(X2896,X2893,X2892)
| ~ c_Orderings_Oord__class_Oless__eq(X2896,c_Groups_Ozero__class_Ozero(X2896),X2894)
| ~ c_Orderings_Oord__class_Oless__eq(X2896,c_Groups_Ozero__class_Ozero(X2896),X2893)
| c_Orderings_Oord__class_Oless__eq(X2896,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2896),X2895),X2893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2896),X2894),X2892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1425,plain,
! [X3000,X3001,X3002,X3003,X3004] :
( ~ class_Rings_Olinordered__semiring__strict(X3004)
| ~ c_Orderings_Oord__class_Oless(X3004,X3003,X3002)
| ~ c_Orderings_Oord__class_Oless__eq(X3004,X3001,X3000)
| ~ c_Orderings_Oord__class_Oless__eq(X3004,c_Groups_Ozero__class_Ozero(X3004),X3003)
| ~ c_Orderings_Oord__class_Oless(X3004,c_Groups_Ozero__class_Ozero(X3004),X3001)
| c_Orderings_Oord__class_Oless(X3004,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3004),X3003),X3001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3004),X3002),X3000)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1426,plain,
! [X2995,X2996,X2997,X2998,X2999] :
( ~ class_Rings_Olinordered__semiring__strict(X2999)
| ~ c_Orderings_Oord__class_Oless__eq(X2999,X2998,X2997)
| ~ c_Orderings_Oord__class_Oless(X2999,X2996,X2995)
| ~ c_Orderings_Oord__class_Oless(X2999,c_Groups_Ozero__class_Ozero(X2999),X2998)
| ~ c_Orderings_Oord__class_Oless__eq(X2999,c_Groups_Ozero__class_Ozero(X2999),X2996)
| c_Orderings_Oord__class_Oless(X2999,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2999),X2998),X2996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2999),X2997),X2995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1427,plain,
! [X3005,X3006,X3007,X3008,X3009] :
( ~ class_Rings_Olinordered__semiring__strict(X3009)
| ~ c_Orderings_Oord__class_Oless(X3009,X3008,X3007)
| ~ c_Orderings_Oord__class_Oless(X3009,X3006,X3005)
| ~ c_Orderings_Oord__class_Oless__eq(X3009,c_Groups_Ozero__class_Ozero(X3009),X3008)
| ~ c_Orderings_Oord__class_Oless__eq(X3009,c_Groups_Ozero__class_Ozero(X3009),X3006)
| c_Orderings_Oord__class_Oless(X3009,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3009),X3008),X3006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3009),X3007),X3005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1428,plain,
! [X3010,X3011,X3012,X3013,X3014] :
( ~ class_Rings_Olinordered__semiring__strict(X3014)
| ~ c_Orderings_Oord__class_Oless(X3014,X3013,X3012)
| ~ c_Orderings_Oord__class_Oless(X3014,X3011,X3010)
| ~ c_Orderings_Oord__class_Oless(X3014,c_Groups_Ozero__class_Ozero(X3014),X3012)
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3011)
| c_Orderings_Oord__class_Oless(X3014,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3014),X3013),X3011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3014),X3012),X3010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1429,plain,
! [X2794,X2795,X2796,X2797,X2798] :
( ~ class_RealVector_Oreal__normed__algebra(X2798)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2798,X2797),X2796)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2798,X2795),X2794)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2798),X2797),X2795)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2796),X2794)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1430,plain,
! [X4903,X4904,X4905] :
( ~ class_Rings_Ocomm__semiring__0(X4905)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4905),X4904,c_Polynomial_Osmult(X4905,X4903,c_Polynomial_Osynthetic__div(X4905,X4904,X4903))) = c_Polynomial_OpCons(X4905,hAPP(c_Polynomial_Opoly(X4905,X4904),X4903),c_Polynomial_Osynthetic__div(X4905,X4904,X4903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct])]) ).
fof(i_0_1431,plain,
! [X4353,X4354,X4355,X4356] :
( ~ class_Rings_Ocomm__semiring__1(X4356)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4354)),X4353) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),hAPP(hAPP(c_Power_Opower__class_Opower(X4356),X4355),X4353)),hAPP(hAPP(c_Power_Opower__class_Opower(X4356),X4354),X4353)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1432,plain,
! [X3123,X3124,X3125,X3126] :
( ~ class_Groups_Ocomm__monoid__mult(X3126)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3126),X3125),X3124)),X3123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3126),hAPP(hAPP(c_Power_Opower__class_Opower(X3126),X3125),X3123)),hAPP(hAPP(c_Power_Opower__class_Opower(X3126),X3124),X3123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1433,plain,
! [X3026,X3027,X3028] :
( ~ class_Rings_Olinordered__ring(X3028)
| c_Orderings_Oord__class_Oless__eq(X3028,c_Groups_Ozero__class_Ozero(X3028),c_Groups_Oplus__class_Oplus(X3028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3028),X3027),X3027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3028),X3026),X3026))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_1434,plain,
! [X3855,X3856] :
( ~ class_Rings_Oring__1(X3856)
| c_Groups_Ominus__class_Ominus(X3856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3856),X3855),X3855),c_Groups_Oone__class_Oone(X3856)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3856),c_Groups_Oplus__class_Oplus(X3856,X3855,c_Groups_Oone__class_Oone(X3856))),c_Groups_Ominus__class_Ominus(X3856,X3855,c_Groups_Oone__class_Oone(X3856))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
fof(i_0_1435,plain,
! [X4868,X4869,X4870,X4871] :
( ~ class_Rings_Ocomm__semiring__0(X4871)
| hAPP(c_Polynomial_Opoly(X4871,c_Polynomial_OpCons(X4871,X4870,X4869)),X4868) = c_Groups_Oplus__class_Oplus(X4871,X4870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4871),X4868),hAPP(c_Polynomial_Opoly(X4871,X4869),X4868))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(i_0_1436,plain,
! [X2804,X2805,X2806] :
( ~ class_Rings_Olinordered__semidom(X2806)
| ~ c_Orderings_Oord__class_Oless(X2806,c_Groups_Oone__class_Oone(X2806),X2805)
| c_Orderings_Oord__class_Oless(X2806,hAPP(hAPP(c_Power_Opower__class_Opower(X2806),X2805),X2804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2806),X2805),hAPP(hAPP(c_Power_Opower__class_Opower(X2806),X2805),X2804))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1437,plain,
! [X2975,X2976,X2977,X2978] :
( ~ class_Rings_Olinordered__semiring__strict(X2978)
| ~ c_Orderings_Oord__class_Oless__eq(X2978,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2978),X2977),X2976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2978),X2975),X2976))
| ~ c_Orderings_Oord__class_Oless(X2978,c_Groups_Ozero__class_Ozero(X2978),X2976)
| c_Orderings_Oord__class_Oless__eq(X2978,X2977,X2975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1438,plain,
! [X2971,X2972,X2973,X2974] :
( ~ class_Rings_Olinordered__semiring__strict(X2974)
| ~ c_Orderings_Oord__class_Oless__eq(X2974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2974),X2973),X2972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2974),X2973),X2971))
| ~ c_Orderings_Oord__class_Oless(X2974,c_Groups_Ozero__class_Ozero(X2974),X2973)
| c_Orderings_Oord__class_Oless__eq(X2974,X2972,X2971) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1439,plain,
! [X3019,X3020,X3021,X3022] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3022,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3022),X3021),X3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3022),X3021),X3019))
| c_Orderings_Oord__class_Oless__eq(X3022,X3020,X3019)
| ~ c_Orderings_Oord__class_Oless(X3022,c_Groups_Ozero__class_Ozero(X3022),X3021)
| ~ class_Rings_Olinordered__ring__strict(X3022) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3022,X3020,X3019)
| c_Orderings_Oord__class_Oless__eq(X3022,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3022),X3021),X3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3022),X3021),X3019))
| ~ c_Orderings_Oord__class_Oless(X3022,c_Groups_Ozero__class_Ozero(X3022),X3021)
| ~ class_Rings_Olinordered__ring__strict(X3022) ) ),
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,
! [X2991,X2992,X2993,X2994] :
( ~ class_Rings_Olinordered__semiring(X2994)
| ~ c_Orderings_Oord__class_Oless(X2994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),X2993),X2992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2994),X2991),X2992))
| ~ c_Orderings_Oord__class_Oless__eq(X2994,c_Groups_Ozero__class_Ozero(X2994),X2992)
| c_Orderings_Oord__class_Oless(X2994,X2993,X2991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1441,plain,
! [X2987,X2988,X2989,X2990] :
( ~ class_Rings_Olinordered__semiring__strict(X2990)
| ~ c_Orderings_Oord__class_Oless(X2990,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),X2989),X2988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2990),X2987),X2988))
| ~ c_Orderings_Oord__class_Oless__eq(X2990,c_Groups_Ozero__class_Ozero(X2990),X2988)
| c_Orderings_Oord__class_Oless(X2990,X2989,X2987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1442,plain,
! [X3035,X3036,X3037,X3038] :
( ~ class_Rings_Olinordered__semidom(X3038)
| ~ c_Orderings_Oord__class_Oless(X3038,hAPP(hAPP(c_Power_Opower__class_Opower(X3038),X3037),X3036),hAPP(hAPP(c_Power_Opower__class_Opower(X3038),X3035),X3036))
| ~ c_Orderings_Oord__class_Oless__eq(X3038,c_Groups_Ozero__class_Ozero(X3038),X3035)
| c_Orderings_Oord__class_Oless(X3038,X3037,X3035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1443,plain,
! [X2983,X2984,X2985,X2986] :
( ~ class_Rings_Olinordered__semiring(X2986)
| ~ c_Orderings_Oord__class_Oless(X2986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2985),X2984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2986),X2985),X2983))
| ~ c_Orderings_Oord__class_Oless__eq(X2986,c_Groups_Ozero__class_Ozero(X2986),X2985)
| c_Orderings_Oord__class_Oless(X2986,X2984,X2983) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1444,plain,
! [X2979,X2980,X2981,X2982] :
( ~ class_Rings_Olinordered__semiring__strict(X2982)
| ~ c_Orderings_Oord__class_Oless(X2982,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2982),X2981),X2980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2982),X2981),X2979))
| ~ c_Orderings_Oord__class_Oless__eq(X2982,c_Groups_Ozero__class_Ozero(X2982),X2981)
| c_Orderings_Oord__class_Oless(X2982,X2980,X2979) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1445,plain,
! [X3179,X3180,X3181,X3182] :
( ( ~ c_Orderings_Oord__class_Oless(X3182,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3182),X3181),X3180),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3182),X3181),X3179))
| c_Orderings_Oord__class_Oless(X3182,X3180,X3179)
| ~ c_Orderings_Oord__class_Oless(X3182,c_Groups_Ozero__class_Ozero(X3182),X3181)
| ~ class_Rings_Olinordered__ring__strict(X3182) )
& ( ~ c_Orderings_Oord__class_Oless(X3182,X3180,X3179)
| c_Orderings_Oord__class_Oless(X3182,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3182),X3181),X3180),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3182),X3181),X3179))
| ~ c_Orderings_Oord__class_Oless(X3182,c_Groups_Ozero__class_Ozero(X3182),X3181)
| ~ class_Rings_Olinordered__ring__strict(X3182) ) ),
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,
! [X3015,X3016,X3017,X3018] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3018),X3017),X3016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3018),X3017),X3015))
| c_Orderings_Oord__class_Oless__eq(X3018,X3015,X3016)
| ~ c_Orderings_Oord__class_Oless(X3018,X3017,c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Rings_Olinordered__ring__strict(X3018) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3018,X3015,X3016)
| c_Orderings_Oord__class_Oless__eq(X3018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3018),X3017),X3016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3018),X3017),X3015))
| ~ c_Orderings_Oord__class_Oless(X3018,X3017,c_Groups_Ozero__class_Ozero(X3018))
| ~ class_Rings_Olinordered__ring__strict(X3018) ) ),
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,
! [X3160,X3161,X3162,X3163] :
( ( ~ c_Orderings_Oord__class_Oless(X3163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3163),X3162),X3161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3163),X3162),X3160))
| c_Orderings_Oord__class_Oless(X3163,X3160,X3161)
| ~ c_Orderings_Oord__class_Oless(X3163,X3162,c_Groups_Ozero__class_Ozero(X3163))
| ~ class_Rings_Olinordered__ring__strict(X3163) )
& ( ~ c_Orderings_Oord__class_Oless(X3163,X3160,X3161)
| c_Orderings_Oord__class_Oless(X3163,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3163),X3162),X3161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3163),X3162),X3160))
| ~ c_Orderings_Oord__class_Oless(X3163,X3162,c_Groups_Ozero__class_Ozero(X3163))
| ~ class_Rings_Olinordered__ring__strict(X3163) ) ),
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,
! [X2873,X2874,X2875,X2876] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2876,hAPP(hAPP(c_Power_Opower__class_Opower(X2876),X2875),X2874),hAPP(hAPP(c_Power_Opower__class_Opower(X2876),X2875),X2873))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2874,X2873)
| ~ c_Orderings_Oord__class_Oless(X2876,c_Groups_Oone__class_Oone(X2876),X2875)
| ~ class_Rings_Olinordered__semidom(X2876) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2874,X2873)
| c_Orderings_Oord__class_Oless__eq(X2876,hAPP(hAPP(c_Power_Opower__class_Opower(X2876),X2875),X2874),hAPP(hAPP(c_Power_Opower__class_Opower(X2876),X2875),X2873))
| ~ c_Orderings_Oord__class_Oless(X2876,c_Groups_Oone__class_Oone(X2876),X2875)
| ~ class_Rings_Olinordered__semidom(X2876) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1449,plain,
! [X2869,X2870,X2871,X2872] :
( ~ class_Rings_Olinordered__semidom(X2872)
| ~ c_Orderings_Oord__class_Oless(X2872,c_Groups_Oone__class_Oone(X2872),X2871)
| ~ c_Orderings_Oord__class_Oless__eq(X2872,hAPP(hAPP(c_Power_Opower__class_Opower(X2872),X2871),X2870),hAPP(hAPP(c_Power_Opower__class_Opower(X2872),X2871),X2869))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2870,X2869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1450,plain,
! [X3220,X3221,X3222,X3223] :
( ( ~ c_Orderings_Oord__class_Oless(X3223,hAPP(hAPP(c_Power_Opower__class_Opower(X3223),X3222),X3221),hAPP(hAPP(c_Power_Opower__class_Opower(X3223),X3222),X3220))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3221,X3220)
| ~ c_Orderings_Oord__class_Oless(X3223,c_Groups_Oone__class_Oone(X3223),X3222)
| ~ class_Rings_Olinordered__semidom(X3223) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3221,X3220)
| c_Orderings_Oord__class_Oless(X3223,hAPP(hAPP(c_Power_Opower__class_Opower(X3223),X3222),X3221),hAPP(hAPP(c_Power_Opower__class_Opower(X3223),X3222),X3220))
| ~ c_Orderings_Oord__class_Oless(X3223,c_Groups_Oone__class_Oone(X3223),X3222)
| ~ class_Rings_Olinordered__semidom(X3223) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1451,plain,
! [X3216,X3217,X3218,X3219] :
( ~ class_Rings_Olinordered__semidom(X3219)
| ~ c_Orderings_Oord__class_Oless(X3219,c_Groups_Oone__class_Oone(X3219),X3218)
| ~ c_Orderings_Oord__class_Oless(X3219,hAPP(hAPP(c_Power_Opower__class_Opower(X3219),X3218),X3217),hAPP(hAPP(c_Power_Opower__class_Opower(X3219),X3218),X3216))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3217,X3216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1452,plain,
! [X4770,X4771,X4772,X4773,X4774] :
( ~ class_Groups_Oab__group__add(X4774)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4774),c_Polynomial_OpCons(X4774,X4773,X4772),c_Polynomial_OpCons(X4774,X4771,X4770)) = c_Polynomial_OpCons(X4774,c_Groups_Ominus__class_Ominus(X4774,X4773,X4771),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4774),X4772,X4770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__pCons])]) ).
fof(i_0_1453,plain,
! [X4847,X4848,X4849,X4850,X4851] :
( ~ class_Groups_Ocomm__monoid__add(X4851)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4851),c_Polynomial_OpCons(X4851,X4850,X4849),c_Polynomial_OpCons(X4851,X4848,X4847)) = c_Polynomial_OpCons(X4851,c_Groups_Oplus__class_Oplus(X4851,X4850,X4848),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4851),X4849,X4847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pCons])]) ).
fof(i_0_1454,plain,
! [X4766,X4767,X4768,X4769] :
( ~ class_Rings_Ocomm__semiring__1(X4769)
| hAPP(c_Polynomial_Opoly(X4769,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4769)),X4768),X4767)),X4766) = hAPP(hAPP(c_Power_Opower__class_Opower(X4769),hAPP(c_Polynomial_Opoly(X4769,X4768),X4766)),X4767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1455,plain,
! [X5160,X5161] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5160)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X5161)),c_RComplete_Onatfloor(X5160)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5161),X5160))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1456,plain,
! [X4348,X4349,X4350,X4351,X4352] :
( ~ class_Groups_Oab__group__add(X4352)
| c_Groups_Ominus__class_Ominus(X4352,c_Groups_Oplus__class_Oplus(X4352,X4351,X4350),c_Groups_Oplus__class_Oplus(X4352,X4349,X4348)) = c_Groups_Oplus__class_Oplus(X4352,c_Groups_Ominus__class_Ominus(X4352,X4351,X4349),c_Groups_Ominus__class_Ominus(X4352,X4350,X4348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1457,plain,
! [X4286,X4287,X4288,X4289,X4290] :
( ~ class_Rings_Ocomm__semiring__1(X4290)
| c_Groups_Oplus__class_Oplus(X4290,c_Groups_Oplus__class_Oplus(X4290,X4289,X4288),c_Groups_Oplus__class_Oplus(X4290,X4287,X4286)) = c_Groups_Oplus__class_Oplus(X4290,c_Groups_Oplus__class_Oplus(X4290,X4289,X4287),c_Groups_Oplus__class_Oplus(X4290,X4288,X4286)) ),
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,
! [X2865,X2866,X2867,X2868] :
( ~ class_Rings_Olinordered__semidom(X2868)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2867,X2866)
| ~ c_Orderings_Oord__class_Oless__eq(X2868,c_Groups_Ozero__class_Ozero(X2868),X2865)
| ~ c_Orderings_Oord__class_Oless__eq(X2868,X2865,c_Groups_Oone__class_Oone(X2868))
| c_Orderings_Oord__class_Oless__eq(X2868,hAPP(hAPP(c_Power_Opower__class_Opower(X2868),X2865),X2866),hAPP(hAPP(c_Power_Opower__class_Opower(X2868),X2865),X2867)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1459,plain,
! [X2807,X2808,X2809,X2810] :
( ~ class_Rings_Olinordered__semidom(X2810)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2809,X2808)
| ~ c_Orderings_Oord__class_Oless(X2810,c_Groups_Ozero__class_Ozero(X2810),X2807)
| ~ c_Orderings_Oord__class_Oless(X2810,X2807,c_Groups_Oone__class_Oone(X2810))
| c_Orderings_Oord__class_Oless(X2810,hAPP(hAPP(c_Power_Opower__class_Opower(X2810),X2807),X2808),hAPP(hAPP(c_Power_Opower__class_Opower(X2810),X2807),X2809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1460,plain,
! [X3039,X3040,X3041,X3042] :
( ~ class_Rings_Olinordered__semidom(X3042)
| ~ c_Orderings_Oord__class_Oless(X3042,X3041,X3040)
| ~ c_Orderings_Oord__class_Oless__eq(X3042,c_Groups_Ozero__class_Ozero(X3042),X3041)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3039)
| c_Orderings_Oord__class_Oless(X3042,hAPP(hAPP(c_Power_Opower__class_Opower(X3042),X3041),X3039),hAPP(hAPP(c_Power_Opower__class_Opower(X3042),X3040),X3039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1461,plain,
! [X3183,X3184,X3185,X3186] :
( ( c_Orderings_Oord__class_Oless(X3186,X3185,c_Groups_Ozero__class_Ozero(X3186))
| c_Orderings_Oord__class_Oless(X3186,c_Groups_Ozero__class_Ozero(X3186),X3185)
| ~ c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) )
& ( c_Orderings_Oord__class_Oless(X3186,X3183,X3184)
| c_Orderings_Oord__class_Oless(X3186,c_Groups_Ozero__class_Ozero(X3186),X3185)
| ~ c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) )
& ( c_Orderings_Oord__class_Oless(X3186,X3185,c_Groups_Ozero__class_Ozero(X3186))
| c_Orderings_Oord__class_Oless(X3186,X3184,X3183)
| ~ c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) )
& ( c_Orderings_Oord__class_Oless(X3186,X3183,X3184)
| c_Orderings_Oord__class_Oless(X3186,X3184,X3183)
| ~ c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) )
& ( ~ c_Orderings_Oord__class_Oless(X3186,c_Groups_Ozero__class_Ozero(X3186),X3185)
| ~ c_Orderings_Oord__class_Oless(X3186,X3184,X3183)
| c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) )
& ( ~ c_Orderings_Oord__class_Oless(X3186,X3185,c_Groups_Ozero__class_Ozero(X3186))
| ~ c_Orderings_Oord__class_Oless(X3186,X3183,X3184)
| c_Orderings_Oord__class_Oless(X3186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3186),X3185),X3183))
| ~ class_Rings_Olinordered__ring__strict(X3186) ) ),
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,
! [X3187,X3188,X3189,X3190] :
( ( c_Orderings_Oord__class_Oless(X3190,X3188,c_Groups_Ozero__class_Ozero(X3190))
| c_Orderings_Oord__class_Oless(X3190,c_Groups_Ozero__class_Ozero(X3190),X3188)
| ~ c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) )
& ( c_Orderings_Oord__class_Oless(X3190,X3187,X3189)
| c_Orderings_Oord__class_Oless(X3190,c_Groups_Ozero__class_Ozero(X3190),X3188)
| ~ c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) )
& ( c_Orderings_Oord__class_Oless(X3190,X3188,c_Groups_Ozero__class_Ozero(X3190))
| c_Orderings_Oord__class_Oless(X3190,X3189,X3187)
| ~ c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) )
& ( c_Orderings_Oord__class_Oless(X3190,X3187,X3189)
| c_Orderings_Oord__class_Oless(X3190,X3189,X3187)
| ~ c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) )
& ( ~ c_Orderings_Oord__class_Oless(X3190,c_Groups_Ozero__class_Ozero(X3190),X3188)
| ~ c_Orderings_Oord__class_Oless(X3190,X3189,X3187)
| c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) )
& ( ~ c_Orderings_Oord__class_Oless(X3190,X3188,c_Groups_Ozero__class_Ozero(X3190))
| ~ c_Orderings_Oord__class_Oless(X3190,X3187,X3189)
| c_Orderings_Oord__class_Oless(X3190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3189),X3188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3190),X3187),X3188))
| ~ class_Rings_Olinordered__ring__strict(X3190) ) ),
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,
! [X5140,X5141,X5143] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_2(X5140,X5141))
| ~ class_RealVector_Oreal__normed__algebra(X5141) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5141),X5143),X5140)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5141,X5143)),esk28_2(X5140,X5141)))
| ~ class_RealVector_Oreal__normed__algebra(X5141) ) ),
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,
! [X3045,X3046,X3047] :
( ~ class_RealVector_Oreal__normed__algebra(X3047)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3047,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3047),X3046),X3045)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3047,X3046)),c_RealVector_Onorm__class_Onorm(X3047,X3045))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1465,plain,
! [X5148,X5149,X5151] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk30_2(X5148,X5149))
| ~ class_RealVector_Oreal__normed__algebra(X5149) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5149),X5148),X5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5149,X5151)),esk30_2(X5148,X5149)))
| ~ class_RealVector_Oreal__normed__algebra(X5149) ) ),
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,
! [X4335,X4336,X4337,X4338] :
( ~ class_Rings_Ocomm__semiring__1(X4338)
| c_Groups_Oplus__class_Oplus(X4338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4338),X4337),X4336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4338),X4335),X4336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4338),c_Groups_Oplus__class_Oplus(X4338,X4337,X4335)),X4336) ),
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,
! [X3701,X3702,X3703,X3704] :
( ~ class_RealVector_Oreal__normed__algebra(X3704)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),c_Groups_Ominus__class_Ominus(X3704,X3703,X3702)),X3701) = c_Groups_Ominus__class_Ominus(X3704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3703),X3701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3704),X3702),X3701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1468,plain,
! [X3697,X3698,X3699,X3700] :
( ~ class_RealVector_Oreal__normed__algebra(X3700)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3700),c_Groups_Ominus__class_Ominus(X3700,X3699,X3698)),X3697) = c_Groups_Ominus__class_Ominus(X3700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3700),X3699),X3697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3700),X3698),X3697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1469,plain,
! [X4331,X4332,X4333,X4334] :
( ~ class_Rings_Ocomm__semiring__1(X4334)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4334),c_Groups_Oplus__class_Oplus(X4334,X4333,X4332)),X4331) = c_Groups_Oplus__class_Oplus(X4334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4334),X4333),X4331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4334),X4332),X4331)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1470,plain,
! [X3105,X3106,X3107,X3108] :
( ~ class_Rings_Ocomm__semiring(X3108)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),c_Groups_Oplus__class_Oplus(X3108,X3107,X3106)),X3105) = c_Groups_Oplus__class_Oplus(X3108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),X3107),X3105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),X3106),X3105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1471,plain,
! [X3101,X3102,X3103,X3104] :
( ~ class_RealVector_Oreal__normed__algebra(X3104)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3104),c_Groups_Oplus__class_Oplus(X3104,X3103,X3102)),X3101) = c_Groups_Oplus__class_Oplus(X3104,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3104),X3103),X3101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3104),X3102),X3101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1472,plain,
! [X3097,X3098,X3099,X3100] :
( ~ class_RealVector_Oreal__normed__algebra(X3100)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3100),c_Groups_Oplus__class_Oplus(X3100,X3099,X3098)),X3097) = c_Groups_Oplus__class_Oplus(X3100,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3100),X3099),X3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3100),X3098),X3097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1473,plain,
! [X4056,X4057,X4058,X4059] :
( ~ class_Rings_Ocomm__semiring__1(X4059)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4059),hAPP(hAPP(c_Power_Opower__class_Opower(X4059),X4058),X4057)),hAPP(hAPP(c_Power_Opower__class_Opower(X4059),X4058),X4056)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4059),X4058),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4057,X4056)) ),
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,
! [X3231,X3232,X3233,X3234] :
( ~ class_Groups_Omonoid__mult(X3234)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3234),X3233),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3232,X3231)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3234),hAPP(hAPP(c_Power_Opower__class_Opower(X3234),X3233),X3232)),hAPP(hAPP(c_Power_Opower__class_Opower(X3234),X3233),X3231)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1475,plain,
! [X4248,X4249,X4250,X4251] :
( ~ class_Rings_Ocomm__semiring__1(X4251)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),X4250),X4249)),X4248) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4251),X4250),X4248)),X4249) ),
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,
! [X4445,X4446,X4447] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4447)
| c_Orderings_Oord__class_Oless__eq(X4447,c_Groups_Ominus__class_Ominus(X4447,c_Groups_Oabs__class_Oabs(X4447,X4446),c_Groups_Oabs__class_Oabs(X4447,X4445)),c_Groups_Oabs__class_Oabs(X4447,c_Groups_Ominus__class_Ominus(X4447,X4446,X4445))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_1477,plain,
! [X4448,X4449,X4450] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4450)
| c_Orderings_Oord__class_Oless__eq(X4450,c_Groups_Ominus__class_Ominus(X4450,c_Groups_Oabs__class_Oabs(X4450,X4449),c_Groups_Oabs__class_Oabs(X4450,X4448)),c_Groups_Oabs__class_Oabs(X4450,c_Groups_Ominus__class_Ominus(X4450,X4448,X4449))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).
fof(i_0_1478,plain,
! [X4498,X4499,X4500] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4500)
| c_Orderings_Oord__class_Oless__eq(X4500,c_Groups_Oabs__class_Oabs(X4500,c_Groups_Ominus__class_Ominus(X4500,X4499,X4498)),c_Groups_Oplus__class_Oplus(X4500,c_Groups_Oabs__class_Oabs(X4500,X4499),c_Groups_Oabs__class_Oabs(X4500,X4498))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_1479,plain,
! [X4439,X4440,X4441] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4441)
| c_Orderings_Oord__class_Oless__eq(X4441,c_Groups_Oabs__class_Oabs(X4441,c_Groups_Oplus__class_Oplus(X4441,X4440,X4439)),c_Groups_Oplus__class_Oplus(X4441,c_Groups_Oabs__class_Oabs(X4441,X4440),c_Groups_Oabs__class_Oabs(X4441,X4439))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
fof(i_0_1480,plain,
! [X4363,X4364,X4365,X4366,X4367,X4368] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4368)
| X4367 = c_Groups_Ozero__class_Ozero(X4368)
| X4366 != X4365
| X4364 = X4363
| c_Groups_Oplus__class_Oplus(X4368,X4366,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4368),X4367),X4364)) != c_Groups_Oplus__class_Oplus(X4368,X4365,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4368),X4367),X4363)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1481,plain,
! [X3357,X3358,X3359] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3359),X3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3357),X3358))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3358)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3359,X3357) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3358)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3359),X3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3357),X3358)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3359,X3357)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3359),X3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3357),X3358)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1482,plain,
! [X3570,X3571,X3572] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3572),X3571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3572),X3570))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3571,X3570)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3572) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3571,X3570)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3572),X3571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3572),X3570))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3572) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1483,plain,
! [X3360,X3361,X3362] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3360))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3362)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3361,X3360) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3362)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3360)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3361,X3360)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3362),X3360)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1484,plain,
! [X3566,X3567,X3568] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3567),X3568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3566),X3568))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3567,X3566)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3568) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3567,X3566)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3567),X3568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3566),X3568))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3568) ) ),
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,
! [X3273,X3274,X3275] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3275),X3274),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3275),X3273))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3274,X3273)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3275) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3274,X3273)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3275),X3274),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3275),X3273))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3275) ) ),
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,
! [X4032,X4033,X4034] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4034),X4033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4034),X4032))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4033,X4032)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4034) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4033,X4032)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4034),X4033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4034),X4032))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4034) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1487,plain,
! [X2829,X2830,X2831] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2831)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2831),X2830),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2831),X2829))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2830,X2829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1488,plain,
! [X3535,X3536,X3537] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3536),X3537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3535),X3537))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3536,X3535)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3537) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3536,X3535)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3536),X3537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3535),X3537))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3537) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1489,plain,
! [X5182,X5183] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5183),X5182)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5182,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5183),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X5182) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5183,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,
! [X3694,X3695,X3696] :
( ~ class_RealVector_Oreal__normed__vector(X3696)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3696,X3695),c_RealVector_Onorm__class_Onorm(X3696,X3694)),c_RealVector_Onorm__class_Onorm(X3696,c_Groups_Ominus__class_Ominus(X3696,X3695,X3694))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1491,plain,
! [X4176,X4177,X4178] :
( ~ class_RealVector_Oreal__normed__vector(X4178)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4178,X4177),c_RealVector_Onorm__class_Onorm(X4178,X4176)),c_RealVector_Onorm__class_Onorm(X4178,c_Groups_Oplus__class_Oplus(X4178,X4177,X4176))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(i_0_1492,plain,
! [X3863,X3864,X3865] :
( ~ class_RealVector_Oreal__normed__vector(X3865)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3865,c_Groups_Ominus__class_Ominus(X3865,X3864,X3863)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3865,X3864),c_RealVector_Onorm__class_Onorm(X3865,X3863))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).
fof(i_0_1493,plain,
! [X2957,X2958,X2959] :
( ~ class_RealVector_Oreal__normed__vector(X2959)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2959,c_Groups_Oplus__class_Oplus(X2959,X2958,X2957)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2959,X2958),c_RealVector_Onorm__class_Onorm(X2959,X2957))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1494,plain,
! [X4737,X4738,X4739,X4740] :
( ~ class_Rings_Ocomm__semiring__0(X4740)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4740)),c_Polynomial_Osmult(X4740,X4739,X4738)),X4737) = c_Polynomial_Osmult(X4740,X4739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4740)),X4738),X4737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
fof(i_0_1495,plain,
! [X4759,X4760,X4761,X4762] :
( ~ class_Rings_Ocomm__ring(X4762)
| hAPP(c_Polynomial_Opoly(X4762,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4762),X4761,X4760)),X4759) = c_Groups_Ominus__class_Ominus(X4762,hAPP(c_Polynomial_Opoly(X4762,X4761),X4759),hAPP(c_Polynomial_Opoly(X4762,X4760),X4759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).
fof(i_0_1496,plain,
! [X4843,X4844,X4845,X4846] :
( ~ class_Rings_Ocomm__semiring__0(X4846)
| hAPP(c_Polynomial_Opoly(X4846,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4846),X4845,X4844)),X4843) = c_Groups_Oplus__class_Oplus(X4846,hAPP(c_Polynomial_Opoly(X4846,X4845),X4843),hAPP(c_Polynomial_Opoly(X4846,X4844),X4843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1497,plain,
! [X4157,X4158,X4159] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4158,X4159))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4157,X4159),X4158)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4159,X4158) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4157,X4159),X4158)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4157,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4158,X4159))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4159,X4158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1498,plain,
! [X4558,X4559,X4560] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4560,X4559)),X4558) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4560),X4558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4559),X4558)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1499,plain,
! [X4584,X4585,X4586] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4586,X4585)),X4584) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4586),X4584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4585),X4584)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1500,plain,
! [X4110,X4111,X4112] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4112,X4111)),X4110) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4112),X4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4111),X4110)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1501,plain,
! [X3414,X3415,X3416] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3416,X3415)),X3414) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3416),X3414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3415),X3414)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1502,plain,
! [X3422,X3423,X3424] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3424,X3423)),X3422) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3424),X3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3423),X3422)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(i_0_1503,plain,
! [X3051,X3052,X3053] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3053)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3053,hAPP(hAPP(c_Power_Opower__class_Opower(X3053),X3052),X3051)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3053,X3052)),X3051)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1504,plain,
! [X3940,X3941,X3942,X3943] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3943,c_Groups_Oplus__class_Oplus(X3943,X3942,X3941),c_Groups_Oplus__class_Oplus(X3943,X3940,X3941))
| c_Orderings_Oord__class_Oless__eq(X3943,X3942,X3940)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3943) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3943,X3942,X3940)
| c_Orderings_Oord__class_Oless__eq(X3943,c_Groups_Oplus__class_Oplus(X3943,X3942,X3941),c_Groups_Oplus__class_Oplus(X3943,X3940,X3941))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3943) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1505,plain,
! [X3919,X3920,X3921,X3922] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3922)
| ~ c_Orderings_Oord__class_Oless__eq(X3922,c_Groups_Oplus__class_Oplus(X3922,X3921,X3920),c_Groups_Oplus__class_Oplus(X3922,X3919,X3920))
| c_Orderings_Oord__class_Oless__eq(X3922,X3921,X3919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1506,plain,
! [X3936,X3937,X3938,X3939] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3939,c_Groups_Oplus__class_Oplus(X3939,X3938,X3937),c_Groups_Oplus__class_Oplus(X3939,X3938,X3936))
| c_Orderings_Oord__class_Oless__eq(X3939,X3937,X3936)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3939) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3939,X3937,X3936)
| c_Orderings_Oord__class_Oless__eq(X3939,c_Groups_Oplus__class_Oplus(X3939,X3938,X3937),c_Groups_Oplus__class_Oplus(X3939,X3938,X3936))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3939) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_1507,plain,
! [X3915,X3916,X3917,X3918] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3918)
| ~ c_Orderings_Oord__class_Oless__eq(X3918,c_Groups_Oplus__class_Oplus(X3918,X3917,X3916),c_Groups_Oplus__class_Oplus(X3918,X3917,X3915))
| c_Orderings_Oord__class_Oless__eq(X3918,X3916,X3915) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1508,plain,
! [X3969,X3970,X3971,X3972] :
( ( ~ c_Orderings_Oord__class_Oless(X3972,c_Groups_Oplus__class_Oplus(X3972,X3971,X3970),c_Groups_Oplus__class_Oplus(X3972,X3969,X3970))
| c_Orderings_Oord__class_Oless(X3972,X3971,X3969)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3972) )
& ( ~ c_Orderings_Oord__class_Oless(X3972,X3971,X3969)
| c_Orderings_Oord__class_Oless(X3972,c_Groups_Oplus__class_Oplus(X3972,X3971,X3970),c_Groups_Oplus__class_Oplus(X3972,X3969,X3970))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3972) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1509,plain,
! [X3948,X3949,X3950,X3951] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3951)
| ~ c_Orderings_Oord__class_Oless(X3951,c_Groups_Oplus__class_Oplus(X3951,X3950,X3949),c_Groups_Oplus__class_Oplus(X3951,X3948,X3949))
| c_Orderings_Oord__class_Oless(X3951,X3950,X3948) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1510,plain,
! [X3965,X3966,X3967,X3968] :
( ( ~ c_Orderings_Oord__class_Oless(X3968,c_Groups_Oplus__class_Oplus(X3968,X3967,X3966),c_Groups_Oplus__class_Oplus(X3968,X3967,X3965))
| c_Orderings_Oord__class_Oless(X3968,X3966,X3965)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3968) )
& ( ~ c_Orderings_Oord__class_Oless(X3968,X3966,X3965)
| c_Orderings_Oord__class_Oless(X3968,c_Groups_Oplus__class_Oplus(X3968,X3967,X3966),c_Groups_Oplus__class_Oplus(X3968,X3967,X3965))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3968) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1511,plain,
! [X3944,X3945,X3946,X3947] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3947)
| ~ c_Orderings_Oord__class_Oless(X3947,c_Groups_Oplus__class_Oplus(X3947,X3946,X3945),c_Groups_Oplus__class_Oplus(X3947,X3946,X3944))
| c_Orderings_Oord__class_Oless(X3947,X3945,X3944) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1512,plain,
! [X4101,X4102,X4103] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4103,X4102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4103,X4101)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4102,X4103),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4101,X4103)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4102,X4101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1513,plain,
! [X5421,X5422,X5423,X5424] :
( ( ~ c_Rings_Odvd__class_Odvd(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5421))
| X5423 = c_Groups_Ozero__class_Ozero(X5424)
| c_Rings_Odvd__class_Odvd(X5424,X5422,X5421)
| ~ class_Rings_Oidom(X5424) )
& ( X5423 != c_Groups_Ozero__class_Ozero(X5424)
| c_Rings_Odvd__class_Odvd(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5421))
| ~ class_Rings_Oidom(X5424) )
& ( ~ c_Rings_Odvd__class_Odvd(X5424,X5422,X5421)
| c_Rings_Odvd__class_Odvd(X5424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5424),X5423),X5421))
| ~ class_Rings_Oidom(X5424) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_1514,plain,
! [X5425,X5426,X5427,X5428] :
( ( ~ c_Rings_Odvd__class_Odvd(X5428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5427),X5426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5425),X5426))
| X5426 = c_Groups_Ozero__class_Ozero(X5428)
| c_Rings_Odvd__class_Odvd(X5428,X5427,X5425)
| ~ class_Rings_Oidom(X5428) )
& ( X5426 != c_Groups_Ozero__class_Ozero(X5428)
| c_Rings_Odvd__class_Odvd(X5428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5427),X5426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5425),X5426))
| ~ class_Rings_Oidom(X5428) )
& ( ~ c_Rings_Odvd__class_Odvd(X5428,X5427,X5425)
| c_Rings_Odvd__class_Odvd(X5428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5427),X5426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5428),X5425),X5426))
| ~ class_Rings_Oidom(X5428) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_1515,plain,
! [X2801,X2802,X2803] :
( ~ class_Rings_Olinordered__semidom(X2803)
| ~ c_Orderings_Oord__class_Oless(X2803,c_Groups_Oone__class_Oone(X2803),X2802)
| c_Orderings_Oord__class_Oless(X2803,c_Groups_Oone__class_Oone(X2803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2803),X2802),hAPP(hAPP(c_Power_Opower__class_Opower(X2803),X2802),X2801))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1516,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_1517,plain,
! [X4535,X4536,X4537] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4537),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4536,X4535)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4537),X4536)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4537),X4535)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1518,plain,
! [X4696,X4697,X4698,X4699] :
( ~ class_Rings_Ocomm__semiring__0(X4699)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4699),c_Polynomial_Osmult(X4699,X4698,X4697),c_Polynomial_OpCons(X4699,X4696,X4697)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4699))
| X4697 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4699)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(i_0_1519,plain,
! [X3332,X3333,X3334] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3334,X3333),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3334,X3332))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3333,X3332) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3333,X3332)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3334,X3333),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3334,X3332)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1520,plain,
! [X3471,X3472,X3473] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3473,X3472),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3473,X3471))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3472,X3471) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3472,X3471)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3473,X3472),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3473,X3471)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1521,plain,
! [X4654,X4655,X4656] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4656)
| X4656 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4656),X4654))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4655)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4654,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_1522,plain,
! [X4657,X4658,X4659] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4659)
| X4659 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4659),X4657))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4658,X4659)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1523,plain,
! [X4730,X4731,X4732,X4733] :
( ~ class_Rings_Ocomm__ring(X4733)
| c_Polynomial_Osmult(X4733,X4732,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4733),X4731,X4730)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4733),c_Polynomial_Osmult(X4733,X4732,X4731),c_Polynomial_Osmult(X4733,X4732,X4730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__right])]) ).
fof(i_0_1524,plain,
! [X4809,X4810,X4811,X4812] :
( ~ class_Rings_Ocomm__semiring__0(X4812)
| c_Polynomial_Osmult(X4812,X4811,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4812),X4810,X4809)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4812),c_Polynomial_Osmult(X4812,X4811,X4810),c_Polynomial_Osmult(X4812,X4811,X4809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__right])]) ).
fof(i_0_1525,plain,
! [X2857,X2858,X2859,X2860] :
( ~ class_Rings_Olinordered__semidom(X2860)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2860),X2859),X2858) != hAPP(hAPP(c_Power_Opower__class_Opower(X2860),X2857),X2858)
| ~ c_Orderings_Oord__class_Oless__eq(X2860,c_Groups_Ozero__class_Ozero(X2860),X2859)
| ~ c_Orderings_Oord__class_Oless__eq(X2860,c_Groups_Ozero__class_Ozero(X2860),X2857)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2858)
| X2859 = X2857 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1526,plain,
! [X4374,X4375,X4376] :
( ~ class_Rings_Ocomm__semiring__1(X4376)
| c_Groups_Oplus__class_Oplus(X4376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),X4375),X4374),X4374) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4376),c_Groups_Oplus__class_Oplus(X4376,X4375,c_Groups_Oone__class_Oone(X4376))),X4374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1527,plain,
! [X4371,X4372,X4373] :
( ~ class_Rings_Ocomm__semiring__1(X4373)
| c_Groups_Oplus__class_Oplus(X4373,X4372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4373),X4371),X4372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4373),c_Groups_Oplus__class_Oplus(X4373,X4371,c_Groups_Oone__class_Oone(X4373))),X4372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1528,plain,
! [X5251,X5252] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5252),X5251)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5251,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5252),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X5251) = X5252 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
fof(i_0_1529,plain,
! [X3032,X3033,X3034] :
( ~ class_Rings_Olinordered__idom(X3034)
| ~ c_Orderings_Oord__class_Oless__eq(X3034,c_Groups_Ozero__class_Ozero(X3034),X3033)
| ~ c_Orderings_Oord__class_Oless__eq(X3034,c_Groups_Ozero__class_Ozero(X3034),X3032)
| ~ c_Orderings_Oord__class_Oless__eq(X3034,X3032,c_Groups_Oone__class_Oone(X3034))
| c_Orderings_Oord__class_Oless__eq(X3034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3034),X3033),X3032),X3033) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1530,plain,
! [X3029,X3030,X3031] :
( ~ class_Rings_Olinordered__idom(X3031)
| ~ c_Orderings_Oord__class_Oless__eq(X3031,c_Groups_Ozero__class_Ozero(X3031),X3030)
| ~ c_Orderings_Oord__class_Oless__eq(X3031,c_Groups_Ozero__class_Ozero(X3031),X3029)
| ~ c_Orderings_Oord__class_Oless__eq(X3031,X3029,c_Groups_Oone__class_Oone(X3031))
| c_Orderings_Oord__class_Oless__eq(X3031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3031),X3029),X3030),X3030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1531,plain,
! [X3253,X3254,X3255,X3256] :
( ~ class_RealVector_Oreal__normed__vector(X3256)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3255,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3256,X3254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3255),c_RealVector_Onorm__class_Onorm(X3256,X3253)))
| X3254 = c_Groups_Ozero__class_Ozero(X3256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1532,plain,
! [X2918,X2919,X2920,X2921] :
( ~ class_Rings_Oordered__semiring(X2921)
| ~ c_Orderings_Oord__class_Oless__eq(X2921,X2920,X2919)
| ~ c_Orderings_Oord__class_Oless__eq(X2921,c_Groups_Ozero__class_Ozero(X2921),X2918)
| c_Orderings_Oord__class_Oless__eq(X2921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2921),X2920),X2918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2921),X2919),X2918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1533,plain,
! [X2910,X2911,X2912,X2913] :
( ~ class_Rings_Oordered__comm__semiring(X2913)
| ~ c_Orderings_Oord__class_Oless__eq(X2913,X2912,X2911)
| ~ c_Orderings_Oord__class_Oless__eq(X2913,c_Groups_Ozero__class_Ozero(X2913),X2910)
| c_Orderings_Oord__class_Oless__eq(X2913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2913),X2910),X2912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2913),X2910),X2911)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1534,plain,
! [X2914,X2915,X2916,X2917] :
( ~ class_Rings_Oordered__semiring(X2917)
| ~ c_Orderings_Oord__class_Oless__eq(X2917,X2916,X2915)
| ~ c_Orderings_Oord__class_Oless__eq(X2917,c_Groups_Ozero__class_Ozero(X2917),X2914)
| c_Orderings_Oord__class_Oless__eq(X2917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2917),X2914),X2916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2917),X2914),X2915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1535,plain,
! [X2947,X2948,X2949,X2950] :
( ~ class_Rings_Olinordered__semidom(X2950)
| ~ c_Orderings_Oord__class_Oless__eq(X2950,X2949,X2948)
| ~ c_Orderings_Oord__class_Oless__eq(X2950,c_Groups_Ozero__class_Ozero(X2950),X2949)
| c_Orderings_Oord__class_Oless__eq(X2950,hAPP(hAPP(c_Power_Opower__class_Opower(X2950),X2949),X2947),hAPP(hAPP(c_Power_Opower__class_Opower(X2950),X2948),X2947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1536,plain,
! [X3150,X3151,X3152,X3153] :
( ~ class_Rings_Olinordered__semiring__strict(X3153)
| ~ c_Orderings_Oord__class_Oless(X3153,X3152,X3151)
| ~ c_Orderings_Oord__class_Oless(X3153,c_Groups_Ozero__class_Ozero(X3153),X3150)
| c_Orderings_Oord__class_Oless(X3153,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3151),X3150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1537,plain,
! [X3142,X3143,X3144,X3145] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3145)
| ~ c_Orderings_Oord__class_Oless(X3145,X3144,X3143)
| ~ c_Orderings_Oord__class_Oless(X3145,c_Groups_Ozero__class_Ozero(X3145),X3142)
| c_Orderings_Oord__class_Oless(X3145,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3145),X3142),X3144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3145),X3142),X3143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1538,plain,
! [X3146,X3147,X3148,X3149] :
( ~ class_Rings_Olinordered__semiring__strict(X3149)
| ~ c_Orderings_Oord__class_Oless(X3149,X3148,X3147)
| ~ c_Orderings_Oord__class_Oless(X3149,c_Groups_Ozero__class_Ozero(X3149),X3146)
| c_Orderings_Oord__class_Oless(X3149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3149),X3146),X3148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3149),X3146),X3147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1539,plain,
! [X2906,X2907,X2908,X2909] :
( ~ class_Rings_Oordered__ring(X2909)
| ~ c_Orderings_Oord__class_Oless__eq(X2909,X2908,X2907)
| ~ c_Orderings_Oord__class_Oless__eq(X2909,X2906,c_Groups_Ozero__class_Ozero(X2909))
| c_Orderings_Oord__class_Oless__eq(X2909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2909),X2907),X2906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2909),X2908),X2906)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1540,plain,
! [X2902,X2903,X2904,X2905] :
( ~ class_Rings_Oordered__ring(X2905)
| ~ c_Orderings_Oord__class_Oless__eq(X2905,X2904,X2903)
| ~ c_Orderings_Oord__class_Oless__eq(X2905,X2902,c_Groups_Ozero__class_Ozero(X2905))
| c_Orderings_Oord__class_Oless__eq(X2905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2905),X2902),X2903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2905),X2902),X2904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1541,plain,
! [X3138,X3139,X3140,X3141] :
( ~ class_Rings_Olinordered__ring__strict(X3141)
| ~ c_Orderings_Oord__class_Oless(X3141,X3140,X3139)
| ~ c_Orderings_Oord__class_Oless(X3141,X3138,c_Groups_Ozero__class_Ozero(X3141))
| c_Orderings_Oord__class_Oless(X3141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3141),X3139),X3138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3141),X3140),X3138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1542,plain,
! [X3134,X3135,X3136,X3137] :
( ~ class_Rings_Olinordered__ring__strict(X3137)
| ~ c_Orderings_Oord__class_Oless(X3137,X3136,X3135)
| ~ c_Orderings_Oord__class_Oless(X3137,X3134,c_Groups_Ozero__class_Ozero(X3137))
| c_Orderings_Oord__class_Oless(X3137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3137),X3134),X3135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3137),X3134),X3136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1543,plain,
! [X4149,X4150,X4151] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4151,X4150)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4149,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4150,X4149),X4151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1544,plain,
! [X3923,X3924,X3925,X3926,X3927] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3927)
| ~ c_Orderings_Oord__class_Oless__eq(X3927,X3926,X3925)
| ~ c_Orderings_Oord__class_Oless__eq(X3927,X3924,X3923)
| c_Orderings_Oord__class_Oless__eq(X3927,c_Groups_Oplus__class_Oplus(X3927,X3926,X3924),c_Groups_Oplus__class_Oplus(X3927,X3925,X3923)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1545,plain,
! [X4024,X4025,X4026,X4027,X4028] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4028)
| ~ c_Orderings_Oord__class_Oless(X4028,X4027,X4026)
| ~ c_Orderings_Oord__class_Oless__eq(X4028,X4025,X4024)
| c_Orderings_Oord__class_Oless(X4028,c_Groups_Oplus__class_Oplus(X4028,X4027,X4025),c_Groups_Oplus__class_Oplus(X4028,X4026,X4024)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1546,plain,
! [X4019,X4020,X4021,X4022,X4023] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4023)
| ~ c_Orderings_Oord__class_Oless__eq(X4023,X4022,X4021)
| ~ c_Orderings_Oord__class_Oless(X4023,X4020,X4019)
| c_Orderings_Oord__class_Oless(X4023,c_Groups_Oplus__class_Oplus(X4023,X4022,X4020),c_Groups_Oplus__class_Oplus(X4023,X4021,X4019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1547,plain,
! [X3952,X3953,X3954,X3955,X3956] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3956)
| ~ c_Orderings_Oord__class_Oless(X3956,X3955,X3954)
| ~ c_Orderings_Oord__class_Oless(X3956,X3953,X3952)
| c_Orderings_Oord__class_Oless(X3956,c_Groups_Oplus__class_Oplus(X3956,X3955,X3953),c_Groups_Oplus__class_Oplus(X3956,X3954,X3952)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1548,plain,
! [X2861,X2862,X2863,X2864] :
( ~ class_Rings_Olinordered__semidom(X2864)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2863,X2862)
| ~ c_Orderings_Oord__class_Oless__eq(X2864,c_Groups_Oone__class_Oone(X2864),X2861)
| c_Orderings_Oord__class_Oless__eq(X2864,hAPP(hAPP(c_Power_Opower__class_Opower(X2864),X2861),X2863),hAPP(hAPP(c_Power_Opower__class_Opower(X2864),X2861),X2862)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1549,plain,
! [X3212,X3213,X3214,X3215] :
( ~ class_Rings_Olinordered__semidom(X3215)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3214,X3213)
| ~ c_Orderings_Oord__class_Oless(X3215,c_Groups_Oone__class_Oone(X3215),X3212)
| c_Orderings_Oord__class_Oless(X3215,hAPP(hAPP(c_Power_Opower__class_Opower(X3215),X3212),X3214),hAPP(hAPP(c_Power_Opower__class_Opower(X3215),X3212),X3213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1550,plain,
! [X4476,X4477,X4478] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4478,c_Groups_Ozero__class_Ozero(X4478),X4476)
| ~ c_Orderings_Oord__class_Oless__eq(X4478,c_Groups_Ozero__class_Ozero(X4478),X4477)
| c_Groups_Oabs__class_Oabs(X4478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),X4477),X4476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),c_Groups_Oabs__class_Oabs(X4478,X4477)),c_Groups_Oabs__class_Oabs(X4478,X4476))
| ~ class_Rings_Oordered__ring__abs(X4478) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4478,X4476,c_Groups_Ozero__class_Ozero(X4478))
| ~ c_Orderings_Oord__class_Oless__eq(X4478,c_Groups_Ozero__class_Ozero(X4478),X4477)
| c_Groups_Oabs__class_Oabs(X4478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),X4477),X4476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),c_Groups_Oabs__class_Oabs(X4478,X4477)),c_Groups_Oabs__class_Oabs(X4478,X4476))
| ~ class_Rings_Oordered__ring__abs(X4478) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4478,c_Groups_Ozero__class_Ozero(X4478),X4476)
| ~ c_Orderings_Oord__class_Oless__eq(X4478,X4477,c_Groups_Ozero__class_Ozero(X4478))
| c_Groups_Oabs__class_Oabs(X4478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),X4477),X4476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),c_Groups_Oabs__class_Oabs(X4478,X4477)),c_Groups_Oabs__class_Oabs(X4478,X4476))
| ~ class_Rings_Oordered__ring__abs(X4478) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4478,X4476,c_Groups_Ozero__class_Ozero(X4478))
| ~ c_Orderings_Oord__class_Oless__eq(X4478,X4477,c_Groups_Ozero__class_Ozero(X4478))
| c_Groups_Oabs__class_Oabs(X4478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),X4477),X4476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4478),c_Groups_Oabs__class_Oabs(X4478,X4477)),c_Groups_Oabs__class_Oabs(X4478,X4476))
| ~ class_Rings_Oordered__ring__abs(X4478) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
fof(i_0_1551,plain,
! [X4798,X4799,X4800,X4801] :
( ~ class_Groups_Oab__group__add(X4801)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4801),c_Polynomial_Omonom(X4801,X4800,X4799),c_Polynomial_Omonom(X4801,X4798,X4799)) = c_Polynomial_Omonom(X4801,c_Groups_Ominus__class_Ominus(X4801,X4800,X4798),X4799) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__monom])]) ).
fof(i_0_1552,plain,
! [X4864,X4865,X4866,X4867] :
( ~ class_Groups_Ocomm__monoid__add(X4867)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4867),c_Polynomial_Omonom(X4867,X4866,X4865),c_Polynomial_Omonom(X4867,X4864,X4865)) = c_Polynomial_Omonom(X4867,c_Groups_Oplus__class_Oplus(X4867,X4866,X4864),X4865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__monom])]) ).
fof(i_0_1553,plain,
! [X4787,X4788,X4789,X4790] :
( ~ class_Rings_Ocomm__ring(X4790)
| c_Polynomial_Osmult(X4790,c_Groups_Ominus__class_Ominus(X4790,X4789,X4788),X4787) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4790),c_Polynomial_Osmult(X4790,X4789,X4787),c_Polynomial_Osmult(X4790,X4788,X4787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__left])]) ).
fof(i_0_1554,plain,
! [X4856,X4857,X4858,X4859] :
( ~ class_Rings_Ocomm__semiring__0(X4859)
| c_Polynomial_Osmult(X4859,c_Groups_Oplus__class_Oplus(X4859,X4858,X4857),X4856) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4859),c_Polynomial_Osmult(X4859,X4858,X4856),c_Polynomial_Osmult(X4859,X4857,X4856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
fof(i_0_1555,plain,
! [X4305,X4306,X4307] :
( ( X4306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4307),X4305),X4306) = c_Groups_Oone__class_Oone(X4307)
| ~ class_Power_Opower(X4307) )
& ( X4306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4307),X4305),X4306) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4307),X4305),hAPP(hAPP(c_Power_Opower__class_Opower(X4307),X4305),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4306,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X4307) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1556,plain,
! [X4829,X4830,X4831,X4832] :
( ~ class_Rings_Ocomm__semiring__0(X4832)
| c_Polynomial_Osmult(X4832,X4831,c_Polynomial_OpCons(X4832,X4830,X4829)) = c_Polynomial_OpCons(X4832,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4832),X4831),X4830),c_Polynomial_Osmult(X4832,X4831,X4829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
fof(i_0_1557,plain,
! [X3344,X3345,X3346,X3347] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3347,X3346)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3345,X3344)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3347,X3345),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3346,X3344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1558,plain,
! [X4568,X4569,X4570,X4571] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4571,X4570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4569,X4568)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4571,X4569),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4570,X4568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1559,plain,
! [X4133,X4134,X4135] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4135,X4134)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4133,X4135)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4135,X4133),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4134,X4133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1560,plain,
! [X4069,X4070,X4071] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4071,X4070)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4071,X4069)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4069,X4070),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4069,X4071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1561,plain,
! [X3483,X3484,X3485,X3486] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3486,X3485)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3484,X3483)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3486,X3484),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3485,X3483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1562,plain,
! [X3197,X3198,X3199] :
( ( X3198 = c_Groups_Ozero__class_Ozero(X3199)
| c_Groups_Oplus__class_Oplus(X3199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3198),X3198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3197),X3197)) != c_Groups_Ozero__class_Ozero(X3199)
| ~ class_Rings_Olinordered__ring__strict(X3199) )
& ( X3197 = c_Groups_Ozero__class_Ozero(X3199)
| c_Groups_Oplus__class_Oplus(X3199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3198),X3198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3197),X3197)) != c_Groups_Ozero__class_Ozero(X3199)
| ~ class_Rings_Olinordered__ring__strict(X3199) )
& ( X3198 != c_Groups_Ozero__class_Ozero(X3199)
| X3197 != c_Groups_Ozero__class_Ozero(X3199)
| c_Groups_Oplus__class_Oplus(X3199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3198),X3198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3199),X3197),X3197)) = c_Groups_Ozero__class_Ozero(X3199)
| ~ class_Rings_Olinordered__ring__strict(X3199) ) ),
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,
! [X4501,X4502,X4503] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4503,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,X4502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4503),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4501)))
| X4502 = 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,
! [X3709,X3710,X3711,X3712] :
( ~ class_RealVector_Oreal__normed__algebra(X3712)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3712),X3711),c_Groups_Ominus__class_Ominus(X3712,X3710,X3709)) = c_Groups_Ominus__class_Ominus(X3712,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3712),X3711),X3710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3712),X3711),X3709)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1565,plain,
! [X3705,X3706,X3707,X3708] :
( ~ class_RealVector_Oreal__normed__algebra(X3708)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3708),X3707),c_Groups_Ominus__class_Ominus(X3708,X3706,X3705)) = c_Groups_Ominus__class_Ominus(X3708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3708),X3707),X3706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3708),X3707),X3705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1566,plain,
! [X4322,X4323,X4324,X4325] :
( ~ class_Rings_Ocomm__semiring__1(X4325)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),c_Groups_Oplus__class_Oplus(X4325,X4323,X4322)) = c_Groups_Oplus__class_Oplus(X4325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),X4323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4325),X4324),X4322)) ),
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,
! [X3113,X3114,X3115,X3116] :
( ~ class_RealVector_Oreal__normed__algebra(X3116)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3116),X3115),c_Groups_Oplus__class_Oplus(X3116,X3114,X3113)) = c_Groups_Oplus__class_Oplus(X3116,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3116),X3115),X3114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3116),X3115),X3113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1568,plain,
! [X3109,X3110,X3111,X3112] :
( ~ class_RealVector_Oreal__normed__algebra(X3112)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3112),X3111),c_Groups_Oplus__class_Oplus(X3112,X3110,X3109)) = c_Groups_Oplus__class_Oplus(X3112,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3112),X3111),X3110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3112),X3111),X3109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1569,plain,
! [X3444,X3445,X3446] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3446)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3444)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3445,X3444)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3444)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3446)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3445,X3444)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3444)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1570,plain,
! [X3441,X3442,X3443] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3442)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3443),X3442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3441),X3442)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3443,X3441)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3443),X3442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3441),X3442)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3442)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3443,X3441)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3443),X3442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3441),X3442)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1571,plain,
! [X3164,X3165,X3166] :
( ~ class_Rings_Olinordered__semiring__strict(X3166)
| ~ c_Orderings_Oord__class_Oless(X3166,c_Groups_Ozero__class_Ozero(X3166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3166),X3165),X3164))
| ~ c_Orderings_Oord__class_Oless(X3166,c_Groups_Ozero__class_Ozero(X3166),X3164)
| c_Orderings_Oord__class_Oless(X3166,c_Groups_Ozero__class_Ozero(X3166),X3165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1572,plain,
! [X3167,X3168,X3169] :
( ~ class_Rings_Olinordered__semiring__strict(X3169)
| ~ c_Orderings_Oord__class_Oless(X3169,c_Groups_Ozero__class_Ozero(X3169),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3169),X3168),X3167))
| ~ c_Orderings_Oord__class_Oless(X3169,c_Groups_Ozero__class_Ozero(X3169),X3168)
| c_Orderings_Oord__class_Oless(X3169,c_Groups_Ozero__class_Ozero(X3169),X3167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1573,plain,
! [X4244,X4245,X4246,X4247] :
( ~ class_Rings_Ocomm__semiring__1(X4247)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),X4246),X4245)),X4244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),X4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4247),X4245),X4244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1574,plain,
! [X3870,X3871,X3872,X3873] :
( ~ class_Groups_Oab__semigroup__mult(X3873)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3873),X3872),X3871)),X3870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3873),X3872),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3873),X3871),X3870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1575,plain,
! [X3127,X3128,X3129] :
( ~ class_Groups_Omonoid__mult(X3129)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3129),hAPP(hAPP(c_Power_Opower__class_Opower(X3129),X3128),X3127)),X3128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3129),X3128),hAPP(hAPP(c_Power_Opower__class_Opower(X3129),X3128),X3127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1576,plain,
! [X4240,X4241,X4242,X4243] :
( ~ class_Rings_Ocomm__semiring__1(X4243)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4243),X4242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4243),X4241),X4240)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4243),X4242),X4241)),X4240) ),
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,
! [X5229,X5230] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5230,X5229)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5230),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5229)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5230),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5229))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5230,X5229) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1578,plain,
! [X5231,X5232] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5232,X5231)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5232),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5231),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5232),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5231),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5232,X5231) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
fof(i_0_1579,plain,
! [X4872,X4873,X4874,X4875] :
( ~ class_Rings_Ocomm__semiring__1(X4875)
| hAPP(c_Polynomial_Opoly(X4875,c_Polynomial_Omonom(X4875,X4874,X4873)),X4872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4875),X4874),hAPP(hAPP(c_Power_Opower__class_Opower(X4875),X4872),X4873)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(i_0_1580,plain,
! [X4906,X4907,X4908,X4909,X4910] :
( ( X4906 = hAPP(c_Polynomial_Opoly(X4910,X4909),X4908)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4910),X4909,c_Polynomial_Osmult(X4910,X4908,X4907)) != c_Polynomial_OpCons(X4910,X4906,X4907)
| ~ class_Rings_Ocomm__semiring__0(X4910) )
& ( X4907 = c_Polynomial_Osynthetic__div(X4910,X4909,X4908)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4910),X4909,c_Polynomial_Osmult(X4910,X4908,X4907)) != c_Polynomial_OpCons(X4910,X4906,X4907)
| ~ class_Rings_Ocomm__semiring__0(X4910) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
fof(i_0_1581,plain,
! [X5260] :
( ( 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(X5260),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5260)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5260) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5260,c_RealDef_Oreal(tc_Nat_Onat,esk32_1(X5260)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5260) ) ),
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,
! [X4899,X4900,X4901,X4902] :
( ~ class_Rings_Ocomm__semiring__0(X4902)
| c_Polynomial_Osynthetic__div(X4902,c_Polynomial_OpCons(X4902,X4901,X4900),X4899) = c_Polynomial_OpCons(X4902,hAPP(c_Polynomial_Opoly(X4902,X4900),X4899),c_Polynomial_Osynthetic__div(X4902,X4900,X4899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons])]) ).
fof(i_0_1583,plain,
! [X2851,X2852,X2853,X2854] :
( ~ class_Groups_Omonoid__mult(X2854)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2854),X2853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2852),X2851)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2854),hAPP(hAPP(c_Power_Opower__class_Opower(X2854),X2853),X2852)),X2851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1584,plain,
! [X4357,X4358,X4359,X4360] :
( ~ class_Rings_Ocomm__semiring__1(X4360)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4360),hAPP(hAPP(c_Power_Opower__class_Opower(X4360),X4359),X4358)),X4357) = hAPP(hAPP(c_Power_Opower__class_Opower(X4360),X4359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4358),X4357)) ),
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,
! [X4572,X4573,X4574] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4574,X4573)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4572)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4572),X4574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4572),X4573)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1586,plain,
! [X3436,X3437,X3438] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3438,X3437)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3436)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3438),X3436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3437),X3436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1587,plain,
! [X3433,X3434,X3435] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3435,X3434)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3433)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3433),X3435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3433),X3434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1588,plain,
! [X3540,X3541,X3542] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3541,X3540)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3542),X3541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3542),X3540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1589,plain,
! [X4303,X4304] :
( ( X4304 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4303),X4304) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4303),X4304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4303),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4303),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4304,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,
! [X4146,X4147,X4148] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4148,X4147),X4146)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4148,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4146,X4147)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4148,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4146,X4147))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4148,X4147),X4146) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1591,plain,
! [X4130,X4131,X4132] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4132,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4131,X4130))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4132,X4130),X4131) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4132,X4130),X4131)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4132,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4131,X4130)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1592,plain,
! [X3300,X3301,X3302,X3303] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3303,X3302)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3301,X3300)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3303),X3301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3302),X3300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1593,plain,
! [X4171,X4172,X4173] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4173,X4172)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4172,X4171),X4173) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4172,X4173),X4171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1594,plain,
! [X4168,X4169,X4170] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4170,X4169)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4169,X4170),X4168) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4169,X4168),X4170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1595,plain,
! [X4165,X4166,X4167] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4167,X4166)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4165,X4166),X4167) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4165,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4166,X4167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1596,plain,
! [X4143,X4144,X4145] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4145,X4144)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4143,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4144,X4145)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4143,X4145),X4144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1597,plain,
! [X4154,X4155,X4156] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4156,X4155)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4154,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4155,X4156)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4154,X4155),X4156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1598,plain,
! [X4741,X4742,X4743,X4744] :
( ~ class_Rings_Ocomm__semiring__0(X4744)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4744)),X4743),c_Polynomial_Osmult(X4744,X4742,X4741)) = c_Polynomial_Osmult(X4744,X4742,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4744)),X4743),X4741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(i_0_1599,plain,
! [X4825,X4826,X4827,X4828] :
( ~ class_Rings_Ocomm__semiring__0(X4828)
| hAPP(c_Polynomial_Opoly(X4828,c_Polynomial_Osmult(X4828,X4827,X4826)),X4825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4828),X4827),hAPP(c_Polynomial_Opoly(X4828,X4826),X4825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
fof(i_0_1600,plain,
! [X2937,X2938,X2939] :
( ( c_Orderings_Oord__class_Oless__eq(X2939,X2938,c_Groups_Ozero__class_Ozero(X2939))
| c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2938)
| ~ c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) )
& ( c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2937)
| c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2938)
| ~ c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) )
& ( c_Orderings_Oord__class_Oless__eq(X2939,X2938,c_Groups_Ozero__class_Ozero(X2939))
| c_Orderings_Oord__class_Oless__eq(X2939,X2937,c_Groups_Ozero__class_Ozero(X2939))
| ~ c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) )
& ( c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2937)
| c_Orderings_Oord__class_Oless__eq(X2939,X2937,c_Groups_Ozero__class_Ozero(X2939))
| ~ c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2938)
| ~ c_Orderings_Oord__class_Oless__eq(X2939,X2937,c_Groups_Ozero__class_Ozero(X2939))
| c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2939,X2938,c_Groups_Ozero__class_Ozero(X2939))
| ~ c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2937)
| c_Orderings_Oord__class_Oless__eq(X2939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2939),X2938),X2937),c_Groups_Ozero__class_Ozero(X2939))
| ~ class_Rings_Olinordered__ring__strict(X2939) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1601,plain,
! [X2940,X2941,X2942] :
( ( c_Orderings_Oord__class_Oless__eq(X2942,X2941,c_Groups_Ozero__class_Ozero(X2942))
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2941)
| ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( c_Orderings_Oord__class_Oless__eq(X2942,X2940,c_Groups_Ozero__class_Ozero(X2942))
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2941)
| ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( c_Orderings_Oord__class_Oless__eq(X2942,X2941,c_Groups_Ozero__class_Ozero(X2942))
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2940)
| ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( c_Orderings_Oord__class_Oless__eq(X2942,X2940,c_Groups_Ozero__class_Ozero(X2942))
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2940)
| ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2941)
| ~ c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),X2940)
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2942,X2941,c_Groups_Ozero__class_Ozero(X2942))
| ~ c_Orderings_Oord__class_Oless__eq(X2942,X2940,c_Groups_Ozero__class_Ozero(X2942))
| c_Orderings_Oord__class_Oless__eq(X2942,c_Groups_Ozero__class_Ozero(X2942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940))
| ~ class_Rings_Olinordered__ring__strict(X2942) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1602,plain,
! [X4523,X4524] :
( ( ~ 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,X4524)),X4523))
| X4524 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4523 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4524 = 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,X4524)),X4523)) )
& ( X4523 != 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,X4524)),X4523)) ) ),
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,
! [X4555,X4556,X4557] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4557),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4556,X4555)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4557),X4556),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4557),X4555)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1604,plain,
! [X4592,X4593,X4594] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4594),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4593,X4592)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4594),X4593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4594),X4592)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1605,plain,
! [X4107,X4108,X4109] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4109),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4108,X4107)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4109),X4108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4109),X4107)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1606,plain,
! [X3411,X3412,X3413] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3413),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3412,X3411)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3413),X3412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3413),X3411)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1607,plain,
! [X4895,X4896,X4897,X4898] :
( ~ class_Rings_Ocomm__semiring__0(X4898)
| hAPP(c_Polynomial_Opoly(X4898,c_Polynomial_Opcompose(X4898,X4897,X4896)),X4895) = hAPP(c_Polynomial_Opoly(X4898,X4897),hAPP(c_Polynomial_Opoly(X4898,X4896),X4895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pcompose])]) ).
fof(i_0_1608,plain,
! [X4369,X4370] :
( ~ class_Rings_Ocomm__semiring__1(X4370)
| c_Groups_Oplus__class_Oplus(X4370,X4369,X4369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4370),c_Groups_Oplus__class_Oplus(X4370,c_Groups_Oone__class_Oone(X4370),c_Groups_Oone__class_Oone(X4370))),X4369) ),
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,
! [X3250,X3251,X3252] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3252)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3251,c_RealVector_Onorm__class_Onorm(X3252,X3250))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3251)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3252,c_Rings_Oinverse__class_Oinverse(X3252,X3250)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__inverse__lemma])]) ).
fof(i_0_1610,plain,
! [X3500,X3501] :
( ( X3501 = 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),X3501),X3501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3500),X3500)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3500 = 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),X3501),X3501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3500),X3500)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3501 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3500 != 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),X3501),X3501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3500),X3500)) = 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,
! [X4652] : 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____),X4652))),
inference(variable_rename,[status(thm)],[fact_cq0]) ).
fof(i_0_1612,plain,
! [X3988,X3989,X3990] :
( ~ class_Groups_Oordered__comm__monoid__add(X3990)
| ~ c_Orderings_Oord__class_Oless__eq(X3990,X3989,c_Groups_Ozero__class_Ozero(X3990))
| ~ c_Orderings_Oord__class_Oless__eq(X3990,X3988,c_Groups_Ozero__class_Ozero(X3990))
| c_Orderings_Oord__class_Oless__eq(X3990,c_Groups_Oplus__class_Oplus(X3990,X3989,X3988),c_Groups_Ozero__class_Ozero(X3990)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1613,plain,
! [X4038,X4039,X4040] :
( ~ class_Groups_Oordered__comm__monoid__add(X4040)
| ~ c_Orderings_Oord__class_Oless(X4040,X4039,c_Groups_Ozero__class_Ozero(X4040))
| ~ c_Orderings_Oord__class_Oless__eq(X4040,X4038,c_Groups_Ozero__class_Ozero(X4040))
| c_Orderings_Oord__class_Oless(X4040,c_Groups_Oplus__class_Oplus(X4040,X4039,X4038),c_Groups_Ozero__class_Ozero(X4040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1614,plain,
! [X4035,X4036,X4037] :
( ~ class_Groups_Oordered__comm__monoid__add(X4037)
| ~ c_Orderings_Oord__class_Oless__eq(X4037,X4036,c_Groups_Ozero__class_Ozero(X4037))
| ~ c_Orderings_Oord__class_Oless(X4037,X4035,c_Groups_Ozero__class_Ozero(X4037))
| c_Orderings_Oord__class_Oless(X4037,c_Groups_Oplus__class_Oplus(X4037,X4036,X4035),c_Groups_Ozero__class_Ozero(X4037)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1615,plain,
! [X4009,X4010,X4011] :
( ~ class_Groups_Oordered__comm__monoid__add(X4011)
| ~ c_Orderings_Oord__class_Oless(X4011,X4010,c_Groups_Ozero__class_Ozero(X4011))
| ~ c_Orderings_Oord__class_Oless(X4011,X4009,c_Groups_Ozero__class_Ozero(X4011))
| c_Orderings_Oord__class_Oless(X4011,c_Groups_Oplus__class_Oplus(X4011,X4010,X4009),c_Groups_Ozero__class_Ozero(X4011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1616,plain,
! [X4002,X4003,X4004] :
( ~ class_Groups_Oordered__comm__monoid__add(X4004)
| ~ c_Orderings_Oord__class_Oless__eq(X4004,c_Groups_Ozero__class_Ozero(X4004),X4003)
| ~ c_Orderings_Oord__class_Oless__eq(X4004,c_Groups_Ozero__class_Ozero(X4004),X4002)
| c_Orderings_Oord__class_Oless__eq(X4004,c_Groups_Ozero__class_Ozero(X4004),c_Groups_Oplus__class_Oplus(X4004,X4003,X4002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1617,plain,
! [X3573,X3574,X3575] :
( ~ class_Groups_Oordered__comm__monoid__add(X3575)
| ~ c_Orderings_Oord__class_Oless(X3575,c_Groups_Ozero__class_Ozero(X3575),X3574)
| ~ c_Orderings_Oord__class_Oless__eq(X3575,c_Groups_Ozero__class_Ozero(X3575),X3573)
| c_Orderings_Oord__class_Oless(X3575,c_Groups_Ozero__class_Ozero(X3575),c_Groups_Oplus__class_Oplus(X3575,X3574,X3573)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1618,plain,
! [X3576,X3577,X3578] :
( ~ class_Groups_Oordered__comm__monoid__add(X3578)
| ~ c_Orderings_Oord__class_Oless__eq(X3578,c_Groups_Ozero__class_Ozero(X3578),X3577)
| ~ c_Orderings_Oord__class_Oless(X3578,c_Groups_Ozero__class_Ozero(X3578),X3576)
| c_Orderings_Oord__class_Oless(X3578,c_Groups_Ozero__class_Ozero(X3578),c_Groups_Oplus__class_Oplus(X3578,X3577,X3576)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1619,plain,
! [X4012,X4013,X4014] :
( ~ class_Groups_Oordered__comm__monoid__add(X4014)
| ~ c_Orderings_Oord__class_Oless(X4014,c_Groups_Ozero__class_Ozero(X4014),X4013)
| ~ c_Orderings_Oord__class_Oless(X4014,c_Groups_Ozero__class_Ozero(X4014),X4012)
| c_Orderings_Oord__class_Oless(X4014,c_Groups_Ozero__class_Ozero(X4014),c_Groups_Oplus__class_Oplus(X4014,X4013,X4012)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1620,plain,
! [X3533,X3534] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3534,X3533))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3534)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3533) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3534)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3534,X3533)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3533)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3534,X3533)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1621,plain,
! [X4587,X4588,X4589] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4589),X4588)),X4587) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4588),X4587)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1622,plain,
! [X3284,X3285,X3286] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3286),X3285)),X3284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3285),X3284)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1623,plain,
! [X3419,X3420,X3421] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3421),X3420)),X3419) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3420),X3419)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1624,plain,
! [X4538,X4539,X4540] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4540),X4539)),X4538) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4539),X4538)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1625,plain,
! [X2925,X2926,X2927] :
( ~ class_Rings_Oordered__cancel__semiring(X2927)
| ~ c_Orderings_Oord__class_Oless__eq(X2927,X2926,c_Groups_Ozero__class_Ozero(X2927))
| ~ c_Orderings_Oord__class_Oless__eq(X2927,c_Groups_Ozero__class_Ozero(X2927),X2925)
| c_Orderings_Oord__class_Oless__eq(X2927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2927),X2926),X2925),c_Groups_Ozero__class_Ozero(X2927)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1626,plain,
! [X2886,X2887,X2888] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2888,c_Groups_Ozero__class_Ozero(X2888),X2887)
| ~ c_Orderings_Oord__class_Oless__eq(X2888,X2886,c_Groups_Ozero__class_Ozero(X2888))
| c_Orderings_Oord__class_Oless__eq(X2888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2888),X2887),X2886),c_Groups_Ozero__class_Ozero(X2888))
| ~ class_Rings_Oordered__cancel__semiring(X2888) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2888,X2887,c_Groups_Ozero__class_Ozero(X2888))
| ~ c_Orderings_Oord__class_Oless__eq(X2888,c_Groups_Ozero__class_Ozero(X2888),X2886)
| c_Orderings_Oord__class_Oless__eq(X2888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2888),X2887),X2886),c_Groups_Ozero__class_Ozero(X2888))
| ~ class_Rings_Oordered__cancel__semiring(X2888) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1627,plain,
! [X2931,X2932,X2933] :
( ~ class_Rings_Oordered__cancel__semiring(X2933)
| ~ c_Orderings_Oord__class_Oless__eq(X2933,c_Groups_Ozero__class_Ozero(X2933),X2932)
| ~ c_Orderings_Oord__class_Oless__eq(X2933,X2931,c_Groups_Ozero__class_Ozero(X2933))
| c_Orderings_Oord__class_Oless__eq(X2933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2933),X2932),X2931),c_Groups_Ozero__class_Ozero(X2933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1628,plain,
! [X2928,X2929,X2930] :
( ~ class_Rings_Oordered__cancel__semiring(X2930)
| ~ c_Orderings_Oord__class_Oless__eq(X2930,c_Groups_Ozero__class_Ozero(X2930),X2929)
| ~ c_Orderings_Oord__class_Oless__eq(X2930,X2928,c_Groups_Ozero__class_Ozero(X2930))
| c_Orderings_Oord__class_Oless__eq(X2930,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2930),X2928),X2929),c_Groups_Ozero__class_Ozero(X2930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1629,plain,
! [X3157,X3158,X3159] :
( ~ class_Rings_Olinordered__semiring__strict(X3159)
| ~ c_Orderings_Oord__class_Oless(X3159,X3158,c_Groups_Ozero__class_Ozero(X3159))
| ~ c_Orderings_Oord__class_Oless(X3159,c_Groups_Ozero__class_Ozero(X3159),X3157)
| c_Orderings_Oord__class_Oless(X3159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3159),X3158),X3157),c_Groups_Ozero__class_Ozero(X3159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1630,plain,
! [X3173,X3174,X3175] :
( ~ class_Rings_Olinordered__semiring__strict(X3175)
| ~ c_Orderings_Oord__class_Oless(X3175,c_Groups_Ozero__class_Ozero(X3175),X3174)
| ~ c_Orderings_Oord__class_Oless(X3175,X3173,c_Groups_Ozero__class_Ozero(X3175))
| c_Orderings_Oord__class_Oless(X3175,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3175),X3174),X3173),c_Groups_Ozero__class_Ozero(X3175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1631,plain,
! [X3170,X3171,X3172] :
( ~ class_Rings_Olinordered__semiring__strict(X3172)
| ~ c_Orderings_Oord__class_Oless(X3172,c_Groups_Ozero__class_Ozero(X3172),X3171)
| ~ c_Orderings_Oord__class_Oless(X3172,X3170,c_Groups_Ozero__class_Ozero(X3172))
| c_Orderings_Oord__class_Oless(X3172,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3172),X3170),X3171),c_Groups_Ozero__class_Ozero(X3172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1632,plain,
! [X2889,X2890,X2891] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2891,c_Groups_Ozero__class_Ozero(X2891),X2890)
| ~ c_Orderings_Oord__class_Oless__eq(X2891,c_Groups_Ozero__class_Ozero(X2891),X2889)
| c_Orderings_Oord__class_Oless__eq(X2891,c_Groups_Ozero__class_Ozero(X2891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2891),X2890),X2889))
| ~ class_Rings_Oordered__ring(X2891) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2891,X2890,c_Groups_Ozero__class_Ozero(X2891))
| ~ c_Orderings_Oord__class_Oless__eq(X2891,X2889,c_Groups_Ozero__class_Ozero(X2891))
| c_Orderings_Oord__class_Oless__eq(X2891,c_Groups_Ozero__class_Ozero(X2891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2891),X2890),X2889))
| ~ class_Rings_Oordered__ring(X2891) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1633,plain,
! [X2934,X2935,X2936] :
( ~ class_Rings_Oordered__cancel__semiring(X2936)
| ~ c_Orderings_Oord__class_Oless__eq(X2936,c_Groups_Ozero__class_Ozero(X2936),X2935)
| ~ c_Orderings_Oord__class_Oless__eq(X2936,c_Groups_Ozero__class_Ozero(X2936),X2934)
| c_Orderings_Oord__class_Oless__eq(X2936,c_Groups_Ozero__class_Ozero(X2936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2936),X2935),X2934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1634,plain,
! [X3202,X3203,X3204] :
( ~ class_Rings_Olinordered__semidom(X3204)
| ~ c_Orderings_Oord__class_Oless(X3204,c_Groups_Oone__class_Oone(X3204),X3203)
| ~ c_Orderings_Oord__class_Oless(X3204,c_Groups_Oone__class_Oone(X3204),X3202)
| c_Orderings_Oord__class_Oless(X3204,c_Groups_Oone__class_Oone(X3204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3204),X3203),X3202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1635,plain,
! [X3176,X3177,X3178] :
( ~ class_Rings_Olinordered__semiring__strict(X3178)
| ~ c_Orderings_Oord__class_Oless(X3178,c_Groups_Ozero__class_Ozero(X3178),X3177)
| ~ c_Orderings_Oord__class_Oless(X3178,c_Groups_Ozero__class_Ozero(X3178),X3176)
| c_Orderings_Oord__class_Oless(X3178,c_Groups_Ozero__class_Ozero(X3178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3178),X3177),X3176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1636,plain,
! [X2922,X2923,X2924] :
( ~ class_Rings_Oordered__ring(X2924)
| ~ c_Orderings_Oord__class_Oless__eq(X2924,X2923,c_Groups_Ozero__class_Ozero(X2924))
| ~ c_Orderings_Oord__class_Oless__eq(X2924,X2922,c_Groups_Ozero__class_Ozero(X2924))
| c_Orderings_Oord__class_Oless__eq(X2924,c_Groups_Ozero__class_Ozero(X2924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2924),X2923),X2922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1637,plain,
! [X3154,X3155,X3156] :
( ~ class_Rings_Olinordered__ring__strict(X3156)
| ~ c_Orderings_Oord__class_Oless(X3156,X3155,c_Groups_Ozero__class_Ozero(X3156))
| ~ c_Orderings_Oord__class_Oless(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless(X3156,c_Groups_Ozero__class_Ozero(X3156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1638,plain,
! [X3932,X3933,X3934,X3935] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3935)
| ~ c_Orderings_Oord__class_Oless__eq(X3935,X3934,X3933)
| c_Orderings_Oord__class_Oless__eq(X3935,c_Groups_Oplus__class_Oplus(X3935,X3934,X3932),c_Groups_Oplus__class_Oplus(X3935,X3933,X3932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1639,plain,
! [X3928,X3929,X3930,X3931] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3931)
| ~ c_Orderings_Oord__class_Oless__eq(X3931,X3930,X3929)
| c_Orderings_Oord__class_Oless__eq(X3931,c_Groups_Oplus__class_Oplus(X3931,X3928,X3930),c_Groups_Oplus__class_Oplus(X3931,X3928,X3929)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1640,plain,
! [X3961,X3962,X3963,X3964] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3964)
| ~ c_Orderings_Oord__class_Oless(X3964,X3963,X3962)
| c_Orderings_Oord__class_Oless(X3964,c_Groups_Oplus__class_Oplus(X3964,X3963,X3961),c_Groups_Oplus__class_Oplus(X3964,X3962,X3961)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1641,plain,
! [X3957,X3958,X3959,X3960] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3960)
| ~ c_Orderings_Oord__class_Oless(X3960,X3959,X3958)
| c_Orderings_Oord__class_Oless(X3960,c_Groups_Oplus__class_Oplus(X3960,X3957,X3959),c_Groups_Oplus__class_Oplus(X3960,X3957,X3958)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1642,plain,
! [X4548] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk14_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4548),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____),X4548)),esk14_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,
! [X4516] :
( 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,X4516),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____),X4516)),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,
! [X4386] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4386),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____),X4386)),v_m____) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_m_I2_J])]) ).
fof(i_0_1645,plain,
! [X4549] : 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____),X4549))),
inference(variable_rename,[status(thm)],[fact_c]) ).
fof(i_0_1646,plain,
! [X3048,X3049,X3050] :
( ~ class_Rings_Olinordered__semidom(X3050)
| ~ c_Orderings_Oord__class_Oless(X3050,c_Groups_Oone__class_Oone(X3050),X3049)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3048)
| c_Orderings_Oord__class_Oless(X3050,c_Groups_Oone__class_Oone(X3050),hAPP(hAPP(c_Power_Opower__class_Opower(X3050),X3049),X3048)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1647,plain,
! [X5398,X5399,X5400,X5401] :
( ~ class_Rings_Ocomm__semiring__1(X5401)
| ~ c_Rings_Odvd__class_Odvd(X5401,X5400,X5399)
| c_Rings_Odvd__class_Odvd(X5401,hAPP(hAPP(c_Power_Opower__class_Opower(X5401),X5400),X5398),hAPP(hAPP(c_Power_Opower__class_Opower(X5401),X5399),X5398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_1648,plain,
! [X5270,X5271,X5272,X5273] :
( ( ~ c_SEQ_Odecseq(X5271,X5270)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5272,X5273)
| c_Orderings_Oord__class_Oless__eq(X5271,hAPP(X5270,X5273),hAPP(X5270,X5272))
| ~ class_Orderings_Oorder(X5271) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk34_2(X5270,X5271),esk35_2(X5270,X5271))
| c_SEQ_Odecseq(X5271,X5270)
| ~ class_Orderings_Oorder(X5271) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5271,hAPP(X5270,esk35_2(X5270,X5271)),hAPP(X5270,esk34_2(X5270,X5271)))
| c_SEQ_Odecseq(X5271,X5270)
| ~ class_Orderings_Oorder(X5271) ) ),
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_1649,plain,
! [X5249,X5250] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5250),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5249)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5250,c_RealDef_Oreal(tc_Nat_Onat,X5249)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
fof(i_0_1650,plain,
! [X3995,X3996,X3997,X3998] :
( ~ class_Groups_Oordered__comm__monoid__add(X3998)
| ~ c_Orderings_Oord__class_Oless__eq(X3998,c_Groups_Ozero__class_Ozero(X3998),X3997)
| ~ c_Orderings_Oord__class_Oless__eq(X3998,X3996,X3995)
| c_Orderings_Oord__class_Oless__eq(X3998,X3996,c_Groups_Oplus__class_Oplus(X3998,X3997,X3995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1651,plain,
! [X3991,X3992,X3993,X3994] :
( ~ class_Groups_Oordered__comm__monoid__add(X3994)
| ~ c_Orderings_Oord__class_Oless__eq(X3994,c_Groups_Ozero__class_Ozero(X3994),X3993)
| ~ c_Orderings_Oord__class_Oless__eq(X3994,X3992,X3991)
| c_Orderings_Oord__class_Oless__eq(X3994,X3992,c_Groups_Oplus__class_Oplus(X3994,X3991,X3993)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1652,plain,
! [X3579,X3580,X3581,X3582] :
( ~ class_Groups_Oordered__comm__monoid__add(X3582)
| ~ c_Orderings_Oord__class_Oless(X3582,c_Groups_Ozero__class_Ozero(X3582),X3581)
| ~ c_Orderings_Oord__class_Oless__eq(X3582,X3580,X3579)
| c_Orderings_Oord__class_Oless(X3582,X3580,c_Groups_Oplus__class_Oplus(X3582,X3581,X3579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1653,plain,
! [X4041,X4042,X4043,X4044] :
( ~ class_Groups_Oordered__comm__monoid__add(X4044)
| ~ c_Orderings_Oord__class_Oless__eq(X4044,c_Groups_Ozero__class_Ozero(X4044),X4043)
| ~ c_Orderings_Oord__class_Oless(X4044,X4042,X4041)
| c_Orderings_Oord__class_Oless(X4044,X4042,c_Groups_Oplus__class_Oplus(X4044,X4043,X4041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1654,plain,
! [X3193,X3194,X3195,X3196] :
( ~ class_Rings_Olinordered__semidom(X3196)
| ~ c_Orderings_Oord__class_Oless(X3196,c_Groups_Ozero__class_Ozero(X3196),X3195)
| ~ c_Orderings_Oord__class_Oless(X3196,X3194,X3193)
| c_Orderings_Oord__class_Oless(X3196,X3194,c_Groups_Oplus__class_Oplus(X3196,X3195,X3193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1655,plain,
! [X4120,X4121] : 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),X4121),X4121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4120),X4120)),
inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(i_0_1656,plain,
! [X4633,X4634,X4635] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4635,X4634)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4633,X4635),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4633,X4634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1657,plain,
! [X4093,X4094,X4095] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4095,X4094)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4095,X4093),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4094,X4093)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1658,plain,
! [X4090,X4091,X4092] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4092,X4091)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4090,X4091),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4090,X4092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1659,plain,
! [X3341,X3342,X3343] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3343,X3342)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3343,X3341),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3342,X3341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1660,plain,
! [X3378,X3379,X3380] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3380,X3379)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3378,X3380),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3378,X3379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
fof(i_0_1661,plain,
! [X4575,X4576,X4577] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4577,X4576)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4577,X4575),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4576,X4575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1662,plain,
! [X3480,X3481,X3482] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3482,X3481)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3482,X3480),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3481,X3480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1663,plain,
! [X4467,X4468,X4469] :
( ~ class_Rings_Olinordered__idom(X4469)
| c_Groups_Oabs__class_Oabs(X4469,hAPP(hAPP(c_Power_Opower__class_Opower(X4469),c_Groups_Ouminus__class_Ouminus(X4469,X4468)),X4467)) = c_Groups_Oabs__class_Oabs(X4469,hAPP(hAPP(c_Power_Opower__class_Opower(X4469),X4468),X4467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).
fof(i_0_1664,plain,
! [X5356,X5357,X5358,X5359] :
( ~ class_Rings_Ocomm__ring__1(X5359)
| ~ c_Rings_Odvd__class_Odvd(X5359,X5358,X5357)
| ~ c_Rings_Odvd__class_Odvd(X5359,X5358,X5356)
| c_Rings_Odvd__class_Odvd(X5359,X5358,c_Groups_Ominus__class_Ominus(X5359,X5357,X5356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_1665,plain,
! [X5409,X5410,X5411,X5412] :
( ~ class_Rings_Ocomm__semiring__1(X5412)
| ~ c_Rings_Odvd__class_Odvd(X5412,X5411,X5410)
| ~ c_Rings_Odvd__class_Odvd(X5412,X5411,X5409)
| c_Rings_Odvd__class_Odvd(X5412,X5411,c_Groups_Oplus__class_Oplus(X5412,X5410,X5409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_1666,plain,
! [X5303,X5305] :
( ~ class_RealVector_Oreal__algebra__1(X5303)
| ~ class_RealVector_Oreal__normed__vector(X5303)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5303,c_RealVector_Oof__real(X5303,X5305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5305)),esk36_1(X5303))) ),
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_1667,plain,
! [X5127,X5129] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk26_1(X5127))
| ~ class_RealVector_Oreal__algebra__1(X5127)
| ~ class_RealVector_Oreal__normed__vector(X5127) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5127,c_RealVector_Oof__real(X5127,X5129)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5129)),esk26_1(X5127)))
| ~ class_RealVector_Oreal__algebra__1(X5127)
| ~ class_RealVector_Oreal__normed__vector(X5127) ) ),
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_1668,plain,
! [X4543,X4545] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk13_1(X4543))
| ~ class_RealVector_Oreal__algebra__1(X4543)
| ~ class_RealVector_Oreal__normed__vector(X4543) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4543,c_RealVector_Oof__real(X4543,X4545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4545)),esk13_1(X4543)))
| ~ class_RealVector_Oreal__algebra__1(X4543)
| ~ class_RealVector_Oreal__normed__vector(X4543) ) ),
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_1669,plain,
! [X4403,X4404,X4405] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4405)
| c_Groups_Oabs__class_Oabs(X4405,c_Groups_Oplus__class_Oplus(X4405,c_Groups_Oabs__class_Oabs(X4405,X4404),c_Groups_Oabs__class_Oabs(X4405,X4403))) = c_Groups_Oplus__class_Oplus(X4405,c_Groups_Oabs__class_Oabs(X4405,X4404),c_Groups_Oabs__class_Oabs(X4405,X4403)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_1670,plain,
! [X4700,X4701] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4701)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4700)
| 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,X4701,X4700)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_1671,plain,
! [X5378,X5379,X5380,X5381] :
( ( X5380 != c_Groups_Ozero__class_Ozero(X5381)
| X5378 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5381))
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) )
& ( X5380 = c_Groups_Ozero__class_Ozero(X5381)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),X5379,X5378)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) )
& ( X5380 != c_Groups_Ozero__class_Ozero(X5381)
| X5380 = c_Groups_Ozero__class_Ozero(X5381)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),X5379,X5378)
| X5380 = c_Groups_Ozero__class_Ozero(X5381)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) )
& ( X5380 != c_Groups_Ozero__class_Ozero(X5381)
| X5378 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5381))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),X5379,X5378)
| X5378 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5381))
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5381),c_Polynomial_Osmult(X5381,X5380,X5379),X5378)
| ~ class_Fields_Ofield(X5381) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__iff])])]) ).
fof(i_0_1672,plain,
! [X4098,X4099,X4100] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4099,X4100) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4098,X4100)
| X4099 = X4098
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4100,X4098)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4100,X4099) )
& ( X4099 != X4098
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4099,X4100) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4098,X4100)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4100,X4098)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4100,X4099) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1673,plain,
! [X4116,X4117] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4117)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4116)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4116,X4117),X4116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1674,plain,
! [X5240,X5241] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5241),X5240)
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5240,c_RealDef_Oreal(tc_Nat_Onat,X5241))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X5240),X5241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).
fof(i_0_1675,plain,
! [X5243,X5244] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5244),X5243)
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5243,c_RealDef_Oreal(tc_Nat_Onat,X5244))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X5243),X5244) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).
fof(i_0_1676,plain,
! [X4007,X4008] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4008,c_Groups_Ozero__class_Ozero(X4008),c_Groups_Oplus__class_Oplus(X4008,X4007,X4007))
| c_Orderings_Oord__class_Oless__eq(X4008,c_Groups_Ozero__class_Ozero(X4008),X4007)
| ~ class_Groups_Olinordered__ab__group__add(X4008) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4008,c_Groups_Ozero__class_Ozero(X4008),X4007)
| c_Orderings_Oord__class_Oless__eq(X4008,c_Groups_Ozero__class_Ozero(X4008),c_Groups_Oplus__class_Oplus(X4008,X4007,X4007))
| ~ class_Groups_Olinordered__ab__group__add(X4008) ) ),
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_1677,plain,
! [X4017,X4018] :
( ( ~ c_Orderings_Oord__class_Oless(X4018,c_Groups_Ozero__class_Ozero(X4018),c_Groups_Oplus__class_Oplus(X4018,X4017,X4017))
| c_Orderings_Oord__class_Oless(X4018,c_Groups_Ozero__class_Ozero(X4018),X4017)
| ~ class_Groups_Olinordered__ab__group__add(X4018) )
& ( ~ c_Orderings_Oord__class_Oless(X4018,c_Groups_Ozero__class_Ozero(X4018),X4017)
| c_Orderings_Oord__class_Oless(X4018,c_Groups_Ozero__class_Ozero(X4018),c_Groups_Oplus__class_Oplus(X4018,X4017,X4017))
| ~ class_Groups_Olinordered__ab__group__add(X4018) ) ),
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_1678,plain,
! [X4005,X4006] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4006,c_Groups_Oplus__class_Oplus(X4006,X4005,X4005),c_Groups_Ozero__class_Ozero(X4006))
| c_Orderings_Oord__class_Oless__eq(X4006,X4005,c_Groups_Ozero__class_Ozero(X4006))
| ~ class_Groups_Olinordered__ab__group__add(X4006) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4006,X4005,c_Groups_Ozero__class_Ozero(X4006))
| c_Orderings_Oord__class_Oless__eq(X4006,c_Groups_Oplus__class_Oplus(X4006,X4005,X4005),c_Groups_Ozero__class_Ozero(X4006))
| ~ class_Groups_Olinordered__ab__group__add(X4006) ) ),
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_1679,plain,
! [X4015,X4016] :
( ( ~ c_Orderings_Oord__class_Oless(X4016,c_Groups_Oplus__class_Oplus(X4016,X4015,X4015),c_Groups_Ozero__class_Ozero(X4016))
| c_Orderings_Oord__class_Oless(X4016,X4015,c_Groups_Ozero__class_Ozero(X4016))
| ~ class_Groups_Olinordered__ab__group__add(X4016) )
& ( ~ c_Orderings_Oord__class_Oless(X4016,X4015,c_Groups_Ozero__class_Ozero(X4016))
| c_Orderings_Oord__class_Oless(X4016,c_Groups_Oplus__class_Oplus(X4016,X4015,X4015),c_Groups_Ozero__class_Ozero(X4016))
| ~ class_Groups_Olinordered__ab__group__add(X4016) ) ),
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_1680,plain,
! [X4521,X4522] :
( ( ~ c_Orderings_Oord__class_Oless(X4522,c_Groups_Oplus__class_Oplus(X4522,X4521,X4521),c_Groups_Ozero__class_Ozero(X4522))
| c_Orderings_Oord__class_Oless(X4522,X4521,c_Groups_Ozero__class_Ozero(X4522))
| ~ class_Rings_Olinordered__idom(X4522) )
& ( ~ c_Orderings_Oord__class_Oless(X4522,X4521,c_Groups_Ozero__class_Ozero(X4522))
| c_Orderings_Oord__class_Oless(X4522,c_Groups_Oplus__class_Oplus(X4522,X4521,X4521),c_Groups_Ozero__class_Ozero(X4522))
| ~ class_Rings_Olinordered__idom(X4522) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1681,plain,
! [X4282,X4283,X4284,X4285] :
( ~ class_Rings_Ocomm__semiring__1(X4285)
| c_Groups_Oplus__class_Oplus(X4285,c_Groups_Oplus__class_Oplus(X4285,X4284,X4283),X4282) = c_Groups_Oplus__class_Oplus(X4285,c_Groups_Oplus__class_Oplus(X4285,X4284,X4282),X4283) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1682,plain,
! [X4278,X4279,X4280,X4281] :
( ~ class_Rings_Ocomm__semiring__1(X4281)
| c_Groups_Oplus__class_Oplus(X4281,c_Groups_Oplus__class_Oplus(X4281,X4280,X4279),X4278) = c_Groups_Oplus__class_Oplus(X4281,X4280,c_Groups_Oplus__class_Oplus(X4281,X4279,X4278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1683,plain,
! [X3894,X3895,X3896,X3897] :
( ~ class_Groups_Oab__semigroup__add(X3897)
| c_Groups_Oplus__class_Oplus(X3897,c_Groups_Oplus__class_Oplus(X3897,X3896,X3895),X3894) = c_Groups_Oplus__class_Oplus(X3897,X3896,c_Groups_Oplus__class_Oplus(X3897,X3895,X3894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1684,plain,
! [X4274,X4275,X4276,X4277] :
( ~ class_Rings_Ocomm__semiring__1(X4277)
| c_Groups_Oplus__class_Oplus(X4277,X4276,c_Groups_Oplus__class_Oplus(X4277,X4275,X4274)) = c_Groups_Oplus__class_Oplus(X4277,c_Groups_Oplus__class_Oplus(X4277,X4276,X4275),X4274) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1685,plain,
! [X4270,X4271,X4272,X4273] :
( ~ class_Rings_Ocomm__semiring__1(X4273)
| c_Groups_Oplus__class_Oplus(X4273,X4272,c_Groups_Oplus__class_Oplus(X4273,X4271,X4270)) = c_Groups_Oplus__class_Oplus(X4273,X4271,c_Groups_Oplus__class_Oplus(X4273,X4272,X4270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1686,plain,
! [X4506] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4506),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4506),
inference(variable_rename,[status(thm)],[i_0_1281]) ).
fof(i_0_1687,plain,
! [X4197,X4198] :
( ( ~ 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,X4198,X4197))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4198),X4197) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4198),X4197)
| 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,X4198,X4197)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).
fof(i_0_1688,plain,
! [X4199,X4200] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4200,X4199))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4200),X4199) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4200),X4199)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4200,X4199)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(i_0_1689,plain,
! [X4195,X4196] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4196,X4195),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4195,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4196)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4195,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4196))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4196,X4195),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_1690,plain,
! [X4201,X4202] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4202,X4201),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4201,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4202)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4201,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4202))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4202,X4201),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_1691,plain,
! [X3549,X3550,X3551] :
( ~ class_Fields_Olinordered__field(X3551)
| ~ c_Orderings_Oord__class_Oless__eq(X3551,c_Rings_Oinverse__class_Oinverse(X3551,X3550),c_Rings_Oinverse__class_Oinverse(X3551,X3549))
| ~ c_Orderings_Oord__class_Oless(X3551,c_Groups_Ozero__class_Ozero(X3551),X3550)
| c_Orderings_Oord__class_Oless__eq(X3551,X3549,X3550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le])]) ).
fof(i_0_1692,plain,
! [X3527,X3528,X3529] :
( ~ class_Fields_Olinordered__field(X3529)
| ~ c_Orderings_Oord__class_Oless(X3529,c_Rings_Oinverse__class_Oinverse(X3529,X3528),c_Rings_Oinverse__class_Oinverse(X3529,X3527))
| ~ c_Orderings_Oord__class_Oless(X3529,c_Groups_Ozero__class_Ozero(X3529),X3528)
| c_Orderings_Oord__class_Oless(X3529,X3527,X3528) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).
fof(i_0_1693,plain,
! [X3552,X3553,X3554] :
( ~ class_Fields_Olinordered__field(X3554)
| ~ c_Orderings_Oord__class_Oless__eq(X3554,c_Rings_Oinverse__class_Oinverse(X3554,X3553),c_Rings_Oinverse__class_Oinverse(X3554,X3552))
| ~ c_Orderings_Oord__class_Oless(X3554,X3552,c_Groups_Ozero__class_Ozero(X3554))
| c_Orderings_Oord__class_Oless__eq(X3554,X3552,X3553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le__neg])]) ).
fof(i_0_1694,plain,
! [X3530,X3531,X3532] :
( ~ class_Fields_Olinordered__field(X3532)
| ~ c_Orderings_Oord__class_Oless(X3532,c_Rings_Oinverse__class_Oinverse(X3532,X3531),c_Rings_Oinverse__class_Oinverse(X3532,X3530))
| ~ c_Orderings_Oord__class_Oless(X3532,X3530,c_Groups_Ozero__class_Ozero(X3532))
| c_Orderings_Oord__class_Oless(X3532,X3530,X3531) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).
fof(i_0_1695,plain,
! [X3747,X3748,X3749] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3749,X3748,X3747)
| c_Orderings_Oord__class_Oless__eq(X3749,c_Groups_Ominus__class_Ominus(X3749,X3748,X3747),c_Groups_Ozero__class_Ozero(X3749))
| ~ class_Groups_Oordered__ab__group__add(X3749) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3749,c_Groups_Ominus__class_Ominus(X3749,X3748,X3747),c_Groups_Ozero__class_Ozero(X3749))
| c_Orderings_Oord__class_Oless__eq(X3749,X3748,X3747)
| ~ class_Groups_Oordered__ab__group__add(X3749) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
fof(i_0_1696,plain,
! [X3750,X3751,X3752] :
( ( ~ c_Orderings_Oord__class_Oless(X3752,X3751,X3750)
| c_Orderings_Oord__class_Oless(X3752,c_Groups_Ominus__class_Ominus(X3752,X3751,X3750),c_Groups_Ozero__class_Ozero(X3752))
| ~ class_Groups_Oordered__ab__group__add(X3752) )
& ( ~ c_Orderings_Oord__class_Oless(X3752,c_Groups_Ominus__class_Ominus(X3752,X3751,X3750),c_Groups_Ozero__class_Ozero(X3752))
| c_Orderings_Oord__class_Oless(X3752,X3751,X3750)
| ~ class_Groups_Oordered__ab__group__add(X3752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_1697,plain,
! [X4860,X4861,X4862,X4863] :
( ~ class_Rings_Ocomm__semiring__0(X4863)
| c_Polynomial_Osmult(X4863,X4862,c_Polynomial_Omonom(X4863,X4861,X4860)) = c_Polynomial_Omonom(X4863,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4863),X4862),X4861),X4860) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__monom])]) ).
fof(i_0_1698,plain,
! [X4775,X4776,X4777,X4778] :
( ~ class_Rings_Ocomm__semiring__0(X4778)
| c_Polynomial_Osmult(X4778,X4777,c_Polynomial_Osmult(X4778,X4776,X4775)) = c_Polynomial_Osmult(X4778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4778),X4777),X4776),X4775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(i_0_1699,plain,
! [X4474,X4475] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4475,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4474))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4474,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4475))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(i_0_1700,plain,
! [X4702,X4703] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4703)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4702)
| 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),X4703),X4702)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_1701,plain,
! [X3448,X3449] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3449)
| ~ 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),X3449),X3448)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3448)
| ~ 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),X3449),X3448)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3449)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3448)
| 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),X3449),X3448)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1702,plain,
! [X3538,X3539] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3539)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3538)
| 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),X3539),X3538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1703,plain,
! [X4479,X4480,X4481] :
( ~ class_Rings_Olinordered__idom(X4481)
| ~ c_Orderings_Oord__class_Oless__eq(X4481,c_Groups_Ozero__class_Ozero(X4481),X4480)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4481),c_Groups_Oabs__class_Oabs(X4481,X4479)),X4480) = c_Groups_Oabs__class_Oabs(X4481,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4481),X4479),X4480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_1704,plain,
! [X3279] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3279,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3279),X3279))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1705,plain,
! [X3613,X3614,X3615,X3616,X3617] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3617,X3616,X3615)
| c_Orderings_Oord__class_Oless__eq(X3617,X3614,X3613)
| c_Groups_Ominus__class_Ominus(X3617,X3616,X3615) != c_Groups_Ominus__class_Ominus(X3617,X3614,X3613)
| ~ class_Groups_Oordered__ab__group__add(X3617) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3617,X3614,X3613)
| c_Orderings_Oord__class_Oless__eq(X3617,X3616,X3615)
| c_Groups_Ominus__class_Ominus(X3617,X3616,X3615) != c_Groups_Ominus__class_Ominus(X3617,X3614,X3613)
| ~ class_Groups_Oordered__ab__group__add(X3617) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_1706,plain,
! [X3630,X3631,X3632,X3633,X3634] :
( ( ~ c_Orderings_Oord__class_Oless(X3634,X3633,X3632)
| c_Orderings_Oord__class_Oless(X3634,X3631,X3630)
| c_Groups_Ominus__class_Ominus(X3634,X3633,X3632) != c_Groups_Ominus__class_Ominus(X3634,X3631,X3630)
| ~ class_Groups_Oordered__ab__group__add(X3634) )
& ( ~ c_Orderings_Oord__class_Oless(X3634,X3631,X3630)
| c_Orderings_Oord__class_Oless(X3634,X3633,X3632)
| c_Groups_Ominus__class_Ominus(X3634,X3633,X3632) != c_Groups_Ominus__class_Ominus(X3634,X3631,X3630)
| ~ class_Groups_Oordered__ab__group__add(X3634) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1707,plain,
! [X3289,X3290,X3291] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3291,X3290)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3291),X3289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3290),X3289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1708,plain,
! [X3292,X3293,X3294] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3294,X3293)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3292),X3294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3292),X3293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1709,plain,
! [X4236,X4237,X4238,X4239] :
( ~ class_Rings_Ocomm__semiring__1(X4239)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4239),X4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4239),X4237),X4236)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4239),X4237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4239),X4238),X4236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1710,plain,
! [X4082,X4083,X4084] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4084,X4083),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4084,X4082)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4083,X4082),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1711,plain,
! [X4085,X4086,X4087] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4087,X4086),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4085,X4086)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4087,X4085),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1712,plain,
! [X4387,X4388,X4389] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4389,X4388),X4387) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4389,X4387),X4388),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1713,plain,
! [X4079,X4080,X4081] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4081,X4080),X4079) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4081,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4080,X4079)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1714,plain,
! [X4630,X4631,X4632] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4632,X4631),X4630) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4632,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4631,X4630)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1715,plain,
! [X3402,X3403,X3404] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3404,X3403),X3402) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3404,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3403,X3402)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1716,plain,
! [X4627,X4628,X4629] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4629,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4628,X4627)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4628,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4629,X4627)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1717,plain,
! [X3399,X3400,X3401] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3400,X3399)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3400,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3399)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1718,plain,
! [X4595,X4596] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4595,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,X4595)
| X4596 = X4595 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,X4595)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4595,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X4596 != X4595
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4595,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_1719,plain,
! [X4590,X4591] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4591,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4590)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4591,X4590) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4591,X4590)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4591,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4590) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
fof(i_0_1720,plain,
! [X4597,X4598] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4598,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4597,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4598,X4597) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4598,X4597)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4598,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4597,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_1721,plain,
! [X4553,X4554] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4554,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4553,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4554,X4553) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4554,X4553)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4554,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4553,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_1722,plain,
! [X4114,X4115] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4115,X4114)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4115,X4114),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,X4115,X4114),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4115,X4114) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_1723,plain,
! [X4551,X4552] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4552,X4551)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4552,X4551),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4552,X4551),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4552,X4551) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1724,plain,
! [X4118,X4119] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4119,X4118))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4118,X4119) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4118,X4119)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4119,X4118)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_1725,plain,
! [X3487,X3488,X3489,X3490] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3490,X3489)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3488,X3489) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3490,X3487)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,X3487) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1726,plain,
! [X5247,X5248] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5248)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5248,c_RealDef_Oreal(tc_Nat_Onat,X5247))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5248),X5247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1727,plain,
! [X5253,X5254] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5254)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5254,c_RealDef_Oreal(tc_Nat_Onat,X5253))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5254),X5253) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1728,plain,
! [X4456,X4457,X4458] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4458)
| ~ c_Orderings_Oord__class_Oless__eq(X4458,X4457,X4456)
| ~ c_Orderings_Oord__class_Oless__eq(X4458,c_Groups_Ouminus__class_Ouminus(X4458,X4457),X4456)
| c_Orderings_Oord__class_Oless__eq(X4458,c_Groups_Oabs__class_Oabs(X4458,X4457),X4456) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).
fof(i_0_1729,plain,
! [X4453,X4454,X4455] :
( ( c_Orderings_Oord__class_Oless__eq(X4455,X4454,X4453)
| ~ c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Oabs__class_Oabs(X4455,X4454),X4453)
| ~ class_Groups_Oordered__ab__group__add__abs(X4455) )
& ( c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Ouminus__class_Ouminus(X4455,X4454),X4453)
| ~ c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Oabs__class_Oabs(X4455,X4454),X4453)
| ~ class_Groups_Oordered__ab__group__add__abs(X4455) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4455,X4454,X4453)
| ~ c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Ouminus__class_Ouminus(X4455,X4454),X4453)
| c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Oabs__class_Oabs(X4455,X4454),X4453)
| ~ class_Groups_Oordered__ab__group__add__abs(X4455) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).
fof(i_0_1730,plain,
! [X4462,X4463,X4464] :
( ( c_Orderings_Oord__class_Oless(X4464,X4463,X4462)
| ~ c_Orderings_Oord__class_Oless(X4464,c_Groups_Oabs__class_Oabs(X4464,X4463),X4462)
| ~ class_Rings_Olinordered__idom(X4464) )
& ( c_Orderings_Oord__class_Oless(X4464,c_Groups_Ouminus__class_Ouminus(X4464,X4463),X4462)
| ~ c_Orderings_Oord__class_Oless(X4464,c_Groups_Oabs__class_Oabs(X4464,X4463),X4462)
| ~ class_Rings_Olinordered__idom(X4464) )
& ( ~ c_Orderings_Oord__class_Oless(X4464,X4463,X4462)
| ~ c_Orderings_Oord__class_Oless(X4464,c_Groups_Ouminus__class_Ouminus(X4464,X4463),X4462)
| c_Orderings_Oord__class_Oless(X4464,c_Groups_Oabs__class_Oabs(X4464,X4463),X4462)
| ~ class_Rings_Olinordered__idom(X4464) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(i_0_1731,plain,
! [X3354,X3355,X3356] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3356,X3354)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3356,X3355),X3354) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3355,X3354)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3356,X3355),X3354) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1282])])]) ).
fof(i_0_1732,plain,
! [X3351,X3352,X3353] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3353,X3352),X3351)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3353,X3351) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1733,plain,
! [X3348,X3349,X3350] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3350,X3349),X3348)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3349,X3348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1734,plain,
! [X3491,X3492,X3493] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3493,X3492),X3491)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1735,plain,
! [X5188,X5189] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5189,X5188)
| c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5188,X5189)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5188),c_RealDef_Oreal(tc_Nat_Onat,X5189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).
fof(i_0_1736,plain,
! [X3999,X4000,X4001] :
( ( X4000 = c_Groups_Ozero__class_Ozero(X4001)
| c_Groups_Oplus__class_Oplus(X4001,X4000,X3999) != c_Groups_Ozero__class_Ozero(X4001)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X3999)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X4000)
| ~ class_Groups_Oordered__comm__monoid__add(X4001) )
& ( X3999 = c_Groups_Ozero__class_Ozero(X4001)
| c_Groups_Oplus__class_Oplus(X4001,X4000,X3999) != c_Groups_Ozero__class_Ozero(X4001)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X3999)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X4000)
| ~ class_Groups_Oordered__comm__monoid__add(X4001) )
& ( X4000 != c_Groups_Ozero__class_Ozero(X4001)
| X3999 != c_Groups_Ozero__class_Ozero(X4001)
| c_Groups_Oplus__class_Oplus(X4001,X4000,X3999) = c_Groups_Ozero__class_Ozero(X4001)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X3999)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,c_Groups_Ozero__class_Ozero(X4001),X4000)
| ~ class_Groups_Oordered__comm__monoid__add(X4001) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1737,plain,
! [X3543,X3544,X3545] :
( ~ class_Fields_Olinordered__field(X3545)
| ~ c_Orderings_Oord__class_Oless__eq(X3545,X3544,X3543)
| ~ c_Orderings_Oord__class_Oless(X3545,c_Groups_Ozero__class_Ozero(X3545),X3544)
| c_Orderings_Oord__class_Oless__eq(X3545,c_Rings_Oinverse__class_Oinverse(X3545,X3543),c_Rings_Oinverse__class_Oinverse(X3545,X3544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le])]) ).
fof(i_0_1738,plain,
! [X3519,X3520,X3521] :
( ~ class_Fields_Olinordered__field(X3521)
| ~ c_Orderings_Oord__class_Oless(X3521,X3520,X3519)
| ~ c_Orderings_Oord__class_Oless(X3521,c_Groups_Ozero__class_Ozero(X3521),X3520)
| c_Orderings_Oord__class_Oless(X3521,c_Rings_Oinverse__class_Oinverse(X3521,X3519),c_Rings_Oinverse__class_Oinverse(X3521,X3520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).
fof(i_0_1739,plain,
! [X3546,X3547,X3548] :
( ~ class_Fields_Olinordered__field(X3548)
| ~ c_Orderings_Oord__class_Oless__eq(X3548,X3547,X3546)
| ~ c_Orderings_Oord__class_Oless(X3548,X3546,c_Groups_Ozero__class_Ozero(X3548))
| c_Orderings_Oord__class_Oless__eq(X3548,c_Rings_Oinverse__class_Oinverse(X3548,X3546),c_Rings_Oinverse__class_Oinverse(X3548,X3547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le__neg])]) ).
fof(i_0_1740,plain,
! [X3522,X3523,X3524] :
( ~ class_Fields_Olinordered__field(X3524)
| ~ c_Orderings_Oord__class_Oless(X3524,X3523,X3522)
| ~ c_Orderings_Oord__class_Oless(X3524,X3522,c_Groups_Ozero__class_Ozero(X3524))
| c_Orderings_Oord__class_Oless(X3524,c_Rings_Oinverse__class_Oinverse(X3524,X3522),c_Rings_Oinverse__class_Oinverse(X3524,X3523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).
fof(i_0_1741,plain,
! [X5117,X5118,X5119,X5120] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5119,X5120),X5118,X5117)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5119,X5120),X5118,X5117)
| ~ class_Orderings_Oord(X5120) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5119,X5120),X5117,X5118)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5119,X5120),X5118,X5117)
| ~ class_Orderings_Oord(X5120) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5119,X5120),X5118,X5117)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X5119,X5120),X5117,X5118)
| c_Orderings_Oord__class_Oless(tc_fun(X5119,X5120),X5118,X5117)
| ~ class_Orderings_Oord(X5120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1283])])]) ).
fof(i_0_1742,plain,
! [X4053,X4054] :
( ( ~ 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),X4054),X4053))
| X4053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4054) )
& ( X4053 != 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),X4054),X4053)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4054)
| 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),X4054),X4053)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1743,plain,
! [X2824,X2825] :
( ( ~ 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),X2825),X2824))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2825)
| X2824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2825)
| 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),X2825),X2824)) )
& ( X2824 != 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),X2825),X2824)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1744,plain,
! [X5282,X5283,X5284,X5285,X5286] :
( ~ class_Groups_Ominus(X5286)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5285,X5286),X5284,X5283),X5282) = c_Groups_Ominus__class_Ominus(X5286,hAPP(X5284,X5282),hAPP(X5283,X5282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_1745,plain,
! [X3262,X3263] :
( ( c_Orderings_Oord__class_Oless(X3263,c_Groups_Ozero__class_Ozero(X3263),X3262)
| ~ c_Orderings_Oord__class_Oless__eq(X3263,c_Groups_Oone__class_Oone(X3263),c_Rings_Oinverse__class_Oinverse(X3263,X3262))
| ~ class_Fields_Olinordered__field__inverse__zero(X3263) )
& ( c_Orderings_Oord__class_Oless__eq(X3263,X3262,c_Groups_Oone__class_Oone(X3263))
| ~ c_Orderings_Oord__class_Oless__eq(X3263,c_Groups_Oone__class_Oone(X3263),c_Rings_Oinverse__class_Oinverse(X3263,X3262))
| ~ class_Fields_Olinordered__field__inverse__zero(X3263) )
& ( ~ c_Orderings_Oord__class_Oless(X3263,c_Groups_Ozero__class_Ozero(X3263),X3262)
| ~ c_Orderings_Oord__class_Oless__eq(X3263,X3262,c_Groups_Oone__class_Oone(X3263))
| c_Orderings_Oord__class_Oless__eq(X3263,c_Groups_Oone__class_Oone(X3263),c_Rings_Oinverse__class_Oinverse(X3263,X3262))
| ~ class_Fields_Olinordered__field__inverse__zero(X3263) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse__iff])])]) ).
fof(i_0_1746,plain,
! [X3258,X3259] :
( ~ class_Fields_Olinordered__field(X3259)
| ~ c_Orderings_Oord__class_Oless(X3259,c_Groups_Ozero__class_Ozero(X3259),X3258)
| ~ c_Orderings_Oord__class_Oless__eq(X3259,X3258,c_Groups_Oone__class_Oone(X3259))
| c_Orderings_Oord__class_Oless__eq(X3259,c_Groups_Oone__class_Oone(X3259),c_Rings_Oinverse__class_Oinverse(X3259,X3258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse])]) ).
fof(i_0_1747,plain,
! [X3560,X3561] :
( ( c_Orderings_Oord__class_Oless(X3561,c_Groups_Ozero__class_Ozero(X3561),X3560)
| ~ c_Orderings_Oord__class_Oless(X3561,c_Groups_Oone__class_Oone(X3561),c_Rings_Oinverse__class_Oinverse(X3561,X3560))
| ~ class_Fields_Olinordered__field__inverse__zero(X3561) )
& ( c_Orderings_Oord__class_Oless(X3561,X3560,c_Groups_Oone__class_Oone(X3561))
| ~ c_Orderings_Oord__class_Oless(X3561,c_Groups_Oone__class_Oone(X3561),c_Rings_Oinverse__class_Oinverse(X3561,X3560))
| ~ class_Fields_Olinordered__field__inverse__zero(X3561) )
& ( ~ c_Orderings_Oord__class_Oless(X3561,c_Groups_Ozero__class_Ozero(X3561),X3560)
| ~ c_Orderings_Oord__class_Oless(X3561,X3560,c_Groups_Oone__class_Oone(X3561))
| c_Orderings_Oord__class_Oless(X3561,c_Groups_Oone__class_Oone(X3561),c_Rings_Oinverse__class_Oinverse(X3561,X3560))
| ~ class_Fields_Olinordered__field__inverse__zero(X3561) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff])])]) ).
fof(i_0_1748,plain,
! [X3562,X3563] :
( ~ class_Fields_Olinordered__field(X3563)
| ~ c_Orderings_Oord__class_Oless(X3563,c_Groups_Ozero__class_Ozero(X3563),X3562)
| ~ c_Orderings_Oord__class_Oless(X3563,X3562,c_Groups_Oone__class_Oone(X3563))
| c_Orderings_Oord__class_Oless(X3563,c_Groups_Oone__class_Oone(X3563),c_Rings_Oinverse__class_Oinverse(X3563,X3562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse])]) ).
fof(i_0_1749,plain,
! [X4470,X4471] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4470),X4471)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4471),X4470) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4471,X4470)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4471),X4470) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4470),X4471)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4471,X4470)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4471),X4470) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])]) ).
fof(i_0_1750,plain,
! [X5213,X5214,X5215] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5215),X5214,X5213)
| X5214 = X5213
| c_Polynomial_Opos__poly(X5215,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5215),X5213,X5214))
| ~ class_Rings_Olinordered__idom(X5215) )
& ( X5214 != X5213
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5215),X5214,X5213)
| ~ class_Rings_Olinordered__idom(X5215) )
& ( ~ c_Polynomial_Opos__poly(X5215,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5215),X5213,X5214))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5215),X5214,X5213)
| ~ class_Rings_Olinordered__idom(X5215) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def])])]) ).
fof(i_0_1751,plain,
! [X5255,X5256,X5257] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5257),X5256,X5255)
| c_Polynomial_Opos__poly(X5257,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5257),X5255,X5256))
| ~ class_Rings_Olinordered__idom(X5257) )
& ( ~ c_Polynomial_Opos__poly(X5257,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5257),X5255,X5256))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5257),X5256,X5255)
| ~ class_Rings_Olinordered__idom(X5257) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])]) ).
fof(i_0_1752,plain,
! [X4486,X4487,X4488] :
( ~ class_Rings_Olinordered__idom(X4488)
| c_Orderings_Oord__class_Oless__eq(X4488,c_Groups_Ozero__class_Ozero(X4488),hAPP(hAPP(c_Power_Opower__class_Opower(X4488),c_Groups_Oabs__class_Oabs(X4488,X4487)),X4486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_1753,plain,
! [X5184,X5185,X5186] :
( ( X5184 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5186))
| c_Polynomial_Opos__poly(X5186,X5184)
| ~ c_Polynomial_Opos__poly(X5186,c_Polynomial_OpCons(X5186,X5185,X5184))
| ~ class_Rings_Olinordered__idom(X5186) )
& ( c_Orderings_Oord__class_Oless(X5186,c_Groups_Ozero__class_Ozero(X5186),X5185)
| c_Polynomial_Opos__poly(X5186,X5184)
| ~ c_Polynomial_Opos__poly(X5186,c_Polynomial_OpCons(X5186,X5185,X5184))
| ~ class_Rings_Olinordered__idom(X5186) )
& ( ~ c_Polynomial_Opos__poly(X5186,X5184)
| c_Polynomial_Opos__poly(X5186,c_Polynomial_OpCons(X5186,X5185,X5184))
| ~ class_Rings_Olinordered__idom(X5186) )
& ( X5184 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5186))
| ~ c_Orderings_Oord__class_Oless(X5186,c_Groups_Ozero__class_Ozero(X5186),X5185)
| c_Polynomial_Opos__poly(X5186,c_Polynomial_OpCons(X5186,X5185,X5184))
| ~ class_Rings_Olinordered__idom(X5186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons])])]) ).
fof(i_0_1754,plain,
! [X4648] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X4648),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,X4648))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X4648),esk15_1(X4648)) = 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_1755,plain,
! [X3224,X3225,X3226,X3227] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3227),X3226),X3225) != hAPP(hAPP(c_Power_Opower__class_Opower(X3227),X3226),X3224)
| X3225 = X3224
| ~ c_Orderings_Oord__class_Oless(X3227,c_Groups_Oone__class_Oone(X3227),X3226)
| ~ class_Rings_Olinordered__semidom(X3227) )
& ( X3225 != X3224
| hAPP(hAPP(c_Power_Opower__class_Opower(X3227),X3226),X3225) = hAPP(hAPP(c_Power_Opower__class_Opower(X3227),X3226),X3224)
| ~ c_Orderings_Oord__class_Oless(X3227,c_Groups_Oone__class_Oone(X3227),X3226)
| ~ class_Rings_Olinordered__semidom(X3227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1756,plain,
! [X5237,X5238] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5238),X5237)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5238,c_RealDef_Oreal(tc_Nat_Onat,X5237))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5238) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5238,c_RealDef_Oreal(tc_Nat_Onat,X5237))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5238),X5237)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5238) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1757,plain,
! [X5245,X5246] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5246)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5246,c_RealDef_Oreal(tc_Nat_Onat,X5245))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X5246),X5245) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1758,plain,
! [X5233,X5234] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5233,c_RComplete_Onatfloor(X5234))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5233),X5234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5234) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5233),X5234)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5233,c_RComplete_Onatfloor(X5234))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5234) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
fof(i_0_1759,plain,
! [X2954,X2955,X2956] :
( ~ class_Rings_Olinordered__semidom(X2956)
| ~ c_Orderings_Oord__class_Oless__eq(X2956,c_Groups_Oone__class_Oone(X2956),X2955)
| c_Orderings_Oord__class_Oless__eq(X2956,c_Groups_Oone__class_Oone(X2956),hAPP(hAPP(c_Power_Opower__class_Opower(X2956),X2955),X2954)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_1760,plain,
! [X2951,X2952,X2953] :
( ~ class_Rings_Olinordered__semidom(X2953)
| ~ c_Orderings_Oord__class_Oless__eq(X2953,c_Groups_Ozero__class_Ozero(X2953),X2952)
| c_Orderings_Oord__class_Oless__eq(X2953,c_Groups_Ozero__class_Ozero(X2953),hAPP(hAPP(c_Power_Opower__class_Opower(X2953),X2952),X2951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_1761,plain,
! [X3205,X3206,X3207] :
( ~ class_Rings_Olinordered__semidom(X3207)
| ~ c_Orderings_Oord__class_Oless(X3207,c_Groups_Ozero__class_Ozero(X3207),X3206)
| c_Orderings_Oord__class_Oless(X3207,c_Groups_Ozero__class_Ozero(X3207),hAPP(hAPP(c_Power_Opower__class_Opower(X3207),X3206),X3205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1762,plain,
! [X3555,X3556] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3556,c_Rings_Oinverse__class_Oinverse(X3556,X3555),c_Groups_Oone__class_Oone(X3556))
| c_Orderings_Oord__class_Oless__eq(X3556,X3555,c_Groups_Ozero__class_Ozero(X3556))
| c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Oone__class_Oone(X3556),X3555)
| ~ class_Fields_Olinordered__field__inverse__zero(X3556) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3556,X3555,c_Groups_Ozero__class_Ozero(X3556))
| c_Orderings_Oord__class_Oless__eq(X3556,c_Rings_Oinverse__class_Oinverse(X3556,X3555),c_Groups_Oone__class_Oone(X3556))
| ~ class_Fields_Olinordered__field__inverse__zero(X3556) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3556,c_Groups_Oone__class_Oone(X3556),X3555)
| c_Orderings_Oord__class_Oless__eq(X3556,c_Rings_Oinverse__class_Oinverse(X3556,X3555),c_Groups_Oone__class_Oone(X3556))
| ~ class_Fields_Olinordered__field__inverse__zero(X3556) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__1__iff])])]) ).
fof(i_0_1763,plain,
! [X3260,X3261] :
( ( ~ c_Orderings_Oord__class_Oless(X3261,c_Rings_Oinverse__class_Oinverse(X3261,X3260),c_Groups_Oone__class_Oone(X3261))
| c_Orderings_Oord__class_Oless__eq(X3261,X3260,c_Groups_Ozero__class_Ozero(X3261))
| c_Orderings_Oord__class_Oless(X3261,c_Groups_Oone__class_Oone(X3261),X3260)
| ~ class_Fields_Olinordered__field__inverse__zero(X3261) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3261,X3260,c_Groups_Ozero__class_Ozero(X3261))
| c_Orderings_Oord__class_Oless(X3261,c_Rings_Oinverse__class_Oinverse(X3261,X3260),c_Groups_Oone__class_Oone(X3261))
| ~ class_Fields_Olinordered__field__inverse__zero(X3261) )
& ( ~ c_Orderings_Oord__class_Oless(X3261,c_Groups_Oone__class_Oone(X3261),X3260)
| c_Orderings_Oord__class_Oless(X3261,c_Rings_Oinverse__class_Oinverse(X3261,X3260),c_Groups_Oone__class_Oone(X3261))
| ~ class_Fields_Olinordered__field__inverse__zero(X3261) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__1__iff])])]) ).
fof(i_0_1764,plain,
! [X5154] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5154)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5154,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5154),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_1765,plain,
! [X5116] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5116)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5116,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5116),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_1766,plain,
! [X2877,X2878,X2879] :
( ~ class_Rings_Odivision__ring(X2879)
| X2878 = c_Groups_Ozero__class_Ozero(X2879)
| X2877 = c_Groups_Ozero__class_Ozero(X2879)
| c_Rings_Oinverse__class_Oinverse(X2879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2879),X2878),X2877)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2879),c_Rings_Oinverse__class_Oinverse(X2879,X2877)),c_Rings_Oinverse__class_Oinverse(X2879,X2878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).
fof(i_0_1767,plain,
! [X3191,X3192] :
( ~ class_Rings_Olinordered__ring(X3192)
| ~ c_Orderings_Oord__class_Oless(X3192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3192),X3191),X3191),c_Groups_Ozero__class_Ozero(X3192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1285])]) ).
fof(i_0_1768,plain,
! [X4608] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4608),X4608) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1769,plain,
! [X5167,X5168] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5167)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X5168,X5167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_1770,plain,
! [X5130,X5131,X5132,X5133] : hAPP(hAPP(c_Power_Opower_Opower(X5133,X5132,X5131),X5130),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5132,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_1771,plain,
! [X4582] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4582)
| 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),X4582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_1772,plain,
! [X5315,X5316,X5317] :
( ~ class_Rings_Olinordered__idom(X5317)
| c_Groups_Osgn__class_Osgn(X5317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5317),X5316),X5315)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5317),c_Groups_Osgn__class_Osgn(X5317,X5316)),c_Groups_Osgn__class_Osgn(X5317,X5315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).
fof(i_0_1773,plain,
! [X5312,X5313,X5314] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5314)
| c_Groups_Osgn__class_Osgn(X5314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5314),X5313),X5312)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5314),c_Groups_Osgn__class_Osgn(X5314,X5313)),c_Groups_Osgn__class_Osgn(X5314,X5312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__mult])]) ).
fof(i_0_1774,plain,
! [X4398,X4399,X4400] :
( ~ class_Rings_Olinordered__idom(X4400)
| c_Groups_Oabs__class_Oabs(X4400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),X4399),X4398)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),c_Groups_Oabs__class_Oabs(X4400,X4399)),c_Groups_Oabs__class_Oabs(X4400,X4398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_1775,plain,
! [X3462,X3463,X3464] :
( ~ class_Fields_Ofield__inverse__zero(X3464)
| c_Rings_Oinverse__class_Oinverse(X3464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3464),X3463),X3462)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3464),c_Rings_Oinverse__class_Oinverse(X3464,X3463)),c_Rings_Oinverse__class_Oinverse(X3464,X3462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib])]) ).
fof(i_0_1776,plain,
! [X4784,X4785,X4786] :
( ~ class_Groups_Oab__group__add(X4786)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4786),c_Polynomial_OpCons(X4786,X4785,X4784)) = c_Polynomial_OpCons(X4786,c_Groups_Ouminus__class_Ouminus(X4786,X4785),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4786),X4784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])]) ).
fof(i_0_1777,plain,
! [X4781,X4782,X4783] :
( ~ class_Groups_Oab__group__add(X4783)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4783),c_Polynomial_OpCons(X4783,X4782,X4781)) = c_Polynomial_OpCons(X4783,c_Groups_Ouminus__class_Ouminus(X4783,X4782),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4783),X4781)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J])]) ).
fof(i_0_1778,plain,
! [X4407,X4408,X4409] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4409)
| c_Groups_Oabs__class_Oabs(X4409,c_Groups_Ominus__class_Ominus(X4409,X4408,X4407)) = c_Groups_Oabs__class_Oabs(X4409,c_Groups_Ominus__class_Ominus(X4409,X4407,X4408)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
fof(i_0_1779,plain,
! [X3740,X3741,X3742] :
( ~ class_RealVector_Oreal__normed__vector(X3742)
| c_RealVector_Onorm__class_Onorm(X3742,c_Groups_Ominus__class_Ominus(X3742,X3741,X3740)) = c_RealVector_Onorm__class_Onorm(X3742,c_Groups_Ominus__class_Ominus(X3742,X3740,X3741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(i_0_1780,plain,
! [X3240,X3241,X3242] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3242)
| c_RealVector_Onorm__class_Onorm(X3242,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3242),X3241),X3240)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3242,X3241)),c_RealVector_Onorm__class_Onorm(X3242,X3240)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_1781,plain,
! [X4578,X4579] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4579,X4578)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4579,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4578) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
fof(i_0_1782,plain,
! [X3467,X3468] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3468,X3467),X3468),
inference(variable_rename,[status(thm)],[i_0_1286]) ).
fof(i_0_1783,plain,
! [X3469,X3470] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3470,X3469),X3469),
inference(variable_rename,[status(thm)],[i_0_1287]) ).
fof(i_0_1784,plain,
! [X4160,X4161] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4161,X4160)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4160,X4161),X4161) = X4160 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_1785,plain,
! [X4096,X4097] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4097,X4096)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4096,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4096,X4097)) = X4097 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_1786,plain,
! [X4152,X4153] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4153,X4152)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4153,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4152,X4153)) = X4152 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_1787,plain,
! [X3812,X3813,X3814] :
( ~ class_RealVector_Oreal__algebra__1(X3814)
| c_RealVector_Oof__real(X3814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3813),X3812)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3814),c_RealVector_Oof__real(X3814,X3813)),c_RealVector_Oof__real(X3814,X3812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__mult])]) ).
fof(i_0_1788,plain,
! [X4969,X4970,X4971,X4972,X4973] :
( ~ class_Orderings_Oord(X4973)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4972,X4973),X4971,X4970)
| c_Orderings_Oord__class_Oless__eq(X4973,hAPP(X4971,X4969),hAPP(X4970,X4969)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_1789,plain,
! [X4931,X4932,X4933,X4934,X4935] :
( ~ class_Orderings_Oord(X4935)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4934,X4935),X4933,X4932)
| c_Orderings_Oord__class_Oless__eq(X4935,hAPP(X4933,X4931),hAPP(X4932,X4931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_1790,plain,
! [X4072,X4073,X4074] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4074,X4073)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4074,X4072),X4073) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_1791,plain,
! [X5164,X5165,X5166] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5166,X5165)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5166,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5165,X5164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_1792,plain,
! [X3335,X3336,X3337] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3337,X3336)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3337,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3336,X3335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_1793,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,X5179,X5180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_1794,plain,
! [X3338,X3339,X3340] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3340,X3339)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3340,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3338,X3339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_1795,plain,
! [X5174,X5175,X5176] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5176,X5175)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5176,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5175,X5174)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_1796,plain,
! [X3474,X3475,X3476] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3476,X3475)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3476,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3475,X3474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_1797,plain,
! [X5171,X5172,X5173] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5173,X5172)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5173,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5171,X5172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_1798,plain,
! [X3477,X3478,X3479] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3479,X3478)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3479,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3477,X3478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_1799,plain,
! [X3684,X3685,X3686] :
( ~ class_RealVector_Oreal__algebra__1(X3686)
| ~ class_RealVector_Oreal__normed__vector(X3686)
| c_RealVector_Oof__real(X3686,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3685,X3684)) = c_Groups_Ominus__class_Ominus(X3686,c_RealVector_Oof__real(X3686,X3685),c_RealVector_Oof__real(X3686,X3684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Odiff])]) ).
fof(i_0_1800,plain,
! [X3815,X3816,X3817] :
( ~ class_RealVector_Oreal__algebra__1(X3817)
| ~ class_RealVector_Oreal__normed__vector(X3817)
| c_RealVector_Oof__real(X3817,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3816,X3815)) = c_Groups_Oplus__class_Oplus(X3817,c_RealVector_Oof__real(X3817,X3816),c_RealVector_Oof__real(X3817,X3815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Oadd])]) ).
fof(i_0_1801,plain,
! [X4561,X4562] : 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,X4562)),X4561)),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_1802,plain,
! [X4055] :
( ( 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),X4055),X4055))
| X4055 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4055 != 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),X4055),X4055)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1288])]) ).
fof(i_0_1803,plain,
! [X4029,X4030,X4031] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4031),X4030) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4031),X4029)
| X4030 = X4029
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4031) )
& ( X4030 != X4029
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4031),X4030) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4031),X4029)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4031) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_1804,plain,
! [X4694,X4695] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4695)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4695),X4694)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_1805,plain,
! [X5413,X5414,X5415,X5416] :
( ~ class_Rings_Ocomm__semiring__1(X5416)
| ~ c_Rings_Odvd__class_Odvd(X5416,X5415,X5414)
| ~ c_Rings_Odvd__class_Odvd(X5416,X5414,X5413)
| c_Rings_Odvd__class_Odvd(X5416,X5415,X5413) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_1806,plain,
! [X4958,X4959,X4960,X4961] :
( ~ class_Orderings_Opreorder(X4961)
| ~ c_Orderings_Oord__class_Oless__eq(X4961,X4960,X4959)
| ~ c_Orderings_Oord__class_Oless__eq(X4961,X4959,X4958)
| c_Orderings_Oord__class_Oless__eq(X4961,X4960,X4958) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_1807,plain,
! [X4965,X4966,X4967,X4968] :
( ~ class_Orderings_Oorder(X4968)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4967,X4966)
| ~ c_Orderings_Oord__class_Oless__eq(X4968,X4965,X4967)
| c_Orderings_Oord__class_Oless__eq(X4968,X4965,X4966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_1808,plain,
! [X5057,X5058,X5059,X5060] :
( ~ class_Orderings_Opreorder(X5060)
| ~ c_Orderings_Oord__class_Oless(X5060,X5059,X5058)
| ~ c_Orderings_Oord__class_Oless__eq(X5060,X5058,X5057)
| c_Orderings_Oord__class_Oless(X5060,X5059,X5057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_1809,plain,
! [X5049,X5050,X5051,X5052] :
( ~ class_Orderings_Opreorder(X5052)
| ~ c_Orderings_Oord__class_Oless__eq(X5052,X5051,X5050)
| ~ c_Orderings_Oord__class_Oless(X5052,X5050,X5049)
| c_Orderings_Oord__class_Oless(X5052,X5051,X5049) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_1810,plain,
! [X4987,X4988,X4989,X4990] :
( ~ class_Orderings_Opreorder(X4990)
| ~ c_Orderings_Oord__class_Oless(X4990,X4989,X4988)
| ~ c_Orderings_Oord__class_Oless(X4990,X4988,X4987)
| c_Orderings_Oord__class_Oless(X4990,X4989,X4987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_1811,plain,
! [X5053,X5054,X5055,X5056] :
( ~ class_Orderings_Oorder(X5056)
| ~ c_Orderings_Oord__class_Oless(X5056,X5055,X5054)
| ~ c_Orderings_Oord__class_Oless__eq(X5056,X5053,X5055)
| c_Orderings_Oord__class_Oless(X5056,X5053,X5054) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_1812,plain,
! [X5045,X5046,X5047,X5048] :
( ~ class_Orderings_Oorder(X5048)
| ~ c_Orderings_Oord__class_Oless__eq(X5048,X5047,X5046)
| ~ c_Orderings_Oord__class_Oless(X5048,X5045,X5047)
| c_Orderings_Oord__class_Oless(X5048,X5045,X5046) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_1813,plain,
! [X4983,X4984,X4985,X4986] :
( ~ class_Orderings_Oorder(X4986)
| ~ c_Orderings_Oord__class_Oless(X4986,X4985,X4984)
| ~ c_Orderings_Oord__class_Oless(X4986,X4983,X4985)
| c_Orderings_Oord__class_Oless(X4986,X4983,X4984) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_1814,plain,
! [X5262,X5263,X5264] :
( ~ class_Groups_Oab__group__add(X5264)
| c_Groups_Ominus__class_Ominus(X5264,c_Groups_Ouminus__class_Ouminus(X5264,X5263),c_Groups_Ouminus__class_Ouminus(X5264,X5262)) = c_Groups_Ouminus__class_Ouminus(X5264,c_Groups_Ominus__class_Ominus(X5264,X5263,X5262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
fof(i_0_1815,plain,
! [X3650,X3651,X3652] :
( ~ class_Groups_Oab__group__add(X3652)
| c_Groups_Ouminus__class_Ouminus(X3652,c_Groups_Oplus__class_Oplus(X3652,X3651,X3650)) = c_Groups_Oplus__class_Oplus(X3652,c_Groups_Ouminus__class_Ouminus(X3652,X3651),c_Groups_Ouminus__class_Ouminus(X3652,X3650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_1816,plain,
! [X3653,X3654,X3655] :
( ~ class_Groups_Ogroup__add(X3655)
| c_Groups_Ouminus__class_Ouminus(X3655,c_Groups_Oplus__class_Oplus(X3655,X3654,X3653)) = c_Groups_Oplus__class_Oplus(X3655,c_Groups_Ouminus__class_Ouminus(X3655,X3653),c_Groups_Ouminus__class_Ouminus(X3655,X3654)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_1817,plain,
! [X5239] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5239,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5239)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(i_0_1818,plain,
! [X2883,X2884,X2885] :
( ~ class_Rings_Odivision__ring(X2885)
| X2884 = c_Groups_Ozero__class_Ozero(X2885)
| c_Rings_Oinverse__class_Oinverse(X2885,hAPP(hAPP(c_Power_Opower__class_Opower(X2885),X2884),X2883)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2885),c_Rings_Oinverse__class_Oinverse(X2885,X2884)),X2883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse])]) ).
fof(i_0_1819,plain,
! [X3687,X3688,X3689] :
( ~ class_RealVector_Oreal__algebra__1(X3689)
| c_RealVector_Oof__real(X3689,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3688,X3687)) = c_Groups_Ominus__class_Ominus(X3689,c_RealVector_Oof__real(X3689,X3688),c_RealVector_Oof__real(X3689,X3687)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__diff])]) ).
fof(i_0_1820,plain,
! [X3818,X3819,X3820] :
( ~ class_RealVector_Oreal__algebra__1(X3820)
| c_RealVector_Oof__real(X3820,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3819,X3818)) = c_Groups_Oplus__class_Oplus(X3820,c_RealVector_Oof__real(X3820,X3819),c_RealVector_Oof__real(X3820,X3818)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__add])]) ).
fof(i_0_1821,plain,
! [X5276,X5277,X5278] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5278,c_Groups_Ouminus__class_Ouminus(X5278,X5277),c_Groups_Ouminus__class_Ouminus(X5278,X5276))
| c_Orderings_Oord__class_Oless__eq(X5278,X5276,X5277)
| ~ class_Lattices_Oboolean__algebra(X5278) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5278,X5276,X5277)
| c_Orderings_Oord__class_Oless__eq(X5278,c_Groups_Ouminus__class_Ouminus(X5278,X5277),c_Groups_Ouminus__class_Ouminus(X5278,X5276))
| ~ class_Lattices_Oboolean__algebra(X5278) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_1822,plain,
! [X3621,X3622,X3623] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3623,c_Groups_Ouminus__class_Ouminus(X3623,X3622),c_Groups_Ouminus__class_Ouminus(X3623,X3621))
| c_Orderings_Oord__class_Oless__eq(X3623,X3621,X3622)
| ~ class_Groups_Oordered__ab__group__add(X3623) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3623,X3621,X3622)
| c_Orderings_Oord__class_Oless__eq(X3623,c_Groups_Ouminus__class_Ouminus(X3623,X3622),c_Groups_Ouminus__class_Ouminus(X3623,X3621))
| ~ class_Groups_Oordered__ab__group__add(X3623) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
fof(i_0_1823,plain,
! [X3641,X3642,X3643] :
( ( ~ c_Orderings_Oord__class_Oless(X3643,c_Groups_Ouminus__class_Ouminus(X3643,X3642),c_Groups_Ouminus__class_Ouminus(X3643,X3641))
| c_Orderings_Oord__class_Oless(X3643,X3641,X3642)
| ~ class_Groups_Oordered__ab__group__add(X3643) )
& ( ~ c_Orderings_Oord__class_Oless(X3643,X3641,X3642)
| c_Orderings_Oord__class_Oless(X3643,c_Groups_Ouminus__class_Ouminus(X3643,X3642),c_Groups_Ouminus__class_Ouminus(X3643,X3641))
| ~ class_Groups_Oordered__ab__group__add(X3643) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_1824,plain,
! [X3725,X3726,X3727] :
( ~ class_RealVector_Oreal__normed__algebra(X3727)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3727),c_Groups_Ouminus__class_Ouminus(X3727,X3726)),X3725) = c_Groups_Ouminus__class_Ouminus(X3727,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3727),X3726),X3725)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_1825,plain,
! [X3722,X3723,X3724] :
( ~ class_RealVector_Oreal__normed__algebra(X3724)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3724),c_Groups_Ouminus__class_Ouminus(X3724,X3723)),X3722) = c_Groups_Ouminus__class_Ouminus(X3724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3724),X3723),X3722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_1826,plain,
! [X4412,X4413,X4414] :
( ~ class_Rings_Olinordered__idom(X4414)
| c_Groups_Oabs__class_Oabs(X4414,hAPP(hAPP(c_Power_Opower__class_Opower(X4414),X4413),X4412)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4414),c_Groups_Oabs__class_Oabs(X4414,X4413)),X4412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_1827,plain,
! [X3734,X3735,X3736] :
( ~ class_Rings_Oring(X3736)
| c_Groups_Ouminus__class_Ouminus(X3736,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3736),X3735),X3734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3736),c_Groups_Ouminus__class_Ouminus(X3736,X3735)),X3734) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_1828,plain,
! [X2848,X2849,X2850] :
( ~ class_Rings_Odivision__ring__inverse__zero(X2850)
| c_Rings_Oinverse__class_Oinverse(X2850,hAPP(hAPP(c_Power_Opower__class_Opower(X2850),X2849),X2848)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2850),c_Rings_Oinverse__class_Oinverse(X2850,X2849)),X2848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inverse])]) ).
fof(i_0_1829,plain,
! [X4734,X4735,X4736] :
( ~ class_Rings_Ocomm__ring(X4736)
| c_Polynomial_Osmult(X4736,X4735,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4736),X4734)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4736),c_Polynomial_Osmult(X4736,X4735,X4734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__right])]) ).
fof(i_0_1830,plain,
! [X4162,X4163,X4164] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4163,X4164) != X4162
| X4163 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4162,X4164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4164,X4163) )
& ( X4163 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4162,X4164)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4163,X4164) = X4162
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4164,X4163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_1831,plain,
! [X3246,X3247,X3248] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3248)
| c_RealVector_Onorm__class_Onorm(X3248,hAPP(hAPP(c_Power_Opower__class_Opower(X3248),X3247),X3246)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3248,X3247)),X3246) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_1832,plain,
! [X3656,X3657,X3658] :
( ~ class_Groups_Ogroup__add(X3658)
| c_Groups_Oplus__class_Oplus(X3658,X3657,c_Groups_Oplus__class_Oplus(X3658,c_Groups_Ouminus__class_Ouminus(X3658,X3657),X3656)) = X3656 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_1833,plain,
! [X4636,X4637,X4638] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4638,X4637)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4637,X4636)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4638,X4636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_1834,plain,
! [X3295,X3296,X3297] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3297,X3296)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3296,X3295)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3297,X3295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_1835,plain,
! [X3375,X3376,X3377] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3377,X3376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3376,X3375)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3377,X3375) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_1836,plain,
! [X5198,X5199,X5200] :
( ~ class_Rings_Olinordered__idom(X5200)
| ~ c_Polynomial_Opos__poly(X5200,X5199)
| ~ c_Polynomial_Opos__poly(X5200,X5198)
| c_Polynomial_Opos__poly(X5200,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5200)),X5199),X5198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__mult])]) ).
fof(i_0_1837,plain,
! [X5196,X5197] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5197),X5196)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5197)),c_RealDef_Oreal(tc_Nat_Onat,X5196)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
fof(i_0_1838,plain,
! [X3824,X3825,X3826] :
( ~ class_RealVector_Oreal__algebra__1(X3826)
| c_RealVector_Oof__real(X3826,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3825),X3824)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3826),c_RealVector_Oof__real(X3826,X3825)),X3824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__power])]) ).
fof(i_0_1839,plain,
! [X4763,X4764,X4765] :
( ~ class_Rings_Ocomm__ring(X4765)
| hAPP(c_Polynomial_Opoly(X4765,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4765),X4764)),X4763) = c_Groups_Ouminus__class_Ouminus(X4765,hAPP(c_Polynomial_Opoly(X4765,X4764),X4763)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_1840,plain,
! [X4459,X4460,X4461] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4461)
| ~ c_Orderings_Oord__class_Oless__eq(X4461,c_Groups_Oabs__class_Oabs(X4461,X4460),X4459)
| c_Orderings_Oord__class_Oless__eq(X4461,c_Groups_Ouminus__class_Ouminus(X4461,X4460),X4459) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).
fof(i_0_1841,plain,
! [X3624,X3625,X3626] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3626,c_Groups_Ouminus__class_Ouminus(X3626,X3625),X3624)
| c_Orderings_Oord__class_Oless__eq(X3626,c_Groups_Ouminus__class_Ouminus(X3626,X3624),X3625)
| ~ class_Groups_Oordered__ab__group__add(X3626) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3626,c_Groups_Ouminus__class_Ouminus(X3626,X3624),X3625)
| c_Orderings_Oord__class_Oless__eq(X3626,c_Groups_Ouminus__class_Ouminus(X3626,X3625),X3624)
| ~ class_Groups_Oordered__ab__group__add(X3626) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_1842,plain,
! [X3638,X3639,X3640] :
( ( ~ c_Orderings_Oord__class_Oless(X3640,c_Groups_Ouminus__class_Ouminus(X3640,X3639),X3638)
| c_Orderings_Oord__class_Oless(X3640,c_Groups_Ouminus__class_Ouminus(X3640,X3638),X3639)
| ~ class_Groups_Oordered__ab__group__add(X3640) )
& ( ~ c_Orderings_Oord__class_Oless(X3640,c_Groups_Ouminus__class_Ouminus(X3640,X3638),X3639)
| c_Orderings_Oord__class_Oless(X3640,c_Groups_Ouminus__class_Ouminus(X3640,X3639),X3638)
| ~ class_Groups_Oordered__ab__group__add(X3640) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_1843,plain,
! [X3627,X3628,X3629] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3629,X3628,c_Groups_Ouminus__class_Ouminus(X3629,X3627))
| c_Orderings_Oord__class_Oless__eq(X3629,X3627,c_Groups_Ouminus__class_Ouminus(X3629,X3628))
| ~ class_Groups_Oordered__ab__group__add(X3629) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3629,X3627,c_Groups_Ouminus__class_Ouminus(X3629,X3628))
| c_Orderings_Oord__class_Oless__eq(X3629,X3628,c_Groups_Ouminus__class_Ouminus(X3629,X3627))
| ~ class_Groups_Oordered__ab__group__add(X3629) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_1844,plain,
! [X3635,X3636,X3637] :
( ( ~ c_Orderings_Oord__class_Oless(X3637,X3636,c_Groups_Ouminus__class_Ouminus(X3637,X3635))
| c_Orderings_Oord__class_Oless(X3637,X3635,c_Groups_Ouminus__class_Ouminus(X3637,X3636))
| ~ class_Groups_Oordered__ab__group__add(X3637) )
& ( ~ c_Orderings_Oord__class_Oless(X3637,X3635,c_Groups_Ouminus__class_Ouminus(X3637,X3636))
| c_Orderings_Oord__class_Oless(X3637,X3636,c_Groups_Ouminus__class_Ouminus(X3637,X3635))
| ~ class_Groups_Oordered__ab__group__add(X3637) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_1845,plain,
! [X5205,X5206] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5206,X5205)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5206),c_RealDef_Oreal(tc_Nat_Onat,X5205)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_1846,plain,
! [X4619,X4620] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4620,X4619)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4620),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4619)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_1847,plain,
! [X4802,X4803,X4804] :
( ~ class_Groups_Oab__group__add(X4804)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4804),c_Polynomial_Omonom(X4804,X4803,X4802)) = c_Polynomial_Omonom(X4804,c_Groups_Ouminus__class_Ouminus(X4804,X4803),X4802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__monom])]) ).
fof(i_0_1848,plain,
! [X4791,X4792,X4793] :
( ~ class_Rings_Ocomm__ring(X4793)
| c_Polynomial_Osmult(X4793,c_Groups_Ouminus__class_Ouminus(X4793,X4792),X4791) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4793),c_Polynomial_Osmult(X4793,X4792,X4791)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__left])]) ).
fof(i_0_1849,plain,
! [X5291,X5292,X5293] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5293)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5293),X5292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5293),X5292),X5291)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5293),X5292),X5291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_1850,plain,
! [X4514] : 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,X4514))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(i_0_1851,plain,
! [X4128,X4129] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4129,X4128)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4128,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4129,X4128)) = X4129 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1289])]) ).
fof(i_0_1852,plain,
! [X3515,X3516] :
( ~ class_Fields_Olinordered__field(X3516)
| ~ c_Orderings_Oord__class_Oless(X3516,c_Groups_Ozero__class_Ozero(X3516),c_Rings_Oinverse__class_Oinverse(X3516,X3515))
| X3515 = c_Groups_Ozero__class_Ozero(X3516)
| c_Orderings_Oord__class_Oless(X3516,c_Groups_Ozero__class_Ozero(X3516),X3515) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).
fof(i_0_1853,plain,
! [X3525,X3526] :
( ~ class_Fields_Olinordered__field(X3526)
| ~ c_Orderings_Oord__class_Oless(X3526,c_Rings_Oinverse__class_Oinverse(X3526,X3525),c_Groups_Ozero__class_Ozero(X3526))
| X3525 = c_Groups_Ozero__class_Ozero(X3526)
| c_Orderings_Oord__class_Oless(X3526,X3525,c_Groups_Ozero__class_Ozero(X3526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).
fof(i_0_1854,plain,
! [X5217,X5218] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5218),c_RealDef_Oreal(tc_Nat_Onat,X5217))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5218,X5217) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5218,X5217)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5218),c_RealDef_Oreal(tc_Nat_Onat,X5217)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_1855,plain,
! [X5191,X5192] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5192),c_RealDef_Oreal(tc_Nat_Onat,X5191))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5192,X5191) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5192,X5191)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5192),c_RealDef_Oreal(tc_Nat_Onat,X5191)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_1856,plain,
! [X3757,X3758] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3758,c_Groups_Ouminus__class_Ouminus(X3758,X3757),c_Groups_Ozero__class_Ozero(X3758))
| c_Orderings_Oord__class_Oless__eq(X3758,c_Groups_Ozero__class_Ozero(X3758),X3757)
| ~ class_Groups_Oordered__ab__group__add(X3758) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3758,c_Groups_Ozero__class_Ozero(X3758),X3757)
| c_Orderings_Oord__class_Oless__eq(X3758,c_Groups_Ouminus__class_Ouminus(X3758,X3757),c_Groups_Ozero__class_Ozero(X3758))
| ~ class_Groups_Oordered__ab__group__add(X3758) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_1857,plain,
! [X3763,X3764] :
( ( ~ c_Orderings_Oord__class_Oless(X3764,c_Groups_Ouminus__class_Ouminus(X3764,X3763),c_Groups_Ozero__class_Ozero(X3764))
| c_Orderings_Oord__class_Oless(X3764,c_Groups_Ozero__class_Ozero(X3764),X3763)
| ~ class_Groups_Oordered__ab__group__add(X3764) )
& ( ~ c_Orderings_Oord__class_Oless(X3764,c_Groups_Ozero__class_Ozero(X3764),X3763)
| c_Orderings_Oord__class_Oless(X3764,c_Groups_Ouminus__class_Ouminus(X3764,X3763),c_Groups_Ozero__class_Ozero(X3764))
| ~ class_Groups_Oordered__ab__group__add(X3764) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_1858,plain,
! [X3507,X3508] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3508,c_Groups_Ozero__class_Ozero(X3508),c_Rings_Oinverse__class_Oinverse(X3508,X3507))
| c_Orderings_Oord__class_Oless__eq(X3508,c_Groups_Ozero__class_Ozero(X3508),X3507)
| ~ class_Fields_Olinordered__field__inverse__zero(X3508) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3508,c_Groups_Ozero__class_Ozero(X3508),X3507)
| c_Orderings_Oord__class_Oless__eq(X3508,c_Groups_Ozero__class_Ozero(X3508),c_Rings_Oinverse__class_Oinverse(X3508,X3507))
| ~ class_Fields_Olinordered__field__inverse__zero(X3508) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative])])]) ).
fof(i_0_1859,plain,
! [X3509,X3510] :
( ( ~ c_Orderings_Oord__class_Oless(X3510,c_Groups_Ozero__class_Ozero(X3510),c_Rings_Oinverse__class_Oinverse(X3510,X3509))
| c_Orderings_Oord__class_Oless(X3510,c_Groups_Ozero__class_Ozero(X3510),X3509)
| ~ class_Fields_Olinordered__field__inverse__zero(X3510) )
& ( ~ c_Orderings_Oord__class_Oless(X3510,c_Groups_Ozero__class_Ozero(X3510),X3509)
| c_Orderings_Oord__class_Oless(X3510,c_Groups_Ozero__class_Ozero(X3510),c_Rings_Oinverse__class_Oinverse(X3510,X3509))
| ~ class_Fields_Olinordered__field__inverse__zero(X3510) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).
fof(i_0_1860,plain,
! [X5308,X5309] :
( ( ~ c_Orderings_Oord__class_Oless(X5309,c_Groups_Ozero__class_Ozero(X5309),c_Groups_Osgn__class_Osgn(X5309,X5308))
| c_Orderings_Oord__class_Oless(X5309,c_Groups_Ozero__class_Ozero(X5309),X5308)
| ~ class_Rings_Olinordered__idom(X5309) )
& ( ~ c_Orderings_Oord__class_Oless(X5309,c_Groups_Ozero__class_Ozero(X5309),X5308)
| c_Orderings_Oord__class_Oless(X5309,c_Groups_Ozero__class_Ozero(X5309),c_Groups_Osgn__class_Osgn(X5309,X5308))
| ~ class_Rings_Olinordered__idom(X5309) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).
fof(i_0_1861,plain,
! [X3505,X3506] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3506,c_Rings_Oinverse__class_Oinverse(X3506,X3505),c_Groups_Ozero__class_Ozero(X3506))
| c_Orderings_Oord__class_Oless__eq(X3506,X3505,c_Groups_Ozero__class_Ozero(X3506))
| ~ class_Fields_Olinordered__field__inverse__zero(X3506) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3506,X3505,c_Groups_Ozero__class_Ozero(X3506))
| c_Orderings_Oord__class_Oless__eq(X3506,c_Rings_Oinverse__class_Oinverse(X3506,X3505),c_Groups_Ozero__class_Ozero(X3506))
| ~ class_Fields_Olinordered__field__inverse__zero(X3506) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive])])]) ).
fof(i_0_1862,plain,
! [X3511,X3512] :
( ( ~ c_Orderings_Oord__class_Oless(X3512,c_Rings_Oinverse__class_Oinverse(X3512,X3511),c_Groups_Ozero__class_Ozero(X3512))
| c_Orderings_Oord__class_Oless(X3512,X3511,c_Groups_Ozero__class_Ozero(X3512))
| ~ class_Fields_Olinordered__field__inverse__zero(X3512) )
& ( ~ c_Orderings_Oord__class_Oless(X3512,X3511,c_Groups_Ozero__class_Ozero(X3512))
| c_Orderings_Oord__class_Oless(X3512,c_Rings_Oinverse__class_Oinverse(X3512,X3511),c_Groups_Ozero__class_Ozero(X3512))
| ~ class_Fields_Olinordered__field__inverse__zero(X3512) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).
fof(i_0_1863,plain,
! [X5310,X5311] :
( ( ~ c_Orderings_Oord__class_Oless(X5311,c_Groups_Osgn__class_Osgn(X5311,X5310),c_Groups_Ozero__class_Ozero(X5311))
| c_Orderings_Oord__class_Oless(X5311,X5310,c_Groups_Ozero__class_Ozero(X5311))
| ~ class_Rings_Olinordered__idom(X5311) )
& ( ~ c_Orderings_Oord__class_Oless(X5311,X5310,c_Groups_Ozero__class_Ozero(X5311))
| c_Orderings_Oord__class_Oless(X5311,c_Groups_Osgn__class_Osgn(X5311,X5310),c_Groups_Ozero__class_Ozero(X5311))
| ~ class_Rings_Olinordered__idom(X5311) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).
fof(i_0_1864,plain,
! [X3753,X3754] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3754,c_Groups_Ozero__class_Ozero(X3754),c_Groups_Ouminus__class_Ouminus(X3754,X3753))
| c_Orderings_Oord__class_Oless__eq(X3754,X3753,c_Groups_Ozero__class_Ozero(X3754))
| ~ class_Groups_Oordered__ab__group__add(X3754) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3754,X3753,c_Groups_Ozero__class_Ozero(X3754))
| c_Orderings_Oord__class_Oless__eq(X3754,c_Groups_Ozero__class_Ozero(X3754),c_Groups_Ouminus__class_Ouminus(X3754,X3753))
| ~ class_Groups_Oordered__ab__group__add(X3754) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_1865,plain,
! [X3765,X3766] :
( ( ~ c_Orderings_Oord__class_Oless(X3766,c_Groups_Ozero__class_Ozero(X3766),c_Groups_Ouminus__class_Ouminus(X3766,X3765))
| c_Orderings_Oord__class_Oless(X3766,X3765,c_Groups_Ozero__class_Ozero(X3766))
| ~ class_Groups_Oordered__ab__group__add(X3766) )
& ( ~ c_Orderings_Oord__class_Oless(X3766,X3765,c_Groups_Ozero__class_Ozero(X3766))
| c_Orderings_Oord__class_Oless(X3766,c_Groups_Ozero__class_Ozero(X3766),c_Groups_Ouminus__class_Ouminus(X3766,X3765))
| ~ class_Groups_Oordered__ab__group__add(X3766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_1866,plain,
! [X5097,X5098,X5099] :
( ( c_Orderings_Oord__class_Oless__eq(X5099,X5098,X5097)
| ~ c_Orderings_Oord__class_Oless(X5099,X5098,X5097)
| ~ class_Orderings_Opreorder(X5099) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5099,X5097,X5098)
| ~ c_Orderings_Oord__class_Oless(X5099,X5098,X5097)
| ~ class_Orderings_Opreorder(X5099) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5099,X5098,X5097)
| c_Orderings_Oord__class_Oless__eq(X5099,X5097,X5098)
| c_Orderings_Oord__class_Oless(X5099,X5098,X5097)
| ~ class_Orderings_Opreorder(X5099) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])])]) ).
fof(i_0_1867,plain,
! [X3731,X3732,X3733] :
( ~ class_RealVector_Oreal__normed__algebra(X3733)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3733),X3732),c_Groups_Ouminus__class_Ouminus(X3733,X3731)) = c_Groups_Ouminus__class_Ouminus(X3733,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3733),X3732),X3731)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_1868,plain,
! [X3728,X3729,X3730] :
( ~ class_RealVector_Oreal__normed__algebra(X3730)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3730),X3729),c_Groups_Ouminus__class_Ouminus(X3730,X3728)) = c_Groups_Ouminus__class_Ouminus(X3730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3730),X3729),X3728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_1869,plain,
! [X3737,X3738,X3739] :
( ~ class_Rings_Oring(X3739)
| c_Groups_Ouminus__class_Ouminus(X3739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3739),X3738),X3737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3739),X3738),c_Groups_Ouminus__class_Ouminus(X3739,X3737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_1870,plain,
! [X5279,X5280,X5281] :
( ~ class_Lattices_Oboolean__algebra(X5281)
| ~ c_Orderings_Oord__class_Oless__eq(X5281,X5280,X5279)
| c_Orderings_Oord__class_Oless__eq(X5281,c_Groups_Ouminus__class_Ouminus(X5281,X5279),c_Groups_Ouminus__class_Ouminus(X5281,X5280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_1871,plain,
! [X3618,X3619,X3620] :
( ~ class_Groups_Oordered__ab__group__add(X3620)
| ~ c_Orderings_Oord__class_Oless__eq(X3620,X3619,X3618)
| c_Orderings_Oord__class_Oless__eq(X3620,c_Groups_Ouminus__class_Ouminus(X3620,X3618),c_Groups_Ouminus__class_Ouminus(X3620,X3619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
fof(i_0_1872,plain,
! [X2811] :
( ~ class_Rings_Olinordered__semidom(X2811)
| c_Orderings_Oord__class_Oless(X2811,c_Groups_Ozero__class_Ozero(X2811),c_Groups_Oplus__class_Oplus(X2811,c_Groups_Oone__class_Oone(X2811),c_Groups_Oone__class_Oone(X2811))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_1873,plain,
! [X5242] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5242,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5242))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(i_0_1874,plain,
! [X3659,X3660,X3661] :
( ~ class_Groups_Ogroup__add(X3661)
| c_Groups_Oplus__class_Oplus(X3661,c_Groups_Ouminus__class_Ouminus(X3661,X3660),c_Groups_Oplus__class_Oplus(X3661,X3660,X3659)) = X3659 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_1875,plain,
! [X3759,X3760] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3760,c_Groups_Ouminus__class_Ouminus(X3760,X3759),X3759)
| c_Orderings_Oord__class_Oless__eq(X3760,c_Groups_Ozero__class_Ozero(X3760),X3759)
| ~ class_Groups_Olinordered__ab__group__add(X3760) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3760,c_Groups_Ozero__class_Ozero(X3760),X3759)
| c_Orderings_Oord__class_Oless__eq(X3760,c_Groups_Ouminus__class_Ouminus(X3760,X3759),X3759)
| ~ class_Groups_Olinordered__ab__group__add(X3760) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_1876,plain,
! [X3761,X3762] :
( ( ~ c_Orderings_Oord__class_Oless(X3762,c_Groups_Ouminus__class_Ouminus(X3762,X3761),X3761)
| c_Orderings_Oord__class_Oless(X3762,c_Groups_Ozero__class_Ozero(X3762),X3761)
| ~ class_Groups_Olinordered__ab__group__add(X3762) )
& ( ~ c_Orderings_Oord__class_Oless(X3762,c_Groups_Ozero__class_Ozero(X3762),X3761)
| c_Orderings_Oord__class_Oless(X3762,c_Groups_Ouminus__class_Ouminus(X3762,X3761),X3761)
| ~ class_Groups_Olinordered__ab__group__add(X3762) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_1877,plain,
! [X3755,X3756] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3756,X3755,c_Groups_Ouminus__class_Ouminus(X3756,X3755))
| c_Orderings_Oord__class_Oless__eq(X3756,X3755,c_Groups_Ozero__class_Ozero(X3756))
| ~ class_Groups_Olinordered__ab__group__add(X3756) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3756,X3755,c_Groups_Ozero__class_Ozero(X3756))
| c_Orderings_Oord__class_Oless__eq(X3756,X3755,c_Groups_Ouminus__class_Ouminus(X3756,X3755))
| ~ class_Groups_Olinordered__ab__group__add(X3756) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_1878,plain,
! [X3779,X3780] :
( ( ~ c_Orderings_Oord__class_Oless(X3780,X3779,c_Groups_Ouminus__class_Ouminus(X3780,X3779))
| c_Orderings_Oord__class_Oless(X3780,X3779,c_Groups_Ozero__class_Ozero(X3780))
| ~ class_Rings_Olinordered__idom(X3780) )
& ( ~ c_Orderings_Oord__class_Oless(X3780,X3779,c_Groups_Ozero__class_Ozero(X3780))
| c_Orderings_Oord__class_Oless(X3780,X3779,c_Groups_Ouminus__class_Ouminus(X3780,X3779))
| ~ class_Rings_Olinordered__idom(X3780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_1879,plain,
! [X4609,X4610] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4610)),X4609) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4610),X4609)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_1880,plain,
! [X3829,X3830] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X3830)),X3829) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X3830),X3829)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__power]) ).
fof(i_0_1881,plain,
! [X5208,X5209] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5209)),X5208) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5209),X5208)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_1882,plain,
! [X5210,X5211] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5211),X5210)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5211)),X5210),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
fof(i_0_1883,plain,
! [X3384,X3385,X3386] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3386)
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| X3386 = X3385
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,X3385) )
& ( ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| X3386 = X3385
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,X3385) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3386)
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,X3385) )
& ( ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,X3385) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3386)
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| X3386 = X3385
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386)) )
& ( ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| X3386 = X3385
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3385,X3386)
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386)) )
& ( ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386))
| ~ hBOOL(hAPP(hAPP(X3384,X3385),X3386)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_1884,plain,
! [X3517,X3518] :
( ~ class_Fields_Olinordered__field(X3518)
| ~ c_Orderings_Oord__class_Oless(X3518,X3517,c_Groups_Ozero__class_Ozero(X3518))
| c_Orderings_Oord__class_Oless(X3518,c_Rings_Oinverse__class_Oinverse(X3518,X3517),c_Groups_Ozero__class_Ozero(X3518)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).
fof(i_0_1885,plain,
! [X3513,X3514] :
( ~ class_Fields_Olinordered__field(X3514)
| ~ c_Orderings_Oord__class_Oless(X3514,c_Groups_Ozero__class_Ozero(X3514),X3513)
| c_Orderings_Oord__class_Oless(X3514,c_Groups_Ozero__class_Ozero(X3514),c_Rings_Oinverse__class_Oinverse(X3514,X3513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).
fof(i_0_1886,plain,
! [X4852,X4853,X4854,X4855] :
( ~ class_Rings_Ocomm__semiring__0(X4855)
| c_Polynomial_Osmult(X4855,X4854,X4853) != c_Polynomial_OpCons(X4855,X4852,X4853)
| X4853 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
fof(i_0_1887,plain,
! [X4401,X4402] :
( ~ class_Rings_Olinordered__idom(X4402)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4402),c_Groups_Oabs__class_Oabs(X4402,X4401)),c_Groups_Oabs__class_Oabs(X4402,X4401)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4402),X4401),X4401) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_1888,plain,
! [X3716,X3717,X3718] :
( ~ class_Rings_Oring(X3718)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3718),c_Groups_Ouminus__class_Ouminus(X3718,X3717)),c_Groups_Ouminus__class_Ouminus(X3718,X3716)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3718),X3717),X3716) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_1889,plain,
! [X3719,X3720,X3721] :
( ~ class_Rings_Oring(X3721)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3721),c_Groups_Ouminus__class_Ouminus(X3721,X3720)),X3719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3721),X3720),c_Groups_Ouminus__class_Ouminus(X3721,X3719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_1890,plain,
! [X5360,X5361,X5362] :
( ( ~ c_Rings_Odvd__class_Odvd(X5362,c_Groups_Ouminus__class_Ouminus(X5362,X5361),X5360)
| c_Rings_Odvd__class_Odvd(X5362,X5361,X5360)
| ~ class_Rings_Ocomm__ring__1(X5362) )
& ( ~ c_Rings_Odvd__class_Odvd(X5362,X5361,X5360)
| c_Rings_Odvd__class_Odvd(X5362,c_Groups_Ouminus__class_Ouminus(X5362,X5361),X5360)
| ~ class_Rings_Ocomm__ring__1(X5362) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_1891,plain,
! [X5392,X5393,X5394] :
( ( ~ c_Rings_Odvd__class_Odvd(X5394,c_Groups_Oabs__class_Oabs(X5394,X5393),X5392)
| c_Rings_Odvd__class_Odvd(X5394,X5393,X5392)
| ~ class_Rings_Olinordered__idom(X5394) )
& ( ~ c_Rings_Odvd__class_Odvd(X5394,X5393,X5392)
| c_Rings_Odvd__class_Odvd(X5394,c_Groups_Oabs__class_Oabs(X5394,X5393),X5392)
| ~ class_Rings_Olinordered__idom(X5394) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff])])]) ).
fof(i_0_1892,plain,
! [X4395,X4396,X4397] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4397)
| ~ c_Orderings_Oord__class_Oless__eq(X4397,c_Groups_Oabs__class_Oabs(X4397,X4396),X4395)
| c_Orderings_Oord__class_Oless__eq(X4397,X4396,X4395) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_1893,plain,
! [X5363,X5364,X5365] :
( ( ~ c_Rings_Odvd__class_Odvd(X5365,X5364,c_Groups_Ouminus__class_Ouminus(X5365,X5363))
| c_Rings_Odvd__class_Odvd(X5365,X5364,X5363)
| ~ class_Rings_Ocomm__ring__1(X5365) )
& ( ~ c_Rings_Odvd__class_Odvd(X5365,X5364,X5363)
| c_Rings_Odvd__class_Odvd(X5365,X5364,c_Groups_Ouminus__class_Ouminus(X5365,X5363))
| ~ class_Rings_Ocomm__ring__1(X5365) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_1894,plain,
! [X5395,X5396,X5397] :
( ( ~ c_Rings_Odvd__class_Odvd(X5397,X5396,c_Groups_Oabs__class_Oabs(X5397,X5395))
| c_Rings_Odvd__class_Odvd(X5397,X5396,X5395)
| ~ class_Rings_Olinordered__idom(X5397) )
& ( ~ c_Rings_Odvd__class_Odvd(X5397,X5396,X5395)
| c_Rings_Odvd__class_Odvd(X5397,X5396,c_Groups_Oabs__class_Oabs(X5397,X5395))
| ~ class_Rings_Olinordered__idom(X5397) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff])])]) ).
fof(i_0_1895,plain,
! [X3713,X3714,X3715] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3714),X3714) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3713),X3713)
| X3714 = X3713
| X3714 = c_Groups_Ouminus__class_Ouminus(X3715,X3713)
| ~ class_Rings_Oidom(X3715) )
& ( X3714 != X3713
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3714),X3714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3713),X3713)
| ~ class_Rings_Oidom(X3715) )
& ( X3714 != c_Groups_Ouminus__class_Ouminus(X3715,X3713)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3714),X3714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3715),X3713),X3713)
| ~ class_Rings_Oidom(X3715) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_1896,plain,
! [X5193,X5194,X5195] :
( ~ class_Rings_Olinordered__idom(X5195)
| ~ c_Polynomial_Opos__poly(X5195,X5194)
| ~ c_Polynomial_Opos__poly(X5195,X5193)
| c_Polynomial_Opos__poly(X5195,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5195),X5194,X5193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])]) ).
fof(i_0_1897,plain,
! [X3676,X3677,X3678,X3679,X3680] :
( ( X3679 != X3678
| X3677 = X3676
| c_Groups_Ominus__class_Ominus(X3680,X3679,X3678) != c_Groups_Ominus__class_Ominus(X3680,X3677,X3676)
| ~ class_Groups_Oab__group__add(X3680) )
& ( X3677 != X3676
| X3679 = X3678
| c_Groups_Ominus__class_Ominus(X3680,X3679,X3678) != c_Groups_Ominus__class_Ominus(X3680,X3677,X3676)
| ~ class_Groups_Oab__group__add(X3680) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_1898,plain,
! [X5226,X5227] :
( X5227 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5227))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5227),X5226)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5227)),X5226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_1899,plain,
! [X5070,X5071,X5072] :
( ( c_Orderings_Oord__class_Oless(X5072,X5071,X5070)
| X5071 = X5070
| ~ c_Orderings_Oord__class_Oless__eq(X5072,X5071,X5070)
| ~ class_Orderings_Olinorder(X5072) )
& ( X5071 != X5070
| ~ c_Orderings_Oord__class_Oless(X5072,X5071,X5070)
| ~ c_Orderings_Oord__class_Oless__eq(X5072,X5071,X5070)
| ~ class_Orderings_Olinorder(X5072) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1291])])]) ).
fof(i_0_1900,plain,
! [X3664,X3665,X3666] :
( ~ class_Groups_Oab__group__add(X3666)
| c_Groups_Ouminus__class_Ouminus(X3666,c_Groups_Ominus__class_Ominus(X3666,X3665,X3664)) = c_Groups_Ominus__class_Ominus(X3666,X3664,X3665) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_1901,plain,
! [X4962,X4963,X4964] :
( ~ class_Orderings_Oorder(X4964)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4963,X4962)
| ~ c_Orderings_Oord__class_Oless__eq(X4964,X4962,X4963)
| X4962 = X4963 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_1902,plain,
! [X4955,X4956,X4957] :
( ~ class_Orderings_Oorder(X4957)
| ~ c_Orderings_Oord__class_Oless__eq(X4957,X4956,X4955)
| ~ c_Orderings_Oord__class_Oless__eq(X4957,X4955,X4956)
| X4956 = X4955 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_1903,plain,
! [X4936,X4937,X4938] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4938,X4936,X4937)
| X4936 = X4937
| ~ c_Orderings_Oord__class_Oless__eq(X4938,X4937,X4936)
| ~ class_Orderings_Oorder(X4938) )
& ( X4936 != X4937
| c_Orderings_Oord__class_Oless__eq(X4938,X4936,X4937)
| ~ c_Orderings_Oord__class_Oless__eq(X4938,X4937,X4936)
| ~ class_Orderings_Oorder(X4938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_1904,plain,
! [X4925,X4926,X4927] :
( ( c_Orderings_Oord__class_Oless__eq(X4927,X4926,X4925)
| X4926 != X4925
| ~ class_Orderings_Oorder(X4927) )
& ( c_Orderings_Oord__class_Oless__eq(X4927,X4925,X4926)
| X4926 != X4925
| ~ class_Orderings_Oorder(X4927) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4927,X4926,X4925)
| ~ c_Orderings_Oord__class_Oless__eq(X4927,X4925,X4926)
| X4926 = X4925
| ~ class_Orderings_Oorder(X4927) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_1905,plain,
! [X5228] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5228))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5228) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5228)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5228)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_1906,plain,
! [X3208,X3209] :
( ~ class_Rings_Olinordered__semidom(X3209)
| c_Orderings_Oord__class_Oless(X3209,X3208,c_Groups_Oplus__class_Oplus(X3209,X3208,c_Groups_Oone__class_Oone(X3209))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_1907,plain,
! [X4725,X4726,X4727,X4728,X4729] :
( ( X4728 = X4726
| c_Polynomial_OpCons(X4729,X4728,X4727) != c_Polynomial_OpCons(X4729,X4726,X4725)
| ~ class_Groups_Ozero(X4729) )
& ( X4727 = X4725
| c_Polynomial_OpCons(X4729,X4728,X4727) != c_Polynomial_OpCons(X4729,X4726,X4725)
| ~ class_Groups_Ozero(X4729) )
& ( X4728 != X4726
| X4727 != X4725
| c_Polynomial_OpCons(X4729,X4728,X4727) = c_Polynomial_OpCons(X4729,X4726,X4725)
| ~ class_Groups_Ozero(X4729) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
fof(i_0_1908,plain,
! [X4749,X4750,X4751,X4752] :
( ( c_Polynomial_Omonom(X4752,X4751,X4750) != c_Polynomial_Omonom(X4752,X4749,X4750)
| X4751 = X4749
| ~ class_Groups_Ozero(X4752) )
& ( X4751 != X4749
| c_Polynomial_Omonom(X4752,X4751,X4750) = c_Polynomial_Omonom(X4752,X4749,X4750)
| ~ class_Groups_Ozero(X4752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__iff])])]) ).
fof(i_0_1909,plain,
! [X3886,X3887,X3888,X3889] :
( ( c_Groups_Oplus__class_Oplus(X3889,X3888,X3887) != c_Groups_Oplus__class_Oplus(X3889,X3886,X3887)
| X3888 = X3886
| ~ class_Groups_Ocancel__semigroup__add(X3889) )
& ( X3888 != X3886
| c_Groups_Oplus__class_Oplus(X3889,X3888,X3887) = c_Groups_Oplus__class_Oplus(X3889,X3886,X3887)
| ~ class_Groups_Ocancel__semigroup__add(X3889) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_1910,plain,
! [X3874,X3875,X3876,X3877] :
( ~ class_Groups_Ocancel__semigroup__add(X3877)
| c_Groups_Oplus__class_Oplus(X3877,X3876,X3875) != c_Groups_Oplus__class_Oplus(X3877,X3874,X3875)
| X3876 = X3874 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_1911,plain,
! [X3878,X3879,X3880,X3881] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3881)
| c_Groups_Oplus__class_Oplus(X3881,X3880,X3879) != c_Groups_Oplus__class_Oplus(X3881,X3880,X3878)
| X3879 = X3878 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_1912,plain,
! [X3890,X3891,X3892,X3893] :
( ( c_Groups_Oplus__class_Oplus(X3893,X3892,X3891) != c_Groups_Oplus__class_Oplus(X3893,X3892,X3890)
| X3891 = X3890
| ~ class_Groups_Ocancel__semigroup__add(X3893) )
& ( X3891 != X3890
| c_Groups_Oplus__class_Oplus(X3893,X3892,X3891) = c_Groups_Oplus__class_Oplus(X3893,X3892,X3890)
| ~ class_Groups_Ocancel__semigroup__add(X3893) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_1913,plain,
! [X3882,X3883,X3884,X3885] :
( ~ class_Groups_Ocancel__semigroup__add(X3885)
| c_Groups_Oplus__class_Oplus(X3885,X3884,X3883) != c_Groups_Oplus__class_Oplus(X3885,X3884,X3882)
| X3883 = X3882 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_1914,plain,
! [X4564,X4565] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4565),X4564)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4565) = 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_1915,plain,
! [X5007,X5008,X5009] :
( ~ class_Orderings_Oorder(X5009)
| ~ c_Orderings_Oord__class_Oless(X5009,X5008,X5007)
| ~ c_Orderings_Oord__class_Oless(X5009,X5007,X5008) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1292])]) ).
fof(i_0_1916,plain,
! [X5106,X5107,X5108] :
( ( c_Orderings_Oord__class_Oless__eq(X5108,X5107,X5106)
| c_Orderings_Oord__class_Oless(X5108,X5106,X5107)
| ~ class_Orderings_Olinorder(X5108) )
& ( ~ c_Orderings_Oord__class_Oless(X5108,X5106,X5107)
| ~ c_Orderings_Oord__class_Oless__eq(X5108,X5107,X5106)
| ~ class_Orderings_Olinorder(X5108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1293])])]) ).
fof(i_0_1917,plain,
! [X5109,X5110,X5111] :
( ( c_Orderings_Oord__class_Oless(X5111,X5110,X5109)
| c_Orderings_Oord__class_Oless__eq(X5111,X5109,X5110)
| ~ class_Orderings_Olinorder(X5111) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5111,X5109,X5110)
| ~ c_Orderings_Oord__class_Oless(X5111,X5110,X5109)
| ~ class_Orderings_Olinorder(X5111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1294])])]) ).
fof(i_0_1918,plain,
! [X5076,X5077,X5078] :
( ~ class_Orderings_Olinorder(X5078)
| ~ c_Orderings_Oord__class_Oless__eq(X5078,X5077,X5076)
| ~ c_Orderings_Oord__class_Oless(X5078,X5076,X5077) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1295])]) ).
fof(i_0_1919,plain,
! [X5037,X5038,X5039] :
( ( c_Orderings_Oord__class_Oless(X5039,X5038,X5037)
| c_Orderings_Oord__class_Oless(X5039,X5037,X5038)
| X5038 = X5037
| ~ class_Orderings_Olinorder(X5039) )
& ( ~ c_Orderings_Oord__class_Oless(X5039,X5037,X5038)
| ~ c_Orderings_Oord__class_Oless(X5039,X5038,X5037)
| ~ class_Orderings_Olinorder(X5039) )
& ( X5038 != X5037
| ~ c_Orderings_Oord__class_Oless(X5039,X5038,X5037)
| ~ class_Orderings_Olinorder(X5039) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1296])])]) ).
fof(i_0_1920,plain,
! [X5022,X5023,X5024] :
( ~ class_Orderings_Opreorder(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_1297])]) ).
fof(i_0_1921,plain,
! [X5019,X5020,X5021] :
( ~ class_Orderings_Opreorder(X5021)
| ~ c_Orderings_Oord__class_Oless(X5021,X5020,X5019)
| ~ c_Orderings_Oord__class_Oless(X5021,X5019,X5020) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1298])]) ).
fof(i_0_1922,plain,
! [X5010,X5011,X5012] :
( ~ class_Orderings_Opreorder(X5012)
| ~ c_Orderings_Oord__class_Oless(X5012,X5011,X5010)
| ~ c_Orderings_Oord__class_Oless(X5012,X5010,X5011) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1299])]) ).
fof(i_0_1923,plain,
! [X4980,X4981,X4982] :
( ~ class_Orderings_Opreorder(X4982)
| ~ c_Orderings_Oord__class_Oless(X4982,X4981,X4980)
| ~ c_Orderings_Oord__class_Oless(X4982,X4980,X4981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1300])]) ).
fof(i_0_1924,plain,
! [X5224,X5225] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5225,c_RealDef_Oreal(tc_Nat_Onat,X5224))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5225),X5224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_1925,plain,
! [X5222,X5223] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5223),X5222)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5223,c_RComplete_Onatfloor(X5222)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
fof(i_0_1926,plain,
! [X4911,X4912,X4913] :
( ( hAPP(c_Polynomial_Opoly(X4913,X4912),X4911) != c_Groups_Ozero__class_Ozero(X4913)
| X4912 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4913))
| c_Polynomial_Oorder(X4913,X4911,X4912) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X4913) )
& ( X4912 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4913))
| hAPP(c_Polynomial_Opoly(X4913,X4912),X4911) = c_Groups_Ozero__class_Ozero(X4913)
| ~ class_Rings_Oidom(X4913) )
& ( c_Polynomial_Oorder(X4913,X4911,X4912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X4913,X4912),X4911) = c_Groups_Ozero__class_Ozero(X4913)
| ~ class_Rings_Oidom(X4913) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_1927,plain,
! [X4064,X4065] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4065,X4064) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4064,X4065) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4065 = X4064 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_1928,plain,
! [X5221] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5221)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5221)),X5221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
fof(i_0_1929,plain,
! [X5306,X5307] :
( ( X5306 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307))
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5307),X5306) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307))
| ~ class_Rings_Olinordered__idom(X5307) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5307),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307)),X5306)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5307),X5306) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5307))
| X5306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307))
| ~ class_Rings_Olinordered__idom(X5307) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5307),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307)),X5306)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5307),X5306) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5307),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5307)))
| X5306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5307))
| ~ class_Rings_Olinordered__idom(X5307) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1301])])]) ).
fof(i_0_1930,plain,
! [X4711,X4712] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4712),X4711,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4712)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4712),X4711) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4712),X4711)
| ~ class_Rings_Olinordered__idom(X4712) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4712),X4711,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4712)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4712),X4711) = X4711
| ~ class_Rings_Olinordered__idom(X4712) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1302])])]) ).
fof(i_0_1931,plain,
! [X2943,X2944] :
( ~ class_Rings_Olinordered__ring(X2944)
| c_Orderings_Oord__class_Oless__eq(X2944,c_Groups_Ozero__class_Ozero(X2944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2944),X2943),X2943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_1932,plain,
! [X4639,X4640] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4640,X4639)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4639,X4640)
| X4640 = X4639 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_1933,plain,
! [X3298,X3299] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3299,X3298)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3298,X3299)
| X3299 = X3298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_1934,plain,
! [X3373,X3374] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3374,X3373)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3373,X3374)
| X3374 = X3373 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_1935,plain,
! [X3647,X3648,X3649] :
( ~ class_Groups_Ogroup__add(X3649)
| c_Groups_Ominus__class_Ominus(X3649,c_Groups_Oplus__class_Oplus(X3649,X3648,X3647),X3647) = X3648 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_1936,plain,
! [X3644,X3645,X3646] :
( ~ class_Groups_Ogroup__add(X3646)
| c_Groups_Oplus__class_Oplus(X3646,c_Groups_Ominus__class_Ominus(X3646,X3645,X3644),X3644) = X3645 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_1937,plain,
! [X4580,X4581] :
( ( X4581 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4581),X4580) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4581) )
& ( X4580 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4581),X4580) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4581) )
& ( X4581 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4580 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4581),X4580) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4581) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
fof(i_0_1938,plain,
! [X3408,X3409,X3410] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3410,X3409) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3408,X3409)
| X3410 = X3408 )
& ( X3410 != X3408
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3410,X3409) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3408,X3409) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_1939,plain,
! [X3405,X3406,X3407] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3407,X3406) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3407,X3405)
| X3406 = X3405 )
& ( X3406 != X3405
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3407,X3406) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3407,X3405) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_1940,plain,
! [X5153] :
( 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),X5153) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X5153)) ),
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_1941,plain,
! [X4651] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk16_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk16_0),X4651) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X4651)) ),
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_1942,plain,
! [X4647] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4647) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X4647)),
inference(variable_rename,[status(thm)],[fact_q_I2_J]) ).
fof(i_0_1943,plain,
! [X5429,X5430,X5431] :
( ~ class_Rings_Ocomm__semiring__1(X5431)
| c_Rings_Odvd__class_Odvd(X5431,X5430,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5431),X5430),X5429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_1944,plain,
! [X3326,X3327,X3329,X3330,X3331] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3327,X3326)
| X3326 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3327,esk5_2(X3326,X3327)) )
& ( X3329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3330,X3331)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3330,X3329) ) ),
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_1945,plain,
! [X3320,X3321,X3323,X3324,X3325] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3321,X3320)
| X3320 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3321,esk4_2(X3320,X3321)) )
& ( X3323 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3324,X3325)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3324,X3323) ) ),
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_1946,plain,
! [X4122,X4123] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4123,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4123,X4122)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_1947,plain,
! [X4077,X4078] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4078,X4077),X4078) = X4077,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_1948,plain,
! [X4075,X4076] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4076,X4075),X4075) = X4076,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_1949,plain,
! [X4088,X4089] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4089,X4088),X4089),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_1950,plain,
! [X3318,X3319] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3319,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3319,X3318)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_1951,plain,
! [X3316,X3317] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3316,X3317)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_1952,plain,
! [X5159] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5159))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5159) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5159)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5159)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_1953,plain,
! [X5125] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5125),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5125,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5125,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5125),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_1954,plain,
! [X4430,X4431] :
( ( ~ c_Orderings_Oord__class_Oless(X4431,c_Groups_Ozero__class_Ozero(X4431),c_Groups_Oabs__class_Oabs(X4431,X4430))
| X4430 != c_Groups_Ozero__class_Ozero(X4431)
| ~ class_Groups_Oordered__ab__group__add__abs(X4431) )
& ( X4430 = c_Groups_Ozero__class_Ozero(X4431)
| c_Orderings_Oord__class_Oless(X4431,c_Groups_Ozero__class_Ozero(X4431),c_Groups_Oabs__class_Oabs(X4431,X4430))
| ~ class_Groups_Oordered__ab__group__add__abs(X4431) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
fof(i_0_1955,plain,
! [X2792] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_1(X2792))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2792) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X2792),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2792) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_1(X2792),X2792)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2792) ) ),
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_1956,plain,
! [X3363,X3364,X3365] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3365),X3364) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3363),X3364)
| X3365 = X3363
| X3364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3365 != X3363
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3365),X3364) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3363),X3364) )
& ( X3364 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3365),X3364) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3363),X3364) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_1957,plain,
! [X3494,X3495,X3496] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3495),X3496) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3494),X3496)
| X3495 = X3494
| X3496 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3495 != X3494
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3495),X3496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3494),X3496)
| X3496 = 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_1958,plain,
! [X3981,X3982,X3983] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3982) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3981)
| X3983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3982 = X3981 )
& ( X3983 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3981) )
& ( X3982 != X3981
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3983),X3981) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_1959,plain,
! [X3366,X3367,X3368] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3367) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3366)
| X3367 = X3366
| X3368 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3367 != X3366
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3366) )
& ( X3368 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3368),X3366) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_1960,plain,
! [X3497,X3498,X3499] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3499),X3498) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3499),X3497)
| X3498 = X3497
| X3499 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3498 != X3497
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3499),X3498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3499),X3497)
| X3499 = 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_1961,plain,
! [X5169,X5170] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5170,X5169)
| c_Nat__Transfer_Otsub(X5169,X5170) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5169,X5170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_1962,plain,
! [X5162,X5163] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5163,X5162)
| c_Nat__Transfer_Otsub(X5162,X5163) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5162,X5163) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5163,X5162)
| c_Nat__Transfer_Otsub(X5162,X5163) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1303])]) ).
fof(i_0_1963,plain,
! [X5100,X5101,X5102] :
( ( c_Orderings_Oord__class_Oless__eq(X5102,X5101,X5100)
| ~ c_Orderings_Oord__class_Oless(X5102,X5101,X5100)
| ~ class_Orderings_Oorder(X5102) )
& ( X5101 != X5100
| ~ c_Orderings_Oord__class_Oless(X5102,X5101,X5100)
| ~ class_Orderings_Oorder(X5102) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5102,X5101,X5100)
| X5101 = X5100
| c_Orderings_Oord__class_Oless(X5102,X5101,X5100)
| ~ class_Orderings_Oorder(X5102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_1964,plain,
! [X5094,X5095,X5096] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5096,X5095,X5094)
| c_Orderings_Oord__class_Oless(X5096,X5095,X5094)
| X5095 = X5094
| ~ class_Orderings_Oorder(X5096) )
& ( ~ c_Orderings_Oord__class_Oless(X5096,X5095,X5094)
| c_Orderings_Oord__class_Oless__eq(X5096,X5095,X5094)
| ~ class_Orderings_Oorder(X5096) )
& ( X5095 != X5094
| c_Orderings_Oord__class_Oless__eq(X5096,X5095,X5094)
| ~ class_Orderings_Oorder(X5096) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_1965,plain,
! [X5082,X5083,X5084] :
( ~ class_Orderings_Oorder(X5084)
| X5083 = X5082
| ~ c_Orderings_Oord__class_Oless__eq(X5084,X5083,X5082)
| c_Orderings_Oord__class_Oless(X5084,X5083,X5082) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_1966,plain,
! [X5067,X5068,X5069] :
( ~ class_Orderings_Oorder(X5069)
| ~ c_Orderings_Oord__class_Oless__eq(X5069,X5068,X5067)
| c_Orderings_Oord__class_Oless(X5069,X5068,X5067)
| X5068 = X5067 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_1967,plain,
! [X5064,X5065,X5066] :
( ~ class_Orderings_Oorder(X5066)
| ~ c_Orderings_Oord__class_Oless__eq(X5066,X5065,X5064)
| X5065 = X5064
| c_Orderings_Oord__class_Oless(X5066,X5065,X5064) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_1968,plain,
! [X5061,X5062,X5063] :
( ~ class_Orderings_Oorder(X5063)
| ~ c_Orderings_Oord__class_Oless__eq(X5063,X5062,X5061)
| X5061 = X5062
| c_Orderings_Oord__class_Oless(X5063,X5062,X5061) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_1969,plain,
! [X5085,X5086,X5087] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5087,X5086,X5085)
| X5086 = X5085
| c_Orderings_Oord__class_Oless(X5087,X5086,X5085)
| ~ class_Orderings_Olinorder(X5087) )
& ( X5086 != X5085
| c_Orderings_Oord__class_Oless__eq(X5087,X5086,X5085)
| c_Orderings_Oord__class_Oless(X5087,X5086,X5085)
| ~ class_Orderings_Olinorder(X5087) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1304])])]) ).
fof(i_0_1970,plain,
! [X5079,X5080,X5081] :
( ~ class_Orderings_Oorder(X5081)
| X5080 = X5079
| ~ c_Orderings_Oord__class_Oless__eq(X5081,X5079,X5080)
| c_Orderings_Oord__class_Oless(X5081,X5079,X5080) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_1971,plain,
! [X4377,X4378] :
( ~ class_Rings_Ocomm__ring__1(X4378)
| c_Groups_Ouminus__class_Ouminus(X4378,X4377) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4378),c_Groups_Ouminus__class_Ouminus(X4378,c_Groups_Oone__class_Oone(X4378))),X4377) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_1972,plain,
! [X5156,X5157] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5157,X5156)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X5157),c_RComplete_Onatfloor(X5156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_1973,plain,
! [X5122,X5123] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5123,X5122)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5123),c_RComplete_Onatceiling(X5122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_1974,plain,
! [X4424,X4425] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4425,c_Groups_Oabs__class_Oabs(X4425,X4424),c_Groups_Ozero__class_Ozero(X4425))
| X4424 = c_Groups_Ozero__class_Ozero(X4425)
| ~ class_Groups_Oordered__ab__group__add__abs(X4425) )
& ( X4424 != c_Groups_Ozero__class_Ozero(X4425)
| c_Orderings_Oord__class_Oless__eq(X4425,c_Groups_Oabs__class_Oabs(X4425,X4424),c_Groups_Ozero__class_Ozero(X4425))
| ~ class_Groups_Oordered__ab__group__add__abs(X4425) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_1975,plain,
! [X5073,X5074,X5075] :
( ~ class_Orderings_Opreorder(X5075)
| ~ c_Orderings_Oord__class_Oless(X5075,X5074,X5073)
| c_Orderings_Oord__class_Oless__eq(X5075,X5074,X5073) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_1976,plain,
! [X4484,X4485] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4485)
| c_Orderings_Oord__class_Oless__eq(X4485,c_Groups_Ouminus__class_Ouminus(X4485,c_Groups_Oabs__class_Oabs(X4485,X4484)),c_Groups_Ozero__class_Ozero(X4485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).
fof(i_0_1977,plain,
! [X4605] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4605)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4605) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4605)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4605) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_1978,plain,
! [X2799,X2800] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2800,X2799))
| X2799 != c_Groups_Ozero__class_Ozero(X2800)
| ~ class_RealVector_Oreal__normed__vector(X2800) )
& ( X2799 = c_Groups_Ozero__class_Ozero(X2800)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2800,X2799))
| ~ class_RealVector_Oreal__normed__vector(X2800) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_1979,plain,
! [X4113] : 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,X4113)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4113)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(i_0_1980,plain,
! [X4432,X4433] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4433)
| ~ c_Orderings_Oord__class_Oless(X4433,c_Groups_Oabs__class_Oabs(X4433,X4432),c_Groups_Ozero__class_Ozero(X4433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1305])]) ).
fof(i_0_1981,plain,
! [X3278] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3278,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3278),X3278)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_1982,plain,
! [X3591,X3592,X3593] :
( ~ class_Groups_Ogroup__add(X3593)
| c_Groups_Ominus__class_Ominus(X3593,X3592,c_Groups_Ouminus__class_Ouminus(X3593,X3591)) = c_Groups_Oplus__class_Oplus(X3593,X3592,X3591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_1983,plain,
! [X4379,X4380,X4381] :
( ~ class_Rings_Ocomm__ring__1(X4381)
| c_Groups_Ominus__class_Ominus(X4381,X4380,X4379) = c_Groups_Oplus__class_Oplus(X4381,X4380,c_Groups_Ouminus__class_Ouminus(X4381,X4379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_1984,plain,
! [X3588,X3589,X3590] :
( ~ class_Groups_Oab__group__add(X3590)
| c_Groups_Ominus__class_Ominus(X3590,X3589,X3588) = c_Groups_Oplus__class_Oplus(X3590,X3589,c_Groups_Ouminus__class_Ouminus(X3590,X3588)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_1985,plain,
! [X3585,X3586,X3587] :
( ~ class_Groups_Ogroup__add(X3587)
| c_Groups_Ominus__class_Ominus(X3587,X3586,X3585) = c_Groups_Oplus__class_Oplus(X3587,X3586,c_Groups_Ouminus__class_Ouminus(X3587,X3585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_1986,plain,
! [X3043,X3044] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3044,X3043),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X3043 = c_Groups_Ozero__class_Ozero(X3044)
| ~ class_RealVector_Oreal__normed__vector(X3044) )
& ( X3043 != c_Groups_Ozero__class_Ozero(X3044)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3044,X3043),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X3044) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_1987,plain,
! [X4124,X4125] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4125,X4124) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4125,X4124) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4125,X4124)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4125,X4124) = 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_1988,plain,
! [X4599,X4600] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4600,X4599)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4600,X4599) )
& ( X4600 != X4599
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4600,X4599) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4600,X4599)
| X4600 = X4599
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4600,X4599) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_1989,plain,
! [X3314,X3315] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3315,X3314)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3315,X3314) )
& ( X3315 != X3314
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3315,X3314) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3315,X3314)
| X3315 = X3314
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3315,X3314) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_1990,plain,
! [X3312,X3313] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3313,X3312)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3313,X3312)
| X3313 = X3312 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3313,X3312)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3313,X3312) )
& ( X3313 != X3312
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3313,X3312) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_1991,plain,
! [X3308,X3309] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3309,X3308)
| X3309 = X3308
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3309,X3308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_1992,plain,
! [X3454,X3455] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3455,X3454)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3455,X3454)
| X3455 = X3454 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3455,X3454)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3455,X3454) )
& ( X3455 != X3454
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3455,X3454) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_1993,plain,
! [X3452,X3453] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3453,X3452)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3453,X3452) )
& ( X3453 != X3452
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3453,X3452) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3453,X3452)
| X3453 = X3452
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3453,X3452) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_1994,plain,
! [X4126,X4127] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4127,X4126)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4127,X4126) = 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_1995,plain,
! [X4612] : 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),X4612)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4612),
inference(variable_rename,[status(thm)],[fact_complex__i__mult__minus]) ).
fof(i_0_1996,plain,
! [X5296,X5297,X5298,X5299] :
( ~ class_Groups_Ouminus(X5299)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5298,X5299),X5297),X5296) = c_Groups_Ouminus__class_Ouminus(X5299,hAPP(X5297,X5296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_1997,plain,
! [X5328,X5329] :
( ~ class_Rings_Olinordered__idom(X5329)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5329),c_Groups_Osgn__class_Osgn(X5329,X5328)),c_Groups_Oabs__class_Oabs(X5329,X5328)) = X5328 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).
fof(i_0_1998,plain,
! [X4709,X4710] :
( ~ class_Groups_Ozero(X4710)
| c_Polynomial_Omonom(X4710,X4709,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X4710,X4709,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4710))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__0])]) ).
fof(i_0_1999,plain,
! [X5341,X5342] :
( ~ class_Rings_Olinordered__idom(X5342)
| ~ c_Orderings_Oord__class_Oless(X5342,X5341,c_Groups_Ozero__class_Ozero(X5342))
| c_Groups_Osgn__class_Osgn(X5342,X5341) = c_Groups_Ouminus__class_Ouminus(X5342,c_Groups_Oone__class_Oone(X5342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).
fof(i_0_2000,plain,
! [X5339,X5340] :
( ( c_Groups_Osgn__class_Osgn(X5340,X5339) != c_Groups_Ouminus__class_Ouminus(X5340,c_Groups_Oone__class_Oone(X5340))
| c_Orderings_Oord__class_Oless(X5340,X5339,c_Groups_Ozero__class_Ozero(X5340))
| ~ class_Rings_Olinordered__idom(X5340) )
& ( ~ c_Orderings_Oord__class_Oless(X5340,X5339,c_Groups_Ozero__class_Ozero(X5340))
| c_Groups_Osgn__class_Osgn(X5340,X5339) = c_Groups_Ouminus__class_Ouminus(X5340,c_Groups_Oone__class_Oone(X5340))
| ~ class_Rings_Olinordered__idom(X5340) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).
fof(i_0_2001,plain,
! [X5177,X5178] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5178,X5177)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5178,X5177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2002,plain,
! [X3310,X3311] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3311,X3310)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3311,X3310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2003,plain,
! [X3306,X3307] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3307,X3306)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3307,X3306) )
& ( X3307 != X3306
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3307,X3306) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2004,plain,
! [X3243,X3244] :
( ~ class_RealVector_Oreal__normed__vector(X3244)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3244,X3243),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])]) ).
fof(i_0_2005,plain,
! [X4489,X4490] :
( ( ~ c_Orderings_Oord__class_Oless(X4490,X4489,c_Groups_Ozero__class_Ozero(X4490))
| c_Groups_Oabs__class_Oabs(X4490,X4489) = c_Groups_Ouminus__class_Ouminus(X4490,X4489)
| ~ class_Groups_Oabs__if(X4490) )
& ( c_Orderings_Oord__class_Oless(X4490,X4489,c_Groups_Ozero__class_Ozero(X4490))
| c_Groups_Oabs__class_Oabs(X4490,X4489) = X4489
| ~ class_Groups_Oabs__if(X4490) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1307])])]) ).
fof(i_0_2006,plain,
! [X4482,X4483] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4483)
| ~ c_Orderings_Oord__class_Oless__eq(X4483,X4482,c_Groups_Ozero__class_Ozero(X4483))
| c_Groups_Oabs__class_Oabs(X4483,X4482) = c_Groups_Ouminus__class_Ouminus(X4483,X4482) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
fof(i_0_2007,plain,
! [X4491,X4492] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4492)
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Ozero__class_Ozero(X4492))
| c_Groups_Oabs__class_Oabs(X4492,X4491) = c_Groups_Ouminus__class_Ouminus(X4492,X4491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).
fof(i_0_2008,plain,
! [X4720,X4721] :
( ~ class_Rings_Ocomm__semiring__0(X4721)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4721)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4721))),X4720) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_2009,plain,
! [X4641,X4642] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4642,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4641)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4642,X4641),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_2010,plain,
! [X4643,X4644] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4644,X4643) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4644,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4643)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_2011,plain,
! [X4048,X4049] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X4049,X4048) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4049,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4048)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(i_0_2012,plain,
! [X4062,X4063] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4063,X4062) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4063,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4062)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(i_0_2013,plain,
! [X4060,X4061] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X4061,X4060) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4061,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4060)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(i_0_2014,plain,
! [X4563] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4563),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X4563 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X4563 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4563),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_2015,plain,
! [X5212] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5212),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X5212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5212),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_2016,plain,
! [X2786,X2787] :
( hAPP(X2787,esk1_2(X2786,X2787)) != hAPP(X2786,esk1_2(X2786,X2787))
| X2787 = X2786 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_2017,plain,
! [X5343,X5344] :
( ( X5343 != c_Groups_Ozero__class_Ozero(X5344)
| c_Groups_Osgn__class_Osgn(X5344,X5343) = c_Groups_Ozero__class_Ozero(X5344)
| ~ class_Groups_Osgn__if(X5344) )
& ( ~ c_Orderings_Oord__class_Oless(X5344,c_Groups_Ozero__class_Ozero(X5344),X5343)
| c_Groups_Osgn__class_Osgn(X5344,X5343) = c_Groups_Oone__class_Oone(X5344)
| X5343 = c_Groups_Ozero__class_Ozero(X5344)
| ~ class_Groups_Osgn__if(X5344) )
& ( c_Orderings_Oord__class_Oless(X5344,c_Groups_Ozero__class_Ozero(X5344),X5343)
| c_Groups_Osgn__class_Osgn(X5344,X5343) = c_Groups_Ouminus__class_Ouminus(X5344,c_Groups_Oone__class_Oone(X5344))
| X5343 = c_Groups_Ozero__class_Ozero(X5344)
| ~ class_Groups_Osgn__if(X5344) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])])]) ).
fof(i_0_2018,plain,
! [X4821,X4822,X4823] :
( ( c_Polynomial_Osmult(X4823,X4822,X4821) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4823))
| X4822 = c_Groups_Ozero__class_Ozero(X4823)
| X4821 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4823))
| ~ class_Rings_Oidom(X4823) )
& ( X4822 != c_Groups_Ozero__class_Ozero(X4823)
| c_Polynomial_Osmult(X4823,X4822,X4821) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4823))
| ~ class_Rings_Oidom(X4823) )
& ( X4821 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4823))
| c_Polynomial_Osmult(X4823,X4822,X4821) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4823))
| ~ class_Rings_Oidom(X4823) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff])])]) ).
fof(i_0_2019,plain,
! [X4139,X4140] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4140,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4139)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4140 = X4139 )
& ( X4140 != X4139
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4140,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4139)) = 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_2020,plain,
! [X5190] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5190),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1309]) ).
fof(i_0_2021,plain,
! [X3120,X3121,X3122] :
( ( X3121 = c_Groups_Ozero__class_Ozero(X3122)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3122),X3121),X3120) != c_Groups_Ozero__class_Ozero(X3122)
| ~ class_Power_Opower(X3122)
| ~ class_Rings_Omult__zero(X3122)
| ~ class_Rings_Ono__zero__divisors(X3122)
| ~ class_Rings_Ozero__neq__one(X3122) )
& ( X3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3122),X3121),X3120) != c_Groups_Ozero__class_Ozero(X3122)
| ~ class_Power_Opower(X3122)
| ~ class_Rings_Omult__zero(X3122)
| ~ class_Rings_Ono__zero__divisors(X3122)
| ~ class_Rings_Ozero__neq__one(X3122) )
& ( X3121 != c_Groups_Ozero__class_Ozero(X3122)
| X3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3122),X3121),X3120) = c_Groups_Ozero__class_Ozero(X3122)
| ~ class_Power_Opower(X3122)
| ~ class_Rings_Omult__zero(X3122)
| ~ class_Rings_Ono__zero__divisors(X3122)
| ~ class_Rings_Ozero__neq__one(X3122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2022,plain,
! [X3810,X3811] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3811),X3810),X3810) != c_Groups_Oone__class_Oone(X3811)
| X3810 = c_Groups_Oone__class_Oone(X3811)
| X3810 = c_Groups_Ouminus__class_Ouminus(X3811,c_Groups_Oone__class_Oone(X3811))
| ~ class_Rings_Oring__1__no__zero__divisors(X3811) )
& ( X3810 != c_Groups_Oone__class_Oone(X3811)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3811),X3810),X3810) = c_Groups_Oone__class_Oone(X3811)
| ~ class_Rings_Oring__1__no__zero__divisors(X3811) )
& ( X3810 != c_Groups_Ouminus__class_Ouminus(X3811,c_Groups_Oone__class_Oone(X3811))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3811),X3810),X3810) = c_Groups_Oone__class_Oone(X3811)
| ~ class_Rings_Oring__1__no__zero__divisors(X3811) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_2023,plain,
! [X5337,X5338] :
( ~ class_Rings_Olinordered__idom(X5338)
| ~ c_Orderings_Oord__class_Oless(X5338,c_Groups_Ozero__class_Ozero(X5338),X5337)
| c_Groups_Osgn__class_Osgn(X5338,X5337) = c_Groups_Oone__class_Oone(X5338) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).
fof(i_0_2024,plain,
! [X5335,X5336] :
( ( c_Groups_Osgn__class_Osgn(X5336,X5335) != c_Groups_Oone__class_Oone(X5336)
| c_Orderings_Oord__class_Oless(X5336,c_Groups_Ozero__class_Ozero(X5336),X5335)
| ~ class_Rings_Olinordered__idom(X5336) )
& ( ~ c_Orderings_Oord__class_Oless(X5336,c_Groups_Ozero__class_Ozero(X5336),X5335)
| c_Groups_Osgn__class_Osgn(X5336,X5335) = c_Groups_Oone__class_Oone(X5336)
| ~ class_Rings_Olinordered__idom(X5336) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).
fof(i_0_2025,plain,
! [X3564,X3565] :
( ~ class_Fields_Ofield(X3565)
| X3564 = c_Groups_Ozero__class_Ozero(X3565)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3565),c_Rings_Oinverse__class_Oinverse(X3565,X3564)),X3564) = c_Groups_Oone__class_Oone(X3565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).
fof(i_0_2026,plain,
! [X2967,X2968] :
( ~ class_Rings_Odivision__ring(X2968)
| X2967 = c_Groups_Ozero__class_Ozero(X2968)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2968),c_Rings_Oinverse__class_Oinverse(X2968,X2967)),X2967) = c_Groups_Oone__class_Oone(X2968) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).
fof(i_0_2027,plain,
! [X4816,X4817,X4818] :
( ( X4817 = c_Groups_Ozero__class_Ozero(X4818)
| c_Polynomial_OpCons(X4818,X4817,X4816) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4818))
| ~ class_Groups_Ozero(X4818) )
& ( X4816 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4818))
| c_Polynomial_OpCons(X4818,X4817,X4816) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4818))
| ~ class_Groups_Ozero(X4818) )
& ( X4817 != c_Groups_Ozero__class_Ozero(X4818)
| X4816 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4818))
| c_Polynomial_OpCons(X4818,X4817,X4816) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4818))
| ~ class_Groups_Ozero(X4818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(i_0_2028,plain,
! [X5404,X5405,X5406] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5406,X5405,X5404) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5406))
| X5405 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5406))
| ~ class_Rings_Ocomm__semiring__0(X5406) )
& ( X5405 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5406))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5406,X5405,X5404) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5406))
| ~ class_Rings_Ocomm__semiring__0(X5406) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
fof(i_0_2029,plain,
! [X5040,X5041,X5042] :
( ( X5041 = X5040
| c_Orderings_Oord__class_Oless(X5042,X5041,X5040)
| c_Orderings_Oord__class_Oless(X5042,X5040,X5041)
| ~ class_Orderings_Olinorder(X5042) )
& ( ~ c_Orderings_Oord__class_Oless(X5042,X5041,X5040)
| X5041 != X5040
| ~ class_Orderings_Olinorder(X5042) )
& ( ~ c_Orderings_Oord__class_Oless(X5042,X5040,X5041)
| X5041 != X5040
| ~ class_Orderings_Olinorder(X5042) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2030,plain,
! [X5034,X5035,X5036] :
( ~ class_Orderings_Olinorder(X5036)
| c_Orderings_Oord__class_Oless(X5036,X5035,X5034)
| X5035 = X5034
| c_Orderings_Oord__class_Oless(X5036,X5034,X5035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2031,plain,
! [X5031,X5032,X5033] :
( ( c_Orderings_Oord__class_Oless(X5033,X5031,X5032)
| X5031 = X5032
| c_Orderings_Oord__class_Oless(X5033,X5032,X5031)
| ~ class_Orderings_Olinorder(X5033) )
& ( X5031 != X5032
| ~ c_Orderings_Oord__class_Oless(X5033,X5031,X5032)
| c_Orderings_Oord__class_Oless(X5033,X5032,X5031)
| ~ class_Orderings_Olinorder(X5033) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1310])])]) ).
fof(i_0_2032,plain,
! [X5028,X5029,X5030] :
( ~ class_Orderings_Olinorder(X5030)
| X5029 = X5028
| c_Orderings_Oord__class_Oless(X5030,X5029,X5028)
| c_Orderings_Oord__class_Oless(X5030,X5028,X5029) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1311])]) ).
fof(i_0_2033,plain,
! [X4977,X4978,X4979] :
( ~ class_Orderings_Olinorder(X4979)
| c_Orderings_Oord__class_Oless(X4979,X4978,X4977)
| X4978 = X4977
| c_Orderings_Oord__class_Oless(X4979,X4977,X4978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1312])]) ).
fof(i_0_2034,plain,
! [X3060,X3061,X3062] :
( ~ class_Rings_Olinordered__idom(X3062)
| X3061 = X3060
| c_Orderings_Oord__class_Oless(X3062,X3061,X3060)
| c_Orderings_Oord__class_Oless(X3062,X3060,X3061) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1313])]) ).
fof(i_0_2035,plain,
! [X4525,X4526,X4527,X4528,X4529,X4530,X4533,X4534] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4527,X4526,X4525)
| hAPP(X4525,X4528) = hAPP(X4525,X4529) )
& ( hAPP(X4530,esk11_1(X4530)) != hAPP(X4530,esk12_1(X4530))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4534,X4533,X4530) ) ),
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_2036,plain,
! [X4426,X4427] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4427)
| ~ c_Orderings_Oord__class_Oless__eq(X4427,c_Groups_Ozero__class_Ozero(X4427),X4426)
| c_Groups_Oabs__class_Oabs(X4427,X4426) = X4426 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_2037,plain,
! [X4428,X4429] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4429)
| ~ c_Orderings_Oord__class_Oless(X4429,c_Groups_Ozero__class_Ozero(X4429),X4428)
| c_Groups_Oabs__class_Oabs(X4429,X4428) = X4428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_2038,plain,
! [X4974,X4975,X4976] :
( ~ class_Orderings_Olinorder(X4976)
| c_Orderings_Oord__class_Oless__eq(X4976,X4975,X4974)
| c_Orderings_Oord__class_Oless__eq(X4976,X4974,X4975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1314])]) ).
fof(i_0_2039,plain,
! [X4922,X4923,X4924] :
( ~ class_Orderings_Olinorder(X4924)
| c_Orderings_Oord__class_Oless__eq(X4924,X4923,X4922)
| c_Orderings_Oord__class_Oless__eq(X4924,X4922,X4923) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2040,plain,
! [X5091,X5092,X5093] :
( ~ class_Orderings_Olinorder(X5093)
| c_Orderings_Oord__class_Oless(X5093,X5092,X5091)
| c_Orderings_Oord__class_Oless__eq(X5093,X5091,X5092) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1315])]) ).
fof(i_0_2041,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)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2042,plain,
! [X5088,X5089,X5090] :
( ~ class_Orderings_Olinorder(X5090)
| c_Orderings_Oord__class_Oless__eq(X5090,X5089,X5088)
| c_Orderings_Oord__class_Oless(X5090,X5088,X5089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1316])]) ).
fof(i_0_2043,plain,
! [X4267,X4268,X4269] :
( ~ class_Rings_Ocomm__semiring__1(X4269)
| c_Groups_Oplus__class_Oplus(X4269,X4268,X4267) = c_Groups_Oplus__class_Oplus(X4269,X4267,X4268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2044,plain,
! [X3767,X3768,X3769] :
( ~ class_Groups_Ogroup__add(X3769)
| c_Groups_Oplus__class_Oplus(X3769,X3768,X3767) != c_Groups_Ozero__class_Ozero(X3769)
| c_Groups_Ouminus__class_Ouminus(X3769,X3768) = X3767 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2045,plain,
! [X3774,X3775,X3776] :
( ( X3775 != c_Groups_Ouminus__class_Ouminus(X3776,X3774)
| c_Groups_Oplus__class_Oplus(X3776,X3775,X3774) = c_Groups_Ozero__class_Ozero(X3776)
| ~ class_Groups_Ogroup__add(X3776) )
& ( c_Groups_Oplus__class_Oplus(X3776,X3775,X3774) != c_Groups_Ozero__class_Ozero(X3776)
| X3775 = c_Groups_Ouminus__class_Ouminus(X3776,X3774)
| ~ class_Groups_Ogroup__add(X3776) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2046,plain,
! [X3785,X3786,X3787] :
( ( c_Groups_Oplus__class_Oplus(X3787,X3786,X3785) != c_Groups_Ozero__class_Ozero(X3787)
| X3785 = c_Groups_Ouminus__class_Ouminus(X3787,X3786)
| ~ class_Groups_Ogroup__add(X3787) )
& ( X3785 != c_Groups_Ouminus__class_Ouminus(X3787,X3786)
| c_Groups_Oplus__class_Oplus(X3787,X3786,X3785) = c_Groups_Ozero__class_Ozero(X3787)
| ~ class_Groups_Ogroup__add(X3787) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2047,plain,
! [X4840,X4841,X4842] :
( ( c_Polynomial_Omonom(X4842,X4841,X4840) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4842))
| X4841 = c_Groups_Ozero__class_Ozero(X4842)
| ~ class_Groups_Ozero(X4842) )
& ( X4841 != c_Groups_Ozero__class_Ozero(X4842)
| c_Polynomial_Omonom(X4842,X4841,X4840) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4842))
| ~ class_Groups_Ozero(X4842) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff])])]) ).
fof(i_0_2048,plain,
! [X4451,X4452] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4452)
| c_Orderings_Oord__class_Oless__eq(X4452,c_Groups_Ouminus__class_Ouminus(X4452,X4451),c_Groups_Oabs__class_Oabs(X4452,X4451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).
fof(i_0_2049,plain,
! [X4550] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4550,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4550) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4550) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4550,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4550) = X4550 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1317])]) ).
fof(i_0_2050,plain,
! [X4505] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4505,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4505) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4505) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4505,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4505) = X4505 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1318])]) ).
fof(i_0_2051,plain,
! [X4504] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4504,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4504) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4504) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4504,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4504) = X4504 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1319])]) ).
fof(i_0_2052,plain,
! [X2946] :
( ~ class_Rings_Olinordered__semidom(X2946)
| ~ c_Orderings_Oord__class_Oless__eq(X2946,c_Groups_Oone__class_Oone(X2946),c_Groups_Ozero__class_Ozero(X2946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1320])]) ).
fof(i_0_2053,plain,
! [X3201] :
( ~ class_Rings_Olinordered__semidom(X3201)
| ~ c_Orderings_Oord__class_Oless(X3201,c_Groups_Oone__class_Oone(X3201),c_Groups_Ozero__class_Ozero(X3201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1321])]) ).
fof(i_0_2054,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_2055,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_2056,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_2057,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_2058,plain,
! [X4718,X4719] :
( ~ class_Rings_Ocomm__semiring__0(X4719)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4719)),X4718),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4719))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
fof(i_0_2059,plain,
! [X4233,X4234,X4235] :
( ~ class_Rings_Ocomm__semiring__1(X4235)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4235),X4234),X4233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4235),X4233),X4234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2060,plain,
! [X2880,X2881,X2882] :
( ~ class_Rings_Odivision__ring(X2882)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2882),X2881),X2880) != c_Groups_Oone__class_Oone(X2882)
| c_Rings_Oinverse__class_Oinverse(X2882,X2881) = X2880 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).
fof(i_0_2061,plain,
! [X4566,X4567] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4567,X4566)
| X4567 = X4566
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4566,X4567) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2062,plain,
! [X3394,X3395] :
( ( X3395 = X3394
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3395,X3394)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3394,X3395) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3395,X3394)
| X3395 != X3394 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3394,X3395)
| X3395 != X3394 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2063,plain,
! [X3392,X3393] :
( X3393 = X3392
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3393,X3392)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3392,X3393) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1322])]) ).
fof(i_0_2064,plain,
! [X5419,X5420] :
( ~ class_Rings_Ocomm__semiring__1(X5420)
| ~ c_Rings_Odvd__class_Odvd(X5420,c_Groups_Ozero__class_Ozero(X5420),X5419)
| X5419 = c_Groups_Ozero__class_Ozero(X5420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_2065,plain,
! [X4625,X4626] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4626,X4625)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4625,X4626) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2066,plain,
! [X3282,X3283] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3283,X3282)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3282,X3283) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2067,plain,
! [X3381,X3382] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3382,X3381)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3381,X3382) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2068,plain,
! [X3075,X3076,X3077] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3077),X3076),X3075) != c_Groups_Ozero__class_Ozero(X3077)
| X3076 = c_Groups_Ozero__class_Ozero(X3077)
| X3075 = c_Groups_Ozero__class_Ozero(X3077)
| ~ class_Rings_Oring__no__zero__divisors(X3077) )
& ( X3076 != c_Groups_Ozero__class_Ozero(X3077)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3077),X3076),X3075) = c_Groups_Ozero__class_Ozero(X3077)
| ~ class_Rings_Oring__no__zero__divisors(X3077) )
& ( X3075 != c_Groups_Ozero__class_Ozero(X3077)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3077),X3076),X3075) = c_Groups_Ozero__class_Ozero(X3077)
| ~ class_Rings_Oring__no__zero__divisors(X3077) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2069,plain,
! [X3072,X3073,X3074] :
( ~ class_Rings_Ono__zero__divisors(X3074)
| X3073 = c_Groups_Ozero__class_Ozero(X3074)
| X3072 = c_Groups_Ozero__class_Ozero(X3074)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3074),X3073),X3072) != c_Groups_Ozero__class_Ozero(X3074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2070,plain,
! [X3069,X3070,X3071] :
( ~ class_Rings_Ono__zero__divisors(X3071)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3071),X3070),X3069) != c_Groups_Ozero__class_Ozero(X3071)
| X3070 = c_Groups_Ozero__class_Ozero(X3071)
| X3069 = c_Groups_Ozero__class_Ozero(X3071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2071,plain,
! [X5389,X5390,X5391] :
( ~ class_Rings_Olinordered__idom(X5391)
| c_Groups_Oabs__class_Oabs(X5391,X5390) != c_Groups_Oabs__class_Oabs(X5391,X5389)
| c_Rings_Odvd__class_Odvd(X5391,X5390,X5389) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq])]) ).
fof(i_0_2072,plain,
! [X4716,X4717] :
( ~ class_Groups_Oab__group__add(X4717)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4717),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4717)),X4716) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4717),X4716) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).
fof(i_0_2073,plain,
! [X4623,X4624] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4624,X4623) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4623,X4624),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2074,plain,
! [X3397,X3398] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3398,X3397) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3397,X3398),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2075,plain,
! [X4541,X4542] :
( ( c_Groups_Oplus__class_Oplus(X4542,X4541,X4541) != c_Groups_Ozero__class_Ozero(X4542)
| X4541 = c_Groups_Ozero__class_Ozero(X4542)
| ~ class_Groups_Olinordered__ab__group__add(X4542) )
& ( X4541 != c_Groups_Ozero__class_Ozero(X4542)
| c_Groups_Oplus__class_Oplus(X4542,X4541,X4541) = c_Groups_Ozero__class_Ozero(X4542)
| ~ class_Groups_Olinordered__ab__group__add(X4542) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2076,plain,
! [X3909,X3910] :
( ( c_Groups_Ozero__class_Ozero(X3910) != c_Groups_Oplus__class_Oplus(X3910,X3909,X3909)
| X3909 = c_Groups_Ozero__class_Ozero(X3910)
| ~ class_Groups_Olinordered__ab__group__add(X3910) )
& ( X3909 != c_Groups_Ozero__class_Ozero(X3910)
| c_Groups_Ozero__class_Ozero(X3910) = c_Groups_Oplus__class_Oplus(X3910,X3909,X3909)
| ~ class_Groups_Olinordered__ab__group__add(X3910) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2077,plain,
! [X3598,X3599,X3600] :
( ( X3599 != X3598
| c_Groups_Ominus__class_Ominus(X3600,X3599,X3598) = c_Groups_Ozero__class_Ozero(X3600)
| ~ class_Groups_Oab__group__add(X3600) )
& ( c_Groups_Ominus__class_Ominus(X3600,X3599,X3598) != c_Groups_Ozero__class_Ozero(X3600)
| X3599 = X3598
| ~ class_Groups_Oab__group__add(X3600) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2078,plain,
! [X3601,X3602,X3603] :
( ( c_Groups_Ominus__class_Ominus(X3603,X3602,X3601) != c_Groups_Ozero__class_Ozero(X3603)
| X3602 = X3601
| ~ class_Groups_Ogroup__add(X3603) )
& ( X3602 != X3601
| c_Groups_Ominus__class_Ominus(X3603,X3602,X3601) = c_Groups_Ozero__class_Ozero(X3603)
| ~ class_Groups_Ogroup__add(X3603) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2079,plain,
! [X3117,X3118,X3119] :
( ~ class_Rings_Oring__1__no__zero__divisors(X3119)
| X3118 = c_Groups_Ozero__class_Ozero(X3119)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3119),X3118),X3117) != c_Groups_Ozero__class_Ozero(X3119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2080,plain,
! [X4141,X4142] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4142,X4141) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4141 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4142) )
& ( X4141 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4142)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4142,X4141) = 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_2081,plain,
! [X4319,X4320,X4321] :
( ( X4320 != c_Groups_Oplus__class_Oplus(X4321,X4320,X4319)
| X4319 = c_Groups_Ozero__class_Ozero(X4321)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4321) )
& ( X4319 != c_Groups_Ozero__class_Ozero(X4321)
| X4320 = c_Groups_Oplus__class_Oplus(X4321,X4320,X4319)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4321) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2082,plain,
! [X5330,X5331] :
( ~ class_Rings_Olinordered__idom(X5331)
| c_Groups_Oabs__class_Oabs(X5331,X5330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5331),X5330),c_Groups_Osgn__class_Osgn(X5331,X5330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).
fof(i_0_2083,plain,
! [X4794,X4795] :
( ( c_Polynomial_Opoly(X4795,X4794) != c_Polynomial_Opoly(X4795,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4795)))
| X4794 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4795))
| ~ class_Int_Oring__char__0(X4795)
| ~ class_Rings_Oidom(X4795) )
& ( X4794 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4795))
| c_Polynomial_Opoly(X4795,X4794) = c_Polynomial_Opoly(X4795,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4795)))
| ~ class_Int_Oring__char__0(X4795)
| ~ class_Rings_Oidom(X4795) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2084,plain,
! [X3264] :
( X3264 = 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,X3264)),X3264) = 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_2085,plain,
! [X5025,X5026,X5027] :
( ~ class_Orderings_Oorder(X5027)
| ~ c_Orderings_Oord__class_Oless(X5027,X5026,X5025)
| X5026 != X5025 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2086,plain,
! [X5016,X5017,X5018] :
( ~ class_Orderings_Oorder(X5018)
| ~ c_Orderings_Oord__class_Oless(X5018,X5017,X5016)
| X5017 != X5016 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2087,plain,
! [X5013,X5014,X5015] :
( ~ class_Orderings_Oorder(X5015)
| ~ c_Orderings_Oord__class_Oless(X5015,X5014,X5013)
| X5013 != X5014 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2088,plain,
! [X4815] :
( ~ class_Groups_Ozero(X4815)
| c_Polynomial_OpCons(X4815,c_Groups_Ozero__class_Ozero(X4815),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4815))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])]) ).
fof(i_0_2089,plain,
! [X4824] :
( ~ class_Rings_Ocomm__semiring__1(X4824)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4824)) = c_Polynomial_OpCons(X4824,c_Groups_Oone__class_Oone(X4824),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4824))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(i_0_2090,plain,
! [X5158] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5158,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X5158) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__neg])]) ).
fof(i_0_2091,plain,
! [X5124] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5124,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X5124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__neg])]) ).
fof(i_0_2092,plain,
! [X2969,X2970] :
( ~ class_Rings_Odivision__ring(X2970)
| X2969 = c_Groups_Ozero__class_Ozero(X2970)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2970),X2969),c_Rings_Oinverse__class_Oinverse(X2970,X2969)) = c_Groups_Oone__class_Oone(X2970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).
fof(i_0_2093,plain,
! [X3450] :
( ( X3450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3450) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3450)
| X3450 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2094,plain,
! [X4422,X4423] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4423)
| c_Orderings_Oord__class_Oless__eq(X4423,c_Groups_Ozero__class_Ozero(X4423),c_Groups_Oabs__class_Oabs(X4423,X4422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_2095,plain,
! [X5043,X5044] :
( ~ class_Orderings_Opreorder(X5044)
| ~ c_Orderings_Oord__class_Oless(X5044,X5043,X5043) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])]) ).
fof(i_0_2096,plain,
! [X2822,X2823] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2823)
| ~ class_Rings_Odivision__ring__inverse__zero(X2823)
| c_RealVector_Onorm__class_Onorm(X2823,c_Rings_Oinverse__class_Oinverse(X2823,X2822)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2823,X2822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__inverse])]) ).
fof(i_0_2097,plain,
! [X4465,X4466] :
( ~ class_Fields_Olinordered__field(X4466)
| X4465 = c_Groups_Ozero__class_Ozero(X4466)
| c_Groups_Oabs__class_Oabs(X4466,c_Rings_Oinverse__class_Oinverse(X4466,X4465)) = c_Rings_Oinverse__class_Oinverse(X4466,c_Groups_Oabs__class_Oabs(X4466,X4465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__inverse])]) ).
fof(i_0_2098,plain,
! [X3822,X3823] :
( ~ class_Rings_Odivision__ring(X3823)
| X3822 = c_Groups_Ozero__class_Ozero(X3823)
| c_Rings_Oinverse__class_Oinverse(X3823,c_Groups_Ouminus__class_Ouminus(X3823,X3822)) = c_Groups_Ouminus__class_Ouminus(X3823,c_Rings_Oinverse__class_Oinverse(X3823,X3822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).
fof(i_0_2099,plain,
! [X3304] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3304,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3304 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3304,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_2100,plain,
! [X4601,X4602] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4602),X4601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4601),X4602),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2101,plain,
! [X3280,X3281] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3281),X3280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3280),X3281),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2102,plain,
! [X3417,X3418] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3418),X3417) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3417),X3418),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2103,plain,
! [X3770,X3771] :
( ~ class_Groups_Oab__group__add(X3771)
| c_Groups_Oplus__class_Oplus(X3771,c_Groups_Ouminus__class_Ouminus(X3771,X3770),X3770) = c_Groups_Ozero__class_Ozero(X3771) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_2104,plain,
! [X3772,X3773] :
( ~ class_Groups_Ogroup__add(X3773)
| c_Groups_Oplus__class_Oplus(X3773,c_Groups_Ouminus__class_Ouminus(X3773,X3772),X3772) = c_Groups_Ozero__class_Ozero(X3773) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_2105,plain,
! [X3777,X3778] :
( ~ class_Groups_Ogroup__add(X3778)
| c_Groups_Oplus__class_Oplus(X3778,X3777,c_Groups_Ouminus__class_Ouminus(X3778,X3777)) = c_Groups_Ozero__class_Ozero(X3778) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2106,plain,
! [X3690,X3691] :
( ~ class_RealVector_Oreal__algebra__1(X3691)
| ~ class_RealVector_Oreal__normed__vector(X3691)
| c_RealVector_Oof__real(X3691,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3690)) = c_Groups_Ouminus__class_Ouminus(X3691,c_RealVector_Oof__real(X3691,X3690)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ominus])]) ).
fof(i_0_2107,plain,
! [X3827,X3828] :
( ~ class_RealVector_Oreal__div__algebra(X3828)
| ~ class_Rings_Odivision__ring__inverse__zero(X3828)
| c_RealVector_Oof__real(X3828,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3827)) = c_Rings_Oinverse__class_Oinverse(X3828,c_RealVector_Oof__real(X3828,X3827)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__inverse])]) ).
fof(i_0_2108,plain,
! [X3458,X3459] :
( ( X3459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3459,X3458) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3459,X3458) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3459 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3458 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3459,X3458) = 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_2109,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_2110,plain,
! [X5407,X5408] :
( ~ class_Rings_Ocomm__semiring__0(X5408)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5408,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5408)),X5407) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5408)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__0])]) ).
fof(i_0_2111,plain,
! [X4893,X4894] :
( ~ class_Rings_Ocomm__semiring__0(X4894)
| c_Polynomial_Opcompose(X4894,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4894)),X4893) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__0])]) ).
fof(i_0_2112,plain,
! [X4891,X4892] :
( ~ class_Rings_Ocomm__semiring__0(X4892)
| c_Polynomial_Osynthetic__div(X4892,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4892)),X4891) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__0])]) ).
fof(i_0_2113,plain,
! [X4796,X4797] :
( ~ class_Rings_Ocomm__semiring__0(X4797)
| c_Polynomial_Osmult(X4797,X4796,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4797))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4797)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
fof(i_0_2114,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____),esk17_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_2115,plain,
! [X3439,X3440] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3440,X3439)
| X3439 != 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_2116,plain,
! [X2960,X2961] :
( ~ class_RealVector_Oreal__normed__vector(X2961)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2961,X2960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2117,plain,
! [X3210,X3211] :
( ( X3210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3211),c_Groups_Ozero__class_Ozero(X3211)),X3210) = c_Groups_Oone__class_Oone(X3211)
| ~ class_Power_Opower(X3211)
| ~ class_Rings_Osemiring__0(X3211) )
& ( X3210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3211),c_Groups_Ozero__class_Ozero(X3211)),X3210) = c_Groups_Ozero__class_Ozero(X3211)
| ~ class_Power_Opower(X3211)
| ~ class_Rings_Osemiring__0(X3211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2118,plain,
! [X3460,X3461] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3461,X3460) != X3461
| X3460 = 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_2119,plain,
! [X3451] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3451,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1324]) ).
fof(i_0_2120,plain,
! [X3447] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3447,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1325]) ).
fof(i_0_2121,plain,
! [X3257] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3257,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1326]) ).
fof(i_0_2122,plain,
! [X5216] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5216,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X5216))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2123,plain,
! [X3866,X3867] :
( ~ class_RealVector_Oreal__div__algebra(X3867)
| X3866 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X3867,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3866)) = c_Rings_Oinverse__class_Oinverse(X3867,c_RealVector_Oof__real(X3867,X3866)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__of__real__inverse])]) ).
fof(i_0_2124,plain,
! [X4757,X4758] :
( ~ class_Rings_Ocomm__semiring__1(X4758)
| hAPP(c_Polynomial_Opoly(X4758,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4758))),X4757) = c_Groups_Oone__class_Oone(X4758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2125,plain,
! [X4813,X4814] :
( ~ class_Rings_Ocomm__semiring__0(X4814)
| hAPP(c_Polynomial_Opoly(X4814,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4814))),X4813) = c_Groups_Ozero__class_Ozero(X4814) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2126,plain,
! [X4393,X4394] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4394)
| c_Orderings_Oord__class_Oless__eq(X4394,X4393,c_Groups_Oabs__class_Oabs(X4394,X4393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_2127,plain,
! [X3389,X3390] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3390,X3389)
| X3389 != X3390 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2128,plain,
! [X3387,X3388] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3388,X3387)
| X3388 != X3387 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2129,plain,
! [X5333,X5334] :
( ~ class_RealVector_Oreal__normed__vector(X5334)
| c_Groups_Osgn__class_Osgn(X5334,c_Groups_Ouminus__class_Ouminus(X5334,X5333)) = c_Groups_Ouminus__class_Ouminus(X5334,c_Groups_Osgn__class_Osgn(X5334,X5333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__minus])]) ).
fof(i_0_2130,plain,
! [X4415,X4416] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4416)
| c_Groups_Oabs__class_Oabs(X4416,c_Rings_Oinverse__class_Oinverse(X4416,X4415)) = c_Rings_Oinverse__class_Oinverse(X4416,c_Groups_Oabs__class_Oabs(X4416,X4415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__inverse])]) ).
fof(i_0_2131,plain,
! [X3745,X3746] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3746)
| c_Rings_Oinverse__class_Oinverse(X3746,c_Groups_Ouminus__class_Ouminus(X3746,X3745)) = c_Groups_Ouminus__class_Ouminus(X3746,c_Rings_Oinverse__class_Oinverse(X3746,X3745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).
fof(i_0_2132,plain,
! [X4805,X4806] :
( ~ class_Groups_Ocomm__monoid__add(X4806)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4806),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4806)),X4805) = X4805 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_2133,plain,
! [X4714,X4715] :
( ~ class_Groups_Oab__group__add(X4715)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4715),X4714,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4715))) = X4714 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).
fof(i_0_2134,plain,
! [X4807,X4808] :
( ~ class_Groups_Ocomm__monoid__add(X4808)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4808),X4807,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4808))) = X4807 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2135,plain,
! [X5235,X5236] :
( ~ class_Rings_Olinordered__idom(X5236)
| X5235 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5236))
| c_Polynomial_Opos__poly(X5236,X5235)
| c_Polynomial_Opos__poly(X5236,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5236),X5235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__total])]) ).
fof(i_0_2136,plain,
! [X3369,X3370] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3370),X3369) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3370),X3369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3369 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3370),X3369) = 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_2137,plain,
! [X3692,X3693] :
( ~ class_RealVector_Oreal__algebra__1(X3693)
| c_RealVector_Oof__real(X3693,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3692)) = c_Groups_Ouminus__class_Ouminus(X3693,c_RealVector_Oof__real(X3693,X3692)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__minus])]) ).
fof(i_0_2138,plain,
! [X5326,X5327] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5327)
| c_Groups_Osgn__class_Osgn(X5327,c_RealVector_Oof__real(X5327,X5326)) = c_RealVector_Oof__real(X5327,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X5326)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__of__real])]) ).
fof(i_0_2139,plain,
! [X3396] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3396,X3396),
inference(variable_rename,[status(thm)],[i_0_1327]) ).
fof(i_0_2140,plain,
! [X3391] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3391,X3391),
inference(variable_rename,[status(thm)],[i_0_1328]) ).
fof(i_0_2141,plain,
! [X3502,X3503] :
( X3503 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3503),X3502)
| X3502 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3503 = 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_2142,plain,
! [X3583,X3584] :
( ~ class_Groups_Ogroup__add(X3584)
| c_Groups_Ominus__class_Ominus(X3584,c_Groups_Ozero__class_Ozero(X3584),X3583) = c_Groups_Ouminus__class_Ouminus(X3584,X3583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_2143,plain,
! [X3429,X3430] :
( ( X3430 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3430),X3429) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3429 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3430),X3429) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3430 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3429 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3430),X3429) = 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_2144,plain,
! [X3426,X3427] :
( ( X3427 = 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),X3427),X3426) )
& ( X3426 = 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),X3427),X3426) )
& ( X3427 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3426 != 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),X3427),X3426) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2145,plain,
! [X5187] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5187)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2146,plain,
! [X4611] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4611),X4611) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2147,plain,
! [X4838,X4839] :
( ~ class_Groups_Ozero(X4839)
| c_Polynomial_Omonom(X4839,c_Groups_Ozero__class_Ozero(X4839),X4838) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0])]) ).
fof(i_0_2148,plain,
! [X4819,X4820] :
( ~ class_Rings_Ocomm__semiring__0(X4820)
| c_Polynomial_Osmult(X4820,c_Groups_Ozero__class_Ozero(X4820),X4819) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4820)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(i_0_2149,plain,
! [X5126] :
( ~ class_Power_Opower(X5126)
| c_Power_Opower__class_Opower(X5126) = c_Power_Opower_Opower(X5126,c_Groups_Oone__class_Oone(X5126),c_Groups_Otimes__class_Otimes(X5126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2150,plain,
! [X4311,X4312] :
( ~ class_Rings_Ocomm__semiring__1(X4312)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4312),c_Groups_Ozero__class_Ozero(X4312)),X4311) = c_Groups_Ozero__class_Ozero(X4312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2151,plain,
! [X3088,X3089] :
( ~ class_Rings_Omult__zero(X3089)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3089),c_Groups_Ozero__class_Ozero(X3089)),X3088) = c_Groups_Ozero__class_Ozero(X3089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2152,plain,
! [X3086,X3087] :
( ~ class_RealVector_Oreal__normed__algebra(X3087)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3087),c_Groups_Ozero__class_Ozero(X3087)),X3086) = c_Groups_Ozero__class_Ozero(X3087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2153,plain,
! [X3084,X3085] :
( ~ class_RealVector_Oreal__normed__algebra(X3085)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3085),c_Groups_Ozero__class_Ozero(X3085)),X3084) = c_Groups_Ozero__class_Ozero(X3085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2154,plain,
! [X3130,X3131] :
( ~ class_Groups_Omonoid__mult(X3131)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3131),c_Groups_Oone__class_Oone(X3131)),X3130) = c_Groups_Oone__class_Oone(X3131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2155,plain,
! [X2945] :
( ~ class_Rings_Olinordered__semidom(X2945)
| c_Orderings_Oord__class_Oless__eq(X2945,c_Groups_Ozero__class_Ozero(X2945),c_Groups_Oone__class_Oone(X2945)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2156,plain,
! [X3200] :
( ~ class_Rings_Olinordered__semidom(X3200)
| c_Orderings_Oord__class_Oless(X3200,c_Groups_Ozero__class_Ozero(X3200),c_Groups_Oone__class_Oone(X3200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2157,plain,
! [X4344,X4345] :
( ~ class_Rings_Ocomm__semiring__1(X4345)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4345),c_Groups_Oone__class_Oone(X4345)),X4344) = X4344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2158,plain,
! [X3977,X3978] :
( ~ class_Groups_Ocomm__monoid__mult(X3978)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3978),c_Groups_Oone__class_Oone(X3978)),X3977) = X3977 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2159,plain,
! [X3979,X3980] :
( ~ class_Groups_Omonoid__mult(X3980)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3980),c_Groups_Oone__class_Oone(X3980)),X3979) = X3979 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2160,plain,
! [X4313,X4314] :
( ~ class_Rings_Ocomm__semiring__1(X4314)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4314),X4313),c_Groups_Ozero__class_Ozero(X4314)) = c_Groups_Ozero__class_Ozero(X4314) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2161,plain,
! [X3082,X3083] :
( ~ class_Rings_Omult__zero(X3083)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3083),X3082),c_Groups_Ozero__class_Ozero(X3083)) = c_Groups_Ozero__class_Ozero(X3083) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2162,plain,
! [X3080,X3081] :
( ~ class_RealVector_Oreal__normed__algebra(X3081)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3081),X3080),c_Groups_Ozero__class_Ozero(X3081)) = c_Groups_Ozero__class_Ozero(X3081) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2163,plain,
! [X3078,X3079] :
( ~ class_RealVector_Oreal__normed__algebra(X3079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),X3078),c_Groups_Ozero__class_Ozero(X3079)) = c_Groups_Ozero__class_Ozero(X3079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2164,plain,
! [X4779,X4780] :
( ~ class_Rings_Ocomm__semiring__1(X4780)
| c_Polynomial_Osmult(X4780,c_Groups_Oone__class_Oone(X4780),X4779) = X4779 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
fof(i_0_2165,plain,
! [X4315,X4316] :
( ~ class_Rings_Ocomm__semiring__1(X4316)
| c_Groups_Oplus__class_Oplus(X4316,c_Groups_Ozero__class_Ozero(X4316),X4315) = X4315 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2166,plain,
! [X3913,X3914] :
( ~ class_Groups_Omonoid__add(X3914)
| c_Groups_Oplus__class_Oplus(X3914,c_Groups_Ozero__class_Ozero(X3914),X3913) = X3913 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2167,plain,
! [X3911,X3912] :
( ~ class_Groups_Ocomm__monoid__add(X3912)
| c_Groups_Oplus__class_Oplus(X3912,c_Groups_Ozero__class_Ozero(X3912),X3911) = X3911 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2168,plain,
! [X3594,X3595] :
( ~ class_Groups_Ogroup__add(X3595)
| c_Groups_Ominus__class_Ominus(X3595,X3594,c_Groups_Ozero__class_Ozero(X3595)) = X3594 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2169,plain,
! [X4317,X4318] :
( ~ class_Rings_Ocomm__semiring__1(X4318)
| c_Groups_Oplus__class_Oplus(X4318,X4317,c_Groups_Ozero__class_Ozero(X4318)) = X4317 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2170,plain,
! [X3907,X3908] :
( ~ class_Groups_Omonoid__add(X3908)
| c_Groups_Oplus__class_Oplus(X3908,X3907,c_Groups_Ozero__class_Ozero(X3908)) = X3907 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2171,plain,
! [X3905,X3906] :
( ~ class_Groups_Ocomm__monoid__add(X3906)
| c_Groups_Oplus__class_Oplus(X3906,X3905,c_Groups_Ozero__class_Ozero(X3906)) = X3905 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2172,plain,
! [X5402,X5403] :
( ~ class_Rings_Ocomm__semiring__1(X5403)
| c_Rings_Odvd__class_Odvd(X5403,c_Groups_Oone__class_Oone(X5403),X5402) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_2173,plain,
! [X5354,X5355] :
( ~ class_Rings_Ocomm__semiring__1(X5355)
| c_Rings_Odvd__class_Odvd(X5355,X5354,c_Groups_Ozero__class_Ozero(X5355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_2174,plain,
! [X4382,X4383] :
( ~ class_Rings_Ocomm__semiring__1(X4383)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4383),X4382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4383) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2175,plain,
! [X2962,X2963] :
( ~ class_Power_Opower(X2963)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2963),X2962),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2963) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2176,plain,
! [X4346,X4347] :
( ~ class_Rings_Ocomm__semiring__1(X4347)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4347),X4346),c_Groups_Oone__class_Oone(X4347)) = X4346 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2177,plain,
! [X3973,X3974] :
( ~ class_Groups_Ocomm__monoid__mult(X3974)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3974),X3973),c_Groups_Oone__class_Oone(X3974)) = X3973 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2178,plain,
! [X3975,X3976] :
( ~ class_Groups_Omonoid__mult(X3976)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3976),X3975),c_Groups_Oone__class_Oone(X3976)) = X3975 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2179,plain,
! [X3596,X3597] :
( ~ class_Groups_Ogroup__add(X3597)
| c_Groups_Ominus__class_Ominus(X3597,X3596,X3596) = c_Groups_Ozero__class_Ozero(X3597) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2180,plain,
! [X4928,X4929,X4930] :
( ~ class_Orderings_Opreorder(X4930)
| X4929 != X4928
| c_Orderings_Oord__class_Oless__eq(X4930,X4929,X4928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2181,plain,
! [X2835,X2836,X2837] :
( ~ class_Rings_Odivision__ring(X2837)
| c_Rings_Oinverse__class_Oinverse(X2837,X2836) != c_Rings_Oinverse__class_Oinverse(X2837,X2835)
| X2836 = c_Groups_Ozero__class_Ozero(X2837)
| X2835 = c_Groups_Ozero__class_Ozero(X2837)
| X2836 = X2835 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).
fof(i_0_2182,plain,
! [X4361,X4362] :
( ~ class_Rings_Ocomm__semiring__1(X4362)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4362),X4361),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4361 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2183,plain,
! [X3132,X3133] :
( ~ class_Groups_Omonoid__mult(X3133)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3133),X3132),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3132 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2184,plain,
! [X5155] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X5155)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2185,plain,
! [X5121] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X5121)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2186,plain,
! [X5417,X5418] :
( ~ class_Rings_Ocomm__semiring__1(X5418)
| c_Rings_Odvd__class_Odvd(X5418,X5417,X5417) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_2187,plain,
! [X4914,X4915] :
( ~ class_Orderings_Opreorder(X4915)
| c_Orderings_Oord__class_Oless__eq(X4915,X4914,X4914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_2188,plain,
! [X5324,X5325] :
( ~ class_Rings_Olinordered__idom(X5325)
| c_Groups_Osgn__class_Osgn(X5325,c_Groups_Osgn__class_Osgn(X5325,X5324)) = c_Groups_Osgn__class_Osgn(X5325,X5324) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).
fof(i_0_2189,plain,
! [X4420,X4421] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4421)
| c_Groups_Oabs__class_Oabs(X4421,c_Groups_Oabs__class_Oabs(X4421,X4420)) = c_Groups_Oabs__class_Oabs(X4421,X4420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_2190,plain,
! [X4410,X4411] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4411)
| c_Groups_Oabs__class_Oabs(X4411,c_Groups_Ouminus__class_Ouminus(X4411,X4410)) = c_Groups_Oabs__class_Oabs(X4411,X4410) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(i_0_2191,plain,
! [X3743,X3744] :
( ~ class_RealVector_Oreal__normed__vector(X3744)
| c_RealVector_Onorm__class_Onorm(X3744,c_Groups_Ouminus__class_Ouminus(X3744,X3743)) = c_RealVector_Onorm__class_Onorm(X3744,X3743) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
fof(i_0_2192,plain,
! [X4722,X4723,X4724] :
( ( c_Polynomial_Opoly(X4724,X4723) != c_Polynomial_Opoly(X4724,X4722)
| X4723 = X4722
| ~ class_Int_Oring__char__0(X4724)
| ~ class_Rings_Oidom(X4724) )
& ( X4723 != X4722
| c_Polynomial_Opoly(X4724,X4723) = c_Polynomial_Opoly(X4724,X4722)
| ~ class_Int_Oring__char__0(X4724)
| ~ class_Rings_Oidom(X4724) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2193,plain,
! [X5289,X5290] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5290)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5290),X5289),X5289) = X5289 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_2194,plain,
! [X5287,X5288] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5288)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5288),X5287),X5287) = X5287 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_2195,plain,
! [X3432] :
( X3432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2196,plain,
! [X4417,X4418] :
( ~ class_RealVector_Oreal__normed__vector(X4418)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4418,X4417)) = c_RealVector_Onorm__class_Onorm(X4418,X4417) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(i_0_2197,plain,
! [X4472,X4473] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4473)
| c_RealVector_Onorm__class_Onorm(X4473,c_RealVector_Oof__real(X4473,X4472)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4472) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(i_0_2198,plain,
! [X5201] :
( ~ class_Rings_Olinordered__idom(X5201)
| ~ c_Polynomial_Opos__poly(X5201,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5201))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1329])]) ).
fof(i_0_2199,plain,
! [X4068] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4068) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2200,plain,
! [X5345,X5346] :
( ( X5345 != c_Groups_Ozero__class_Ozero(X5346)
| c_RealVector_Onorm__class_Onorm(X5346,c_Groups_Osgn__class_Osgn(X5346,X5345)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5346) )
& ( X5345 = c_Groups_Ozero__class_Ozero(X5346)
| c_RealVector_Onorm__class_Onorm(X5346,c_Groups_Osgn__class_Osgn(X5346,X5345)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5346) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__sgn])])]) ).
fof(i_0_2201,plain,
! [X4607] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4607) = X4607,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2202,plain,
! [X3456] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3456) = X3456,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2203,plain,
! [X4067] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4067,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4067,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2204,plain,
! [X4604] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4604,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4604,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2205,plain,
! [X3457] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3457,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3457,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2206,plain,
! [X3287,X3288] :
( X3288 != X3287
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3288,X3287) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2207,plain,
! [X3305] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3305),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2208,plain,
! [X3276] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3276),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2209,plain,
! [X4713] :
( ~ class_Groups_Oab__group__add(X4713)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4713),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4713))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2210,plain,
! [X4066] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4066,X4066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2211,plain,
! [X3372] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3372) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2212,plain,
! [X3681,X3682,X3683] :
( ( c_RealVector_Oof__real(X3683,X3682) != c_RealVector_Oof__real(X3683,X3681)
| X3682 = X3681
| ~ class_RealVector_Oreal__algebra__1(X3683) )
& ( X3682 != X3681
| c_RealVector_Oof__real(X3683,X3682) = c_RealVector_Oof__real(X3683,X3681)
| ~ class_RealVector_Oreal__algebra__1(X3683) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__iff])])]) ).
fof(i_0_2213,plain,
! [X5300,X5301,X5302] :
( ( c_Groups_Ouminus__class_Ouminus(X5302,X5301) != c_Groups_Ouminus__class_Ouminus(X5302,X5300)
| X5301 = X5300
| ~ class_Lattices_Oboolean__algebra(X5302) )
& ( X5301 != X5300
| c_Groups_Ouminus__class_Ouminus(X5302,X5301) = c_Groups_Ouminus__class_Ouminus(X5302,X5300)
| ~ class_Lattices_Oboolean__algebra(X5302) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_2214,plain,
! [X3673,X3674,X3675] :
( ( c_Groups_Ouminus__class_Ouminus(X3675,X3674) != c_Groups_Ouminus__class_Ouminus(X3675,X3673)
| X3674 = X3673
| ~ class_Groups_Ogroup__add(X3675) )
& ( X3674 != X3673
| c_Groups_Ouminus__class_Ouminus(X3675,X3674) = c_Groups_Ouminus__class_Ouminus(X3675,X3673)
| ~ class_Groups_Ogroup__add(X3675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2215,plain,
! [X2832,X2833,X2834] :
( ~ class_Rings_Odivision__ring__inverse__zero(X2834)
| c_Rings_Oinverse__class_Oinverse(X2834,X2833) != c_Rings_Oinverse__class_Oinverse(X2834,X2832)
| X2833 = X2832 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq])]) ).
fof(i_0_2216,plain,
! [X2826,X2827,X2828] :
( ( c_Rings_Oinverse__class_Oinverse(X2828,X2827) != c_Rings_Oinverse__class_Oinverse(X2828,X2826)
| X2827 = X2826
| ~ class_Rings_Odivision__ring__inverse__zero(X2828) )
& ( X2827 != X2826
| c_Rings_Oinverse__class_Oinverse(X2828,X2827) = c_Rings_Oinverse__class_Oinverse(X2828,X2826)
| ~ class_Rings_Odivision__ring__inverse__zero(X2828) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq])])]) ).
fof(i_0_2217,plain,
! [X2840,X2841] :
( ~ class_Rings_Odivision__ring(X2841)
| X2840 = c_Groups_Ozero__class_Ozero(X2841)
| c_Rings_Oinverse__class_Oinverse(X2841,c_Rings_Oinverse__class_Oinverse(X2841,X2840)) = X2840 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).
fof(i_0_2218,plain,
! [X4606] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4606) = X4606,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2219,plain,
! [X3425] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3425) = X3425,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2220,plain,
! [X3504] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3504) = X3504,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2221,plain,
! [X4622] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4622,X4622),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2222,plain,
! [X3277] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3277,X3277),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2223,plain,
! [X3383] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3383,X3383),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2224,plain,
! [X3371] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3371),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,
! [X4603] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4603),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4603,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2226,plain,
! [X3428] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3428),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3428,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2227,plain,
! [X5294,X5295] :
( ~ class_Lattices_Oboolean__algebra(X5295)
| c_Groups_Ouminus__class_Ouminus(X5295,c_Groups_Ouminus__class_Ouminus(X5295,X5294)) = X5294 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_2228,plain,
! [X3662,X3663] :
( ~ class_Groups_Ogroup__add(X3663)
| c_Groups_Ouminus__class_Ouminus(X3663,c_Groups_Ouminus__class_Ouminus(X3663,X3662)) = X3662 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2229,plain,
! [X2820,X2821] :
( ~ class_Rings_Odivision__ring__inverse__zero(X2821)
| c_Rings_Oinverse__class_Oinverse(X2821,c_Rings_Oinverse__class_Oinverse(X2821,X2820)) = X2820 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
fof(i_0_2230,plain,
! [X5207] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5207)) = c_RealDef_Oreal(tc_Nat_Onat,X5207),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(i_0_2231,plain,
! [X3670,X3671,X3672] :
( ( c_Groups_Ouminus__class_Ouminus(X3672,X3671) != X3670
| c_Groups_Ouminus__class_Ouminus(X3672,X3670) = X3671
| ~ class_Groups_Ogroup__add(X3672) )
& ( c_Groups_Ouminus__class_Ouminus(X3672,X3670) != X3671
| c_Groups_Ouminus__class_Ouminus(X3672,X3671) = X3670
| ~ class_Groups_Ogroup__add(X3672) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2232,plain,
! [X3667,X3668,X3669] :
( ( X3668 != c_Groups_Ouminus__class_Ouminus(X3669,X3667)
| X3667 = c_Groups_Ouminus__class_Ouminus(X3669,X3668)
| ~ class_Groups_Ogroup__add(X3669) )
& ( X3667 != c_Groups_Ouminus__class_Ouminus(X3669,X3668)
| X3668 = c_Groups_Ouminus__class_Ouminus(X3669,X3667)
| ~ class_Groups_Ogroup__add(X3669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2233,plain,
! [X4645,X4646] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4646,X4645) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4645 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4646))
| ~ class_Groups_Ozero(X4646) )
& ( X4645 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4646))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4646,X4645) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X4646) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2234,plain,
! [X5203,X5204] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5204) != c_RealDef_Oreal(tc_Nat_Onat,X5203)
| X5204 = X5203 )
& ( X5204 != X5203
| c_RealDef_Oreal(tc_Nat_Onat,X5204) = c_RealDef_Oreal(tc_Nat_Onat,X5203) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2235,plain,
! [X3605,X3606] :
( ( c_Groups_Ozero__class_Ozero(X3606) != c_Groups_Ouminus__class_Ouminus(X3606,X3605)
| c_Groups_Ozero__class_Ozero(X3606) = X3605
| ~ class_Groups_Ogroup__add(X3606) )
& ( c_Groups_Ozero__class_Ozero(X3606) != X3605
| c_Groups_Ozero__class_Ozero(X3606) = c_Groups_Ouminus__class_Ouminus(X3606,X3605)
| ~ class_Groups_Ogroup__add(X3606) ) ),
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,
! [X3465,X3466] :
( ( c_Rings_Oinverse__class_Oinverse(X3466,X3465) != c_Groups_Oone__class_Oone(X3466)
| X3465 = c_Groups_Oone__class_Oone(X3466)
| ~ class_Fields_Ofield__inverse__zero(X3466) )
& ( X3465 != c_Groups_Oone__class_Oone(X3466)
| c_Rings_Oinverse__class_Oinverse(X3466,X3465) = c_Groups_Oone__class_Oone(X3466)
| ~ class_Fields_Ofield__inverse__zero(X3466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).
fof(i_0_2237,plain,
! [X5321,X5322] :
( ( c_Groups_Osgn__class_Osgn(X5322,X5321) != c_Groups_Ozero__class_Ozero(X5322)
| X5321 = c_Groups_Ozero__class_Ozero(X5322)
| ~ class_Rings_Olinordered__idom(X5322) )
& ( X5321 != c_Groups_Ozero__class_Ozero(X5322)
| c_Groups_Osgn__class_Osgn(X5322,X5321) = c_Groups_Ozero__class_Ozero(X5322)
| ~ class_Rings_Olinordered__idom(X5322) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).
fof(i_0_2238,plain,
! [X5319,X5320] :
( ( c_Groups_Osgn__class_Osgn(X5320,X5319) != c_Groups_Ozero__class_Ozero(X5320)
| X5319 = c_Groups_Ozero__class_Ozero(X5320)
| ~ class_RealVector_Oreal__normed__vector(X5320) )
& ( X5319 != c_Groups_Ozero__class_Ozero(X5320)
| c_Groups_Osgn__class_Osgn(X5320,X5319) = c_Groups_Ozero__class_Ozero(X5320)
| ~ class_RealVector_Oreal__normed__vector(X5320) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff])])]) ).
fof(i_0_2239,plain,
! [X4390,X4391] :
( ( c_Groups_Oabs__class_Oabs(X4391,X4390) != c_Groups_Ozero__class_Ozero(X4391)
| X4390 = c_Groups_Ozero__class_Ozero(X4391)
| ~ class_Groups_Oordered__ab__group__add__abs(X4391) )
& ( X4390 != c_Groups_Ozero__class_Ozero(X4391)
| c_Groups_Oabs__class_Oabs(X4391,X4390) = c_Groups_Ozero__class_Ozero(X4391)
| ~ class_Groups_Oordered__ab__group__add__abs(X4391) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_2240,plain,
! [X3609,X3610] :
( ( c_Groups_Ouminus__class_Ouminus(X3610,X3609) != c_Groups_Ozero__class_Ozero(X3610)
| X3609 = c_Groups_Ozero__class_Ozero(X3610)
| ~ class_Groups_Ogroup__add(X3610) )
& ( X3609 != c_Groups_Ozero__class_Ozero(X3610)
| c_Groups_Ouminus__class_Ouminus(X3610,X3609) = c_Groups_Ozero__class_Ozero(X3610)
| ~ class_Groups_Ogroup__add(X3610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2241,plain,
! [X2842,X2843] :
( ~ class_Rings_Odivision__ring(X2843)
| X2842 = c_Groups_Ozero__class_Ozero(X2843)
| c_Rings_Oinverse__class_Oinverse(X2843,X2842) != c_Groups_Ozero__class_Ozero(X2843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).
fof(i_0_2242,plain,
! [X2838,X2839] :
( ~ class_Rings_Odivision__ring(X2839)
| c_Rings_Oinverse__class_Oinverse(X2839,X2838) != c_Groups_Ozero__class_Ozero(X2839)
| X2838 = c_Groups_Ozero__class_Ozero(X2839) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).
fof(i_0_2243,plain,
! [X2844,X2845] :
( ( c_Rings_Oinverse__class_Oinverse(X2845,X2844) != c_Groups_Ozero__class_Ozero(X2845)
| X2844 = c_Groups_Ozero__class_Ozero(X2845)
| ~ class_Rings_Odivision__ring__inverse__zero(X2845) )
& ( X2844 != c_Groups_Ozero__class_Ozero(X2845)
| c_Rings_Oinverse__class_Oinverse(X2845,X2844) = c_Groups_Ozero__class_Ozero(X2845)
| ~ class_Rings_Odivision__ring__inverse__zero(X2845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
fof(i_0_2244,plain,
! [X3781,X3782] :
( ( c_RealVector_Oof__real(X3782,X3781) != c_Groups_Ozero__class_Ozero(X3782)
| X3781 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X3782) )
& ( X3781 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X3782,X3781) = c_Groups_Ozero__class_Ozero(X3782)
| ~ class_RealVector_Oreal__algebra__1(X3782) ) ),
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,
! [X3229,X3230] :
( ( c_RealVector_Onorm__class_Onorm(X3230,X3229) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3229 = c_Groups_Ozero__class_Ozero(X3230)
| ~ class_RealVector_Oreal__normed__vector(X3230) )
& ( X3229 != c_Groups_Ozero__class_Ozero(X3230)
| c_RealVector_Onorm__class_Onorm(X3230,X3229) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X3230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2246,plain,
! [X5441,X5442] :
( ~ class_Groups_Ouminus(X5442)
| class_Groups_Ouminus(tc_fun(X5441,X5442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_2247,plain,
! [X5443,X5444] :
( ~ class_Groups_Ominus(X5444)
| class_Groups_Ominus(tc_fun(X5443,X5444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_2248,plain,
! [X5433,X5434] :
( ~ class_Lattices_Oboolean__algebra(X5434)
| class_Lattices_Oboolean__algebra(tc_fun(X5433,X5434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_2249,plain,
! [X5437,X5438] :
( ~ class_Orderings_Oorder(X5438)
| class_Orderings_Oorder(tc_fun(X5437,X5438)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2250,plain,
! [X5439,X5440] :
( ~ class_Orderings_Oord(X5440)
| class_Orderings_Oord(tc_fun(X5439,X5440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2251,plain,
! [X5435,X5436] :
( ~ class_Orderings_Opreorder(X5436)
| class_Orderings_Opreorder(tc_fun(X5435,X5436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2252,plain,
! [X4621] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4621)) = X4621,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2253,plain,
! [X3611,X3612] :
( ( c_Groups_Ouminus__class_Ouminus(X3612,X3611) != X3611
| X3611 = c_Groups_Ozero__class_Ozero(X3612)
| ~ class_Groups_Olinordered__ab__group__add(X3612) )
& ( X3611 != c_Groups_Ozero__class_Ozero(X3612)
| c_Groups_Ouminus__class_Ouminus(X3612,X3611) = X3611
| ~ class_Groups_Olinordered__ab__group__add(X3612) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2254,plain,
! [X3607,X3608] :
( ( X3607 != c_Groups_Ouminus__class_Ouminus(X3608,X3607)
| X3607 = c_Groups_Ozero__class_Ozero(X3608)
| ~ class_Groups_Olinordered__ab__group__add(X3608) )
& ( X3607 != c_Groups_Ozero__class_Ozero(X3608)
| X3607 = c_Groups_Ouminus__class_Ouminus(X3608,X3607)
| ~ class_Groups_Olinordered__ab__group__add(X3608) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2255,plain,
! [X3783] :
( ~ class_RealVector_Oreal__algebra__1(X3783)
| ~ class_RealVector_Oreal__normed__vector(X3783)
| c_RealVector_Oof__real(X3783,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X3783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ozero])]) ).
fof(i_0_2256,plain,
! [X5332] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5332)
| c_Groups_Osgn__class_Osgn(X5332,c_Groups_Oone__class_Oone(X5332)) = c_Groups_Oone__class_Oone(X5332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__one])]) ).
fof(i_0_2257,plain,
! [X5318] :
( ~ class_Groups_Osgn__if(X5318)
| c_Groups_Osgn__class_Osgn(X5318,c_Groups_Ozero__class_Ozero(X5318)) = c_Groups_Ozero__class_Ozero(X5318) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).
fof(i_0_2258,plain,
! [X5323] :
( ~ class_RealVector_Oreal__normed__vector(X5323)
| c_Groups_Osgn__class_Osgn(X5323,c_Groups_Ozero__class_Ozero(X5323)) = c_Groups_Ozero__class_Ozero(X5323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero])]) ).
fof(i_0_2259,plain,
! [X4406] :
( ~ class_Rings_Olinordered__idom(X4406)
| c_Groups_Oabs__class_Oabs(X4406,c_Groups_Oone__class_Oone(X4406)) = c_Groups_Oone__class_Oone(X4406) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_2260,plain,
! [X4392] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4392)
| c_Groups_Oabs__class_Oabs(X4392,c_Groups_Ozero__class_Ozero(X4392)) = c_Groups_Ozero__class_Ozero(X4392) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_2261,plain,
! [X3604] :
( ~ class_Groups_Ogroup__add(X3604)
| c_Groups_Ouminus__class_Ouminus(X3604,c_Groups_Ozero__class_Ozero(X3604)) = c_Groups_Ozero__class_Ozero(X3604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2262,plain,
! [X2847] :
( ~ class_Rings_Odivision__ring(X2847)
| c_Rings_Oinverse__class_Oinverse(X2847,c_Groups_Oone__class_Oone(X2847)) = c_Groups_Oone__class_Oone(X2847) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).
fof(i_0_2263,plain,
! [X3431] :
( ~ class_Fields_Ofield__inverse__zero(X3431)
| c_Rings_Oinverse__class_Oinverse(X3431,c_Groups_Ozero__class_Ozero(X3431)) = c_Groups_Ozero__class_Ozero(X3431) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).
fof(i_0_2264,plain,
! [X2846] :
( ~ class_Rings_Odivision__ring__inverse__zero(X2846)
| c_Rings_Oinverse__class_Oinverse(X2846,c_Groups_Ozero__class_Ozero(X2846)) = c_Groups_Ozero__class_Ozero(X2846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).
fof(i_0_2265,plain,
! [X3245] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3245)
| c_RealVector_Onorm__class_Onorm(X3245,c_Groups_Oone__class_Oone(X3245)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2266,plain,
! [X3228] :
( ~ class_RealVector_Oreal__normed__vector(X3228)
| c_RealVector_Onorm__class_Onorm(X3228,c_Groups_Ozero__class_Ozero(X3228)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2267,plain,
! [X3821] :
( ~ class_RealVector_Oreal__algebra__1(X3821)
| c_RealVector_Oof__real(X3821,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X3821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])]) ).
fof(i_0_2268,plain,
! [X3784] :
( ~ class_RealVector_Oreal__algebra__1(X3784)
| c_RealVector_Oof__real(X3784,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X3784) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__0])]) ).
fof(i_0_2269,plain,
! [X5220] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X5220)) = X5220,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2270,plain,
! [X5219] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X5219)) = X5219,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2271,plain,
! [X5202] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5202) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X5202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5202 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X5202) = 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,
! [X4419] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4419) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4419),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(i_0_2273,plain,
! [X3091] :
( ~ class_Rings_Ozero__neq__one(X3091)
| c_Groups_Oone__class_Oone(X3091) != c_Groups_Ozero__class_Ozero(X3091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2274,plain,
! [X3090] :
( ~ class_Rings_Ozero__neq__one(X3090)
| c_Groups_Ozero__class_Ozero(X3090) != c_Groups_Oone__class_Oone(X3090) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2275,plain,
! [X5432] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5432)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5432)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2276,plain,
! [X5504] :
( ~ class_Rings_Ocomm__semiring__1(X5504)
| class_Rings_Odvd(tc_Polynomial_Opoly(X5504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd])]) ).
fof(i_0_2277,plain,
! [X5495] :
( ~ class_Rings_Olinordered__idom(X5495)
| class_Groups_Osgn__if(tc_Polynomial_Opoly(X5495)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if])]) ).
fof(i_0_2278,plain,
! [X5494] :
( ~ class_Groups_Oab__group__add(X5494)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X5494)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).
fof(i_0_2279,plain,
! [X5498] :
( ~ class_Groups_Oab__group__add(X5498)
| class_Groups_Ominus(tc_Polynomial_Opoly(X5498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])]) ).
fof(i_0_2280,plain,
! [X5490] :
( ~ class_Rings_Olinordered__idom(X5490)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2281,plain,
! [X5482] :
( ~ class_Rings_Olinordered__idom(X5482)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2282,plain,
! [X5493] :
( ~ class_Rings_Olinordered__idom(X5493)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5493)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2283,plain,
! [X5481] :
( ~ class_Rings_Olinordered__idom(X5481)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2284,plain,
! [X5489] :
( ~ class_Rings_Ocomm__ring(X5489)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2285,plain,
! [X5491] :
( ~ class_Rings_Olinordered__idom(X5491)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2286,plain,
! [X5476] :
( ~ class_Rings_Ocomm__semiring__0(X5476)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2287,plain,
! [X5496] :
( ~ class_Rings_Olinordered__idom(X5496)
| class_Groups_Oabs__if(tc_Polynomial_Opoly(X5496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if])]) ).
fof(i_0_2288,plain,
! [X5470] :
( ~ class_Rings_Olinordered__idom(X5470)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X5470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs])]) ).
fof(i_0_2289,plain,
! [X5452] :
( ~ class_Rings_Olinordered__idom(X5452)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X5452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])]) ).
fof(i_0_2290,plain,
! [X5484] :
( ~ class_Rings_Ocomm__ring__1(X5484)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2291,plain,
! [X5445] :
( ~ class_Rings_Oidom(X5445)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2292,plain,
! [X5475] :
( ~ class_Rings_Ocomm__semiring__1(X5475)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2293,plain,
! [X5446] :
( ~ class_Rings_Olinordered__idom(X5446)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2294,plain,
! [X5451] :
( ~ class_Rings_Olinordered__idom(X5451)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2295,plain,
! [X5447] :
( ~ class_Rings_Olinordered__idom(X5447)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2296,plain,
! [X5485] :
( ~ class_Groups_Ocomm__monoid__add(X5485)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2297,plain,
! [X5472] :
( ~ class_Groups_Ocomm__monoid__add(X5472)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2298,plain,
! [X5503] :
( ~ class_Rings_Ocomm__semiring__1(X5503)
| class_Groups_Oone(tc_Polynomial_Opoly(X5503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2299,plain,
! [X5468] :
( ~ class_Groups_Ocomm__monoid__add(X5468)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5468)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2300,plain,
! [X5455] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5455)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5455)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2301,plain,
! [X5463] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5463)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2302,plain,
! [X5466] :
( ~ class_Rings_Ocomm__semiring__0(X5466)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2303,plain,
! [X5500] :
( ~ class_Groups_Ozero(X5500)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2304,plain,
! [X5497] :
( ~ class_Rings_Ocomm__ring__1(X5497)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5497)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2305,plain,
! [X5501] :
( ~ class_Rings_Ocomm__ring(X5501)
| class_Rings_Oring(tc_Polynomial_Opoly(X5501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2306,plain,
! [X5502] :
( ~ class_Rings_Oidom(X5502)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2307,plain,
! [X5462] :
( ~ class_Rings_Olinordered__idom(X5462)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2308,plain,
! [X5454] :
( ~ class_Rings_Olinordered__idom(X5454)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2309,plain,
! [X5478] :
( ~ class_Groups_Oab__group__add(X5478)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2310,plain,
! [X5487] :
( ~ class_Groups_Oab__group__add(X5487)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5487)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2311,plain,
! [X5453] :
( ~ class_Rings_Olinordered__idom(X5453)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2312,plain,
! [X5486] :
( ~ class_Rings_Ocomm__semiring__0(X5486)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2313,plain,
! [X5448] :
( ~ class_Rings_Olinordered__idom(X5448)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2314,plain,
! [X5467] :
( ~ class_Rings_Ocomm__semiring__1(X5467)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2315,plain,
! [X5456] :
( ~ class_Rings_Oidom(X5456)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5456)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2316,plain,
! [X5477] :
( ~ class_Rings_Ocomm__semiring__0(X5477)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2317,plain,
! [X5492] :
( ~ class_Rings_Ocomm__semiring__0(X5492)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2318,plain,
! [X5479] :
( ~ class_Rings_Ocomm__semiring__1(X5479)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2319,plain,
! [X5488] :
( ~ class_Rings_Ocomm__semiring__0(X5488)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2320,plain,
! [X5459] :
( ~ class_Rings_Oidom(X5459)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5459)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2321,plain,
! [X5471] :
( ~ class_Rings_Oidom(X5471)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2322,plain,
! [X5449] :
( ~ class_Rings_Olinordered__idom(X5449)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2323,plain,
! [X5461] :
( ~ class_Rings_Olinordered__idom(X5461)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2324,plain,
! [X5474] :
( ~ class_Rings_Olinordered__idom(X5474)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2325,plain,
! [X5464] :
( ~ class_Rings_Olinordered__idom(X5464)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5464)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2326,plain,
! [X5450] :
( ~ class_Rings_Olinordered__idom(X5450)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2327,plain,
! [X5499] :
( ~ class_Rings_Ocomm__semiring__1(X5499)
| class_Power_Opower(tc_Polynomial_Opoly(X5499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2328,plain,
! [X5460] :
( ~ class_Rings_Olinordered__idom(X5460)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5460)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2329,plain,
! [X5469] :
( ~ class_Rings_Olinordered__idom(X5469)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2330,plain,
! [X5480] :
( ~ class_Rings_Olinordered__idom(X5480)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2331,plain,
! [X5457] :
( ~ class_Rings_Olinordered__idom(X5457)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2332,plain,
! [X5483] :
( ~ class_Rings_Ocomm__semiring__1(X5483)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2333,plain,
! [X5458] :
( ~ class_Rings_Olinordered__idom(X5458)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2334,plain,
! [X5473] :
( ~ class_Rings_Olinordered__idom(X5473)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2335,plain,
! [X5465] :
( ~ class_Rings_Olinordered__idom(X5465)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5465)) ),
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),esk23_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk24_0,esk25_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____)),esk18_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,esk22_4(X3,X2,X4,X1)),hAPP(X3,esk22_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,esk3_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____)),esk19_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____)),esk20_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))))),esk21_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))),esk29_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,esk25_0),esk23_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_Rings_Ocomm__semiring__1(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_Groups_Ocomm__monoid__mult(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)
| ~ 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_1450]),
[final] ).
cnf(i_0_2498,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_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)),esk30_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__1(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(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_1398]),
[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_1397]),
[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,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,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),X4),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2577,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_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),esk6_0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2579,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_2580,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_2581,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_1517]),
[final] ).
cnf(i_0_2582,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_1518]),
[final] ).
cnf(i_0_2583,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_1519]),
[final] ).
cnf(i_0_2584,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_1520]),
[final] ).
cnf(i_0_2585,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_1521]),
[final] ).
cnf(i_0_2586,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_2587,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_2588,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_2589,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_1522]),
[final] ).
cnf(i_0_2590,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_1523]),
[final] ).
cnf(i_0_2591,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_1524]),
[final] ).
cnf(i_0_2592,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_1525]),
[final] ).
cnf(i_0_2593,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_1526]),
[final] ).
cnf(i_0_2594,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_1527]),
[final] ).
cnf(i_0_2595,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_1528]),
[final] ).
cnf(i_0_2596,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_2597,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_2598,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_1529]),
[final] ).
cnf(i_0_2599,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_1530]),
[final] ).
cnf(i_0_2600,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_1531]),
[final] ).
cnf(i_0_2601,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_1532]),
[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_1533]),
[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_1534]),
[final] ).
cnf(i_0_2604,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_2605,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_1535]),
[final] ).
cnf(i_0_2606,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_2607,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_1536]),
[final] ).
cnf(i_0_2608,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_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__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_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))
| ~ 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_1538]),
[final] ).
cnf(i_0_2611,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_2612,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_1539]),
[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_1540]),
[final] ).
cnf(i_0_2614,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_2615,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_2616,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_1541]),
[final] ).
cnf(i_0_2617,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_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(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_1542]),
[final] ).
cnf(i_0_2620,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_1543]),
[final] ).
cnf(i_0_2621,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_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(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(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__eq(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(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_1547]),
[final] ).
cnf(i_0_2625,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_1548]),
[final] ).
cnf(i_0_2626,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_2627,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_1549]),
[final] ).
cnf(i_0_2628,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_1450]),
[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,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_1550]),
[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,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_1550]),
[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,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_1550]),
[final] ).
cnf(i_0_2632,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_1550]),
[final] ).
cnf(i_0_2633,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_1551]),
[final] ).
cnf(i_0_2634,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_1552]),
[final] ).
cnf(i_0_2635,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_1553]),
[final] ).
cnf(i_0_2636,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_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_Rings_Ocomm__semiring__1(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_Groups_Oab__semigroup__mult(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_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_1593]),
[final] ).
cnf(i_0_2689,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_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))
| ~ 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_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,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_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,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_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,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_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))
| ~ 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_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_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[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_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[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))
| ~ 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_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))
| ~ 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_2741,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_1634]),
[final] ).
cnf(i_0_2742,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_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))
| ~ 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_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))
| ~ 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_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_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[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)),esk14_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),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2761,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_2762,plain,
( c_Rings_Odvd__class_Odvd(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)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_2763,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_1648]),
[final] ).
cnf(i_0_2764,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_1649]),
[final] ).
cnf(i_0_2765,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_1650]),
[final] ).
cnf(i_0_2766,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_1651]),
[final] ).
cnf(i_0_2767,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_1652]),
[final] ).
cnf(i_0_2768,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_1653]),
[final] ).
cnf(i_0_2769,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_1654]),
[final] ).
cnf(i_0_2770,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_1655]),
[final] ).
cnf(i_0_2771,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_1656]),
[final] ).
cnf(i_0_2772,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_1657]),
[final] ).
cnf(i_0_2773,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_1658]),
[final] ).
cnf(i_0_2774,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_1659]),
[final] ).
cnf(i_0_2775,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_1519]),
[final] ).
cnf(i_0_2776,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_1660]),
[final] ).
cnf(i_0_2777,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_1661]),
[final] ).
cnf(i_0_2778,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_1662]),
[final] ).
cnf(i_0_2779,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_1520]),
[final] ).
cnf(i_0_2780,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_1663]),
[final] ).
cnf(i_0_2781,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_1664]),
[final] ).
cnf(i_0_2782,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_2783,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_1666]),
[final] ).
cnf(i_0_2784,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_1667]),
[final] ).
cnf(i_0_2785,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)),esk13_1(X1)))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_2786,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_1669]),
[final] ).
cnf(i_0_2787,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_1670]),
[final] ).
cnf(i_0_2788,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_1671]),
[final] ).
cnf(i_0_2789,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_2790,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_2791,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_2792,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_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_1676]),
[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_1677]),
[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_1678]),
[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_1679]),
[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_1680]),
[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_1681]),
[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_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[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_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[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_1684]),
[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_1685]),
[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_1686]),
[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_1687]),
[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_1688]),
[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_1689]),
[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_1690]),
[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_1691]),
[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_1692]),
[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_1693]),
[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_1694]),
[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_1695]),
[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_1696]),
[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_1697]),
[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_1698]),
[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_1699]),
[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_1700]),
[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_1701]),
[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_1702]),
[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_1703]),
[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_1704]),
[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_1705]),
[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_1705]),
[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_1706]),
[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_1706]),
[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_1707]),
[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_1708]),
[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_1709]),
[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_1710]),
[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_1711]),
[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_1712]),
[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_1713]),
[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_1714]),
[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_1715]),
[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_1716]),
[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_1717]),
[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_1718]),
[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_1719]),
[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_1720]),
[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_1721]),
[final] ).
cnf(i_0_2846,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_1722]),
[final] ).
cnf(i_0_2847,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_1723]),
[final] ).
cnf(i_0_2848,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_1724]),
[final] ).
cnf(i_0_2849,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_1725]),
[final] ).
cnf(i_0_2850,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_1726]),
[final] ).
cnf(i_0_2851,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_1727]),
[final] ).
cnf(i_0_2852,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_1728]),
[final] ).
cnf(i_0_2853,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_1729]),
[final] ).
cnf(i_0_2854,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_1730]),
[final] ).
cnf(i_0_2855,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_1731]),
[final] ).
cnf(i_0_2856,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_1731]),
[final] ).
cnf(i_0_2857,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_1732]),
[final] ).
cnf(i_0_2858,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_1733]),
[final] ).
cnf(i_0_2859,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_1734]),
[final] ).
cnf(i_0_2860,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_1735]),
[final] ).
cnf(i_0_2861,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_1736]),
[final] ).
cnf(i_0_2862,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_1736]),
[final] ).
cnf(i_0_2863,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_1737]),
[final] ).
cnf(i_0_2864,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_1738]),
[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,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[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,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2867,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_1741]),
[final] ).
cnf(i_0_2868,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_1671]),
[final] ).
cnf(i_0_2869,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_1742]),
[final] ).
cnf(i_0_2870,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_1743]),
[final] ).
cnf(i_0_2871,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_2872,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_2873,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_1671]),
[final] ).
cnf(i_0_2874,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_2875,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_1701]),
[final] ).
cnf(i_0_2876,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_1701]),
[final] ).
cnf(i_0_2877,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_1744]),
[final] ).
cnf(i_0_2878,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_1745]),
[final] ).
cnf(i_0_2879,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_1746]),
[final] ).
cnf(i_0_2880,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_1747]),
[final] ).
cnf(i_0_2881,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_1748]),
[final] ).
cnf(i_0_2882,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_1749]),
[final] ).
cnf(i_0_2883,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_1689]),
[final] ).
cnf(i_0_2884,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_1690]),
[final] ).
cnf(i_0_2885,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_1687]),
[final] ).
cnf(i_0_2886,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_1688]),
[final] ).
cnf(i_0_2887,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_1750]),
[final] ).
cnf(i_0_2888,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_1751]),
[final] ).
cnf(i_0_2889,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_1671]),
[final] ).
cnf(i_0_2890,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_2891,plain,
( c_Rings_Odvd__class_Odvd(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2892,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_1736]),
[final] ).
cnf(i_0_2893,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_1752]),
[final] ).
cnf(i_0_2894,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_1753]),
[final] ).
cnf(i_0_2895,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),esk15_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_1754]),
[final] ).
cnf(i_0_2896,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_1678]),
[final] ).
cnf(i_0_2897,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_1679]),
[final] ).
cnf(i_0_2898,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_1680]),
[final] ).
cnf(i_0_2899,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_1676]),
[final] ).
cnf(i_0_2900,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_1677]),
[final] ).
cnf(i_0_2901,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_1755]),
[final] ).
cnf(i_0_2902,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_1756]),
[final] ).
cnf(i_0_2903,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_1757]),
[final] ).
cnf(i_0_2904,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_1758]),
[final] ).
cnf(i_0_2905,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_1759]),
[final] ).
cnf(i_0_2906,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_1760]),
[final] ).
cnf(i_0_2907,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_1761]),
[final] ).
cnf(i_0_2908,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_1762]),
[final] ).
cnf(i_0_2909,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_1763]),
[final] ).
cnf(i_0_2910,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_1764]),
[final] ).
cnf(i_0_2911,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_1765]),
[final] ).
cnf(i_0_2912,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_1766]),
[final] ).
cnf(i_0_2913,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_1767]),
[final] ).
cnf(i_0_2914,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_1741]),
[final] ).
cnf(i_0_2915,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_1695]),
[final] ).
cnf(i_0_2916,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_1696]),
[final] ).
cnf(i_0_2917,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_1768]),
[final] ).
cnf(i_0_2918,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_1769]),
[final] ).
cnf(i_0_2919,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_1758]),
[final] ).
cnf(i_0_2920,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_1756]),
[final] ).
cnf(i_0_2921,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_1770]),
[final] ).
cnf(i_0_2922,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_1771]),
[final] ).
cnf(i_0_2923,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_1772]),
[final] ).
cnf(i_0_2924,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_1773]),
[final] ).
cnf(i_0_2925,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_1774]),
[final] ).
cnf(i_0_2926,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_1775]),
[final] ).
cnf(i_0_2927,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_1776]),
[final] ).
cnf(i_0_2928,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_1777]),
[final] ).
cnf(i_0_2929,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_2930,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_1778]),
[final] ).
cnf(i_0_2931,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_1779]),
[final] ).
cnf(i_0_2932,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_2933,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_2934,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_2935,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_1780]),
[final] ).
cnf(i_0_2936,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_1719]),
[final] ).
cnf(i_0_2937,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_1781]),
[final] ).
cnf(i_0_2938,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_1721]),
[final] ).
cnf(i_0_2939,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_1720]),
[final] ).
cnf(i_0_2940,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_1718]),
[final] ).
cnf(i_0_2941,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_1782]),
[final] ).
cnf(i_0_2942,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_1783]),
[final] ).
cnf(i_0_2943,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_1722]),
[final] ).
cnf(i_0_2944,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_1723]),
[final] ).
cnf(i_0_2945,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_1724]),
[final] ).
cnf(i_0_2946,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_2947,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_1753]),
[final] ).
cnf(i_0_2948,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_1784]),
[final] ).
cnf(i_0_2949,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_1785]),
[final] ).
cnf(i_0_2950,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_1786]),
[final] ).
cnf(i_0_2951,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_2952,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_1787]),
[final] ).
cnf(i_0_2953,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_1788]),
[final] ).
cnf(i_0_2954,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_1789]),
[final] ).
cnf(i_0_2955,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_2956,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_1790]),
[final] ).
cnf(i_0_2957,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_1791]),
[final] ).
cnf(i_0_2958,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_1792]),
[final] ).
cnf(i_0_2959,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_1793]),
[final] ).
cnf(i_0_2960,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_1794]),
[final] ).
cnf(i_0_2961,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_1795]),
[final] ).
cnf(i_0_2962,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_1796]),
[final] ).
cnf(i_0_2963,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_1797]),
[final] ).
cnf(i_0_2964,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_1798]),
[final] ).
cnf(i_0_2965,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_1750]),
[final] ).
cnf(i_0_2966,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_1799]),
[final] ).
cnf(i_0_2967,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_1800]),
[final] ).
cnf(i_0_2968,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_1801]),
[final] ).
cnf(i_0_2969,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_1751]),
[final] ).
cnf(i_0_2970,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_1802]),
[final] ).
cnf(i_0_2971,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_1803]),
[final] ).
cnf(i_0_2972,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_1804]),
[final] ).
cnf(i_0_2973,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_1742]),
[final] ).
cnf(i_0_2974,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_1743]),
[final] ).
cnf(i_0_2975,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_2976,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_1806]),
[final] ).
cnf(i_0_2977,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_1807]),
[final] ).
cnf(i_0_2978,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_1808]),
[final] ).
cnf(i_0_2979,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_1809]),
[final] ).
cnf(i_0_2980,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_1810]),
[final] ).
cnf(i_0_2981,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_1811]),
[final] ).
cnf(i_0_2982,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_1812]),
[final] ).
cnf(i_0_2983,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_1813]),
[final] ).
cnf(i_0_2984,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_1814]),
[final] ).
cnf(i_0_2985,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_1815]),
[final] ).
cnf(i_0_2986,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_1816]),
[final] ).
cnf(i_0_2987,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_1817]),
[final] ).
cnf(i_0_2988,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_1818]),
[final] ).
cnf(i_0_2989,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_1819]),
[final] ).
cnf(i_0_2990,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_1820]),
[final] ).
cnf(i_0_2991,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_1821]),
[final] ).
cnf(i_0_2992,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_1822]),
[final] ).
cnf(i_0_2993,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_1823]),
[final] ).
cnf(i_0_2994,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_1824]),
[final] ).
cnf(i_0_2995,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_1825]),
[final] ).
cnf(i_0_2996,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_1826]),
[final] ).
cnf(i_0_2997,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_1827]),
[final] ).
cnf(i_0_2998,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_1828]),
[final] ).
cnf(i_0_2999,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_1829]),
[final] ).
cnf(i_0_3000,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_1753]),
[final] ).
cnf(i_0_3001,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_1830]),
[final] ).
cnf(i_0_3002,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_1830]),
[final] ).
cnf(i_0_3003,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_3004,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_1831]),
[final] ).
cnf(i_0_3005,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_1832]),
[final] ).
cnf(i_0_3006,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_1833]),
[final] ).
cnf(i_0_3007,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_1834]),
[final] ).
cnf(i_0_3008,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_1835]),
[final] ).
cnf(i_0_3009,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_1648]),
[final] ).
cnf(i_0_3010,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_1836]),
[final] ).
cnf(i_0_3011,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_1837]),
[final] ).
cnf(i_0_3012,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_1838]),
[final] ).
cnf(i_0_3013,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_1839]),
[final] ).
cnf(i_0_3014,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_1741]),
[final] ).
cnf(i_0_3015,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_1840]),
[final] ).
cnf(i_0_3016,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_1729]),
[final] ).
cnf(i_0_3017,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_1841]),
[final] ).
cnf(i_0_3018,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_1841]),
[final] ).
cnf(i_0_3019,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_1730]),
[final] ).
cnf(i_0_3020,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_1842]),
[final] ).
cnf(i_0_3021,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_1842]),
[final] ).
cnf(i_0_3022,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_1843]),
[final] ).
cnf(i_0_3023,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_1843]),
[final] ).
cnf(i_0_3024,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_1844]),
[final] ).
cnf(i_0_3025,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_1844]),
[final] ).
cnf(i_0_3026,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_1845]),
[final] ).
cnf(i_0_3027,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_1846]),
[final] ).
cnf(i_0_3028,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_1847]),
[final] ).
cnf(i_0_3029,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_1848]),
[final] ).
cnf(i_0_3030,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_1849]),
[final] ).
cnf(i_0_3031,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_1850]),
[final] ).
cnf(i_0_3032,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_1851]),
[final] ).
cnf(i_0_3033,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_1852]),
[final] ).
cnf(i_0_3034,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_1853]),
[final] ).
cnf(i_0_3035,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_1854]),
[final] ).
cnf(i_0_3036,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_1855]),
[final] ).
cnf(i_0_3037,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_1856]),
[final] ).
cnf(i_0_3038,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_1857]),
[final] ).
cnf(i_0_3039,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_1858]),
[final] ).
cnf(i_0_3040,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_1745]),
[final] ).
cnf(i_0_3041,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_1747]),
[final] ).
cnf(i_0_3042,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_1859]),
[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_Ozero__class_Ozero(X1),c_Groups_Osgn__class_Osgn(X1,X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3044,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_1861]),
[final] ).
cnf(i_0_3045,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_1862]),
[final] ).
cnf(i_0_3046,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_1863]),
[final] ).
cnf(i_0_3047,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_1745]),
[final] ).
cnf(i_0_3048,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_1864]),
[final] ).
cnf(i_0_3049,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_1747]),
[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_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_1865]),
[final] ).
cnf(i_0_3051,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_1866]),
[final] ).
cnf(i_0_3052,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_1867]),
[final] ).
cnf(i_0_3053,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_1868]),
[final] ).
cnf(i_0_3054,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_1869]),
[final] ).
cnf(i_0_3055,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_1671]),
[final] ).
cnf(i_0_3056,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_1870]),
[final] ).
cnf(i_0_3057,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_1821]),
[final] ).
cnf(i_0_3058,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_1822]),
[final] ).
cnf(i_0_3059,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_1871]),
[final] ).
cnf(i_0_3060,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_1823]),
[final] ).
cnf(i_0_3061,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_1872]),
[final] ).
cnf(i_0_3062,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_1873]),
[final] ).
cnf(i_0_3063,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_1749]),
[final] ).
cnf(i_0_3064,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_1874]),
[final] ).
cnf(i_0_3065,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_1875]),
[final] ).
cnf(i_0_3066,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_1876]),
[final] ).
cnf(i_0_3067,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_1877]),
[final] ).
cnf(i_0_3068,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_1878]),
[final] ).
cnf(i_0_3069,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_1879]),
[final] ).
cnf(i_0_3070,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_1880]),
[final] ).
cnf(i_0_3071,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_1881]),
[final] ).
cnf(i_0_3072,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_1882]),
[final] ).
cnf(i_0_3073,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_1883]),
[final] ).
cnf(i_0_3074,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_1856]),
[final] ).
cnf(i_0_3075,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_1762]),
[final] ).
cnf(i_0_3076,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_1857]),
[final] ).
cnf(i_0_3077,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_1763]),
[final] ).
cnf(i_0_3078,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_1762]),
[final] ).
cnf(i_0_3079,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_1861]),
[final] ).
cnf(i_0_3080,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_1863]),
[final] ).
cnf(i_0_3081,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_1763]),
[final] ).
cnf(i_0_3082,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_1862]),
[final] ).
cnf(i_0_3083,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_1884]),
[final] ).
cnf(i_0_3084,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_1858]),
[final] ).
cnf(i_0_3085,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_1860]),
[final] ).
cnf(i_0_3086,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_1859]),
[final] ).
cnf(i_0_3087,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_1885]),
[final] ).
cnf(i_0_3088,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_1864]),
[final] ).
cnf(i_0_3089,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_1865]),
[final] ).
cnf(i_0_3090,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_1886]),
[final] ).
cnf(i_0_3091,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_1887]),
[final] ).
cnf(i_0_3092,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_1888]),
[final] ).
cnf(i_0_3093,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_1889]),
[final] ).
cnf(i_0_3094,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_1890]),
[final] ).
cnf(i_0_3095,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3096,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_1729]),
[final] ).
cnf(i_0_3097,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_1892]),
[final] ).
cnf(i_0_3098,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_1730]),
[final] ).
cnf(i_0_3099,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_1893]),
[final] ).
cnf(i_0_3100,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3101,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_1895]),
[final] ).
cnf(i_0_3102,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_1896]),
[final] ).
cnf(i_0_3103,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_1897]),
[final] ).
cnf(i_0_3104,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_1897]),
[final] ).
cnf(i_0_3105,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_1875]),
[final] ).
cnf(i_0_3106,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_1876]),
[final] ).
cnf(i_0_3107,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_1877]),
[final] ).
cnf(i_0_3108,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_1878]),
[final] ).
cnf(i_0_3109,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_1898]),
[final] ).
cnf(i_0_3110,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_1899]),
[final] ).
cnf(i_0_3111,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_1854]),
[final] ).
cnf(i_0_3112,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_1855]),
[final] ).
cnf(i_0_3113,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_1900]),
[final] ).
cnf(i_0_3114,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_1901]),
[final] ).
cnf(i_0_3115,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_1902]),
[final] ).
cnf(i_0_3116,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_1903]),
[final] ).
cnf(i_0_3117,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_1904]),
[final] ).
cnf(i_0_3118,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_1905]),
[final] ).
cnf(i_0_3119,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_1906]),
[final] ).
cnf(i_0_3120,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_1907]),
[final] ).
cnf(i_0_3121,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_1907]),
[final] ).
cnf(i_0_3122,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_1908]),
[final] ).
cnf(i_0_3123,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_1909]),
[final] ).
cnf(i_0_3124,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_1910]),
[final] ).
cnf(i_0_3125,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_1911]),
[final] ).
cnf(i_0_3126,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_1912]),
[final] ).
cnf(i_0_3127,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_1913]),
[final] ).
cnf(i_0_3128,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_1914]),
[final] ).
cnf(i_0_3129,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_3130,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_1915]),
[final] ).
cnf(i_0_3131,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_1916]),
[final] ).
cnf(i_0_3132,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_1917]),
[final] ).
cnf(i_0_3133,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_1918]),
[final] ).
cnf(i_0_3134,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_1919]),
[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_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3136,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_1920]),
[final] ).
cnf(i_0_3137,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_1921]),
[final] ).
cnf(i_0_3138,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_1922]),
[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_1923]),
[final] ).
cnf(i_0_3140,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_1924]),
[final] ).
cnf(i_0_3141,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_1925]),
[final] ).
cnf(i_0_3142,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_1926]),
[final] ).
cnf(i_0_3143,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_1927]),
[final] ).
cnf(i_0_3144,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_1928]),
[final] ).
cnf(i_0_3145,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_3146,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3147,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_1890]),
[final] ).
cnf(i_0_3148,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oabs__class_Oabs(X1,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3149,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_1893]),
[final] ).
cnf(i_0_3150,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_1929]),
[final] ).
cnf(i_0_3151,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_1749]),
[final] ).
cnf(i_0_3152,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_1930]),
[final] ).
cnf(i_0_3153,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_1931]),
[final] ).
cnf(i_0_3154,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_1932]),
[final] ).
cnf(i_0_3155,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_1933]),
[final] ).
cnf(i_0_3156,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_1934]),
[final] ).
cnf(i_0_3157,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_1935]),
[final] ).
cnf(i_0_3158,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_1936]),
[final] ).
cnf(i_0_3159,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_1937]),
[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),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_1937]),
[final] ).
cnf(i_0_3161,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_1938]),
[final] ).
cnf(i_0_3162,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_1939]),
[final] ).
cnf(i_0_3163,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_1940]),
[final] ).
cnf(i_0_3164,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk16_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_1941]),
[final] ).
cnf(i_0_3165,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_1942]),
[final] ).
cnf(i_0_3166,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_1905]),
[final] ).
cnf(i_0_3167,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_1718]),
[final] ).
cnf(i_0_3168,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_1943]),
[final] ).
cnf(i_0_3169,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_1944]),
[final] ).
cnf(i_0_3170,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_1945]),
[final] ).
cnf(i_0_3171,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_1946]),
[final] ).
cnf(i_0_3172,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_1947]),
[final] ).
cnf(i_0_3173,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_1948]),
[final] ).
cnf(i_0_3174,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_1949]),
[final] ).
cnf(i_0_3175,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_1950]),
[final] ).
cnf(i_0_3176,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_1951]),
[final] ).
cnf(i_0_3177,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_1929]),
[final] ).
cnf(i_0_3178,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_1952]),
[final] ).
cnf(i_0_3179,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_1953]),
[final] ).
cnf(i_0_3180,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_1742]),
[final] ).
cnf(i_0_3181,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_1743]),
[final] ).
cnf(i_0_3182,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_1954]),
[final] ).
cnf(i_0_3183,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_1753]),
[final] ).
cnf(i_0_3184,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_1952]),
[final] ).
cnf(i_0_3185,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_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_1955]),
[final] ).
cnf(i_0_3186,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_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_1955]),
[final] ).
cnf(i_0_3187,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_1953]),
[final] ).
cnf(i_0_3188,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_1956]),
[final] ).
cnf(i_0_3189,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_1957]),
[final] ).
cnf(i_0_3190,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_1958]),
[final] ).
cnf(i_0_3191,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_1959]),
[final] ).
cnf(i_0_3192,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_1960]),
[final] ).
cnf(i_0_3193,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_1961]),
[final] ).
cnf(i_0_3194,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_1962]),
[final] ).
cnf(i_0_3195,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_1963]),
[final] ).
cnf(i_0_3196,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_1964]),
[final] ).
cnf(i_0_3197,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_1965]),
[final] ).
cnf(i_0_3198,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_1966]),
[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_1967]),
[final] ).
cnf(i_0_3200,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_1968]),
[final] ).
cnf(i_0_3201,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_1969]),
[final] ).
cnf(i_0_3202,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_1899]),
[final] ).
cnf(i_0_3203,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_1970]),
[final] ).
cnf(i_0_3204,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_1802]),
[final] ).
cnf(i_0_3205,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_1971]),
[final] ).
cnf(i_0_3206,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_1937]),
[final] ).
cnf(i_0_3207,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_1972]),
[final] ).
cnf(i_0_3208,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_1973]),
[final] ).
cnf(i_0_3209,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_1974]),
[final] ).
cnf(i_0_3210,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_1963]),
[final] ).
cnf(i_0_3211,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_1964]),
[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_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3213,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_1975]),
[final] ).
cnf(i_0_3214,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk2_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_1955]),
[final] ).
cnf(i_0_3215,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_1976]),
[final] ).
cnf(i_0_3216,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_1977]),
[final] ).
cnf(i_0_3217,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_1977]),
[final] ).
cnf(i_0_3218,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_1978]),
[final] ).
cnf(i_0_3219,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_1979]),
[final] ).
cnf(i_0_3220,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_1980]),
[final] ).
cnf(i_0_3221,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_1981]),
[final] ).
cnf(i_0_3222,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_1982]),
[final] ).
cnf(i_0_3223,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_1983]),
[final] ).
cnf(i_0_3224,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_1984]),
[final] ).
cnf(i_0_3225,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_1985]),
[final] ).
cnf(i_0_3226,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_1986]),
[final] ).
cnf(i_0_3227,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_1987]),
[final] ).
cnf(i_0_3228,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_1988]),
[final] ).
cnf(i_0_3229,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_1989]),
[final] ).
cnf(i_0_3230,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_1990]),
[final] ).
cnf(i_0_3231,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_1991]),
[final] ).
cnf(i_0_3232,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_1992]),
[final] ).
cnf(i_0_3233,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_1993]),
[final] ).
cnf(i_0_3234,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_1994]),
[final] ).
cnf(i_0_3235,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_1987]),
[final] ).
cnf(i_0_3236,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_1995]),
[final] ).
cnf(i_0_3237,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_1996]),
[final] ).
cnf(i_0_3238,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_1944]),
[final] ).
cnf(i_0_3239,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_1945]),
[final] ).
cnf(i_0_3240,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_1997]),
[final] ).
cnf(i_0_3241,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_1998]),
[final] ).
cnf(i_0_3242,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_1999]),
[final] ).
cnf(i_0_3243,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_2000]),
[final] ).
cnf(i_0_3244,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_1988]),
[final] ).
cnf(i_0_3245,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_2001]),
[final] ).
cnf(i_0_3246,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_1989]),
[final] ).
cnf(i_0_3247,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_1990]),
[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_2002]),
[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_2003]),
[final] ).
cnf(i_0_3250,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_1992]),
[final] ).
cnf(i_0_3251,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_1993]),
[final] ).
cnf(i_0_3252,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_3253,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_2004]),
[final] ).
cnf(i_0_3254,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_1895]),
[final] ).
cnf(i_0_3255,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_2005]),
[final] ).
cnf(i_0_3256,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_2006]),
[final] ).
cnf(i_0_3257,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_2007]),
[final] ).
cnf(i_0_3258,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_2008]),
[final] ).
cnf(i_0_3259,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_2009]),
[final] ).
cnf(i_0_3260,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_2010]),
[final] ).
cnf(i_0_3261,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_2011]),
[final] ).
cnf(i_0_3262,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_2012]),
[final] ).
cnf(i_0_3263,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_2013]),
[final] ).
cnf(i_0_3264,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_2014]),
[final] ).
cnf(i_0_3265,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_2015]),
[final] ).
cnf(i_0_3266,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3267,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_1648]),
[final] ).
cnf(i_0_3268,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_2017]),
[final] ).
cnf(i_0_3269,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_2018]),
[final] ).
cnf(i_0_3270,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_2019]),
[final] ).
cnf(i_0_3271,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_2020]),
[final] ).
cnf(i_0_3272,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_2021]),
[final] ).
cnf(i_0_3273,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_2021]),
[final] ).
cnf(i_0_3274,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_2022]),
[final] ).
cnf(i_0_3275,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_2000]),
[final] ).
cnf(i_0_3276,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_2023]),
[final] ).
cnf(i_0_3277,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_2024]),
[final] ).
cnf(i_0_3278,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_2025]),
[final] ).
cnf(i_0_3279,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_2026]),
[final] ).
cnf(i_0_3280,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_1969]),
[final] ).
cnf(i_0_3281,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_2027]),
[final] ).
cnf(i_0_3282,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3283,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_2029]),
[final] ).
cnf(i_0_3284,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_1919]),
[final] ).
cnf(i_0_3285,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_2030]),
[final] ).
cnf(i_0_3286,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_2031]),
[final] ).
cnf(i_0_3287,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_2032]),
[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_2033]),
[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_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3290,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1)
| hAPP(X1,esk11_1(X1)) != hAPP(X1,esk12_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3291,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_2036]),
[final] ).
cnf(i_0_3292,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_2037]),
[final] ).
cnf(i_0_3293,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_2038]),
[final] ).
cnf(i_0_3294,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_2039]),
[final] ).
cnf(i_0_3295,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_1917]),
[final] ).
cnf(i_0_3296,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_2040]),
[final] ).
cnf(i_0_3297,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_1916]),
[final] ).
cnf(i_0_3298,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_2041]),
[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_2042]),
[final] ).
cnf(i_0_3300,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_2043]),
[final] ).
cnf(i_0_3301,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_2044]),
[final] ).
cnf(i_0_3302,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_2045]),
[final] ).
cnf(i_0_3303,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_2046]),
[final] ).
cnf(i_0_3304,plain,
( hAPP(X3,X4) = hAPP(X3,X5)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3305,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_2027]),
[final] ).
cnf(i_0_3306,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_2047]),
[final] ).
cnf(i_0_3307,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_2048]),
[final] ).
cnf(i_0_3308,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_2049]),
[final] ).
cnf(i_0_3309,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_2050]),
[final] ).
cnf(i_0_3310,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_2051]),
[final] ).
cnf(i_0_3311,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_2052]),
[final] ).
cnf(i_0_3312,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_2053]),
[final] ).
cnf(i_0_3313,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_2054]),
[final] ).
cnf(i_0_3314,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_2055]),
[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_pa____)),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[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_p)),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3317,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_2058]),
[final] ).
cnf(i_0_3318,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_2059]),
[final] ).
cnf(i_0_3319,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_2060]),
[final] ).
cnf(i_0_3320,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_2061]),
[final] ).
cnf(i_0_3321,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_2062]),
[final] ).
cnf(i_0_3322,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_2063]),
[final] ).
cnf(i_0_3323,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_1926]),
[final] ).
cnf(i_0_3324,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3325,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_2017]),
[final] ).
cnf(i_0_3326,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_1930]),
[final] ).
cnf(i_0_3327,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_2065]),
[final] ).
cnf(i_0_3328,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_2066]),
[final] ).
cnf(i_0_3329,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_2067]),
[final] ).
cnf(i_0_3330,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_2068]),
[final] ).
cnf(i_0_3331,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_2069]),
[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_2070]),
[final] ).
cnf(i_0_3333,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Olinordered__idom(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Oabs__class_Oabs(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[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_2072]),
[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_2073]),
[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_2074]),
[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_2075]),
[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_2076]),
[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_1974]),
[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_2077]),
[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_2078]),
[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_2079]),
[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_2080]),
[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_2081]),
[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_1954]),
[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_2082]),
[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_2083]),
[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_2027]),
[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_2084]),
[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_1958]),
[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_1959]),
[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_1956]),
[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_1986]),
[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_2021]),
[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_2022]),
[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_1963]),
[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_1919]),
[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_2085]),
[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_2086]),
[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_2087]),
[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_2029]),
[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_2029]),
[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_2024]),
[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_2088]),
[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_2089]),
[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_2090]),
[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_2091]),
[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_2092]),
[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_1978]),
[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_2093]),
[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_2094]),
[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_2095]),
[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_2096]),
[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_2097]),
[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_2098]),
[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_2099]),
[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_2100]),
[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_2101]),
[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_2102]),
[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_2103]),
[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_2104]),
[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_2105]),
[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_2106]),
[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_2107]),
[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_2108]),
[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_2108]),
[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_2109]),
[final] ).
cnf(i_0_3389,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(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_2110]),
[final] ).
cnf(i_0_3390,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_2111]),
[final] ).
cnf(i_0_3391,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_2112]),
[final] ).
cnf(i_0_3392,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_2113]),
[final] ).
cnf(i_0_3393,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk17_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_2114]),
[final] ).
cnf(i_0_3394,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3395,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_2018]),
[final] ).
cnf(i_0_3396,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_2115]),
[final] ).
cnf(i_0_3397,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_2045]),
[final] ).
cnf(i_0_3398,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_2046]),
[final] ).
cnf(i_0_3399,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_2116]),
[final] ).
cnf(i_0_3400,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk30_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_3401,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_3402,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_2117]),
[final] ).
cnf(i_0_3403,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_2118]),
[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_2119]),
[final] ).
cnf(i_0_3405,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_2120]),
[final] ).
cnf(i_0_3406,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_3407,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_2122]),
[final] ).
cnf(i_0_3408,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_2123]),
[final] ).
cnf(i_0_3409,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_2124]),
[final] ).
cnf(i_0_3410,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_2125]),
[final] ).
cnf(i_0_3411,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_2126]),
[final] ).
cnf(i_0_3412,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3413,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3414,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3415,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3416,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3417,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3418,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3419,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_2129]),
[final] ).
cnf(i_0_3420,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_2130]),
[final] ).
cnf(i_0_3421,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_2131]),
[final] ).
cnf(i_0_3422,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_2132]),
[final] ).
cnf(i_0_3423,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_2133]),
[final] ).
cnf(i_0_3424,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_2134]),
[final] ).
cnf(i_0_3425,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_2117]),
[final] ).
cnf(i_0_3426,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_2135]),
[final] ).
cnf(i_0_3427,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_2015]),
[final] ).
cnf(i_0_3428,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_2014]),
[final] ).
cnf(i_0_3429,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_2136]),
[final] ).
cnf(i_0_3430,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_2137]),
[final] ).
cnf(i_0_3431,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_2138]),
[final] ).
cnf(i_0_3432,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3433,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3434,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_2005]),
[final] ).
cnf(i_0_3435,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_2019]),
[final] ).
cnf(i_0_3436,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_2141]),
[final] ).
cnf(i_0_3437,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_2142]),
[final] ).
cnf(i_0_3438,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_2143]),
[final] ).
cnf(i_0_3439,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_2143]),
[final] ).
cnf(i_0_3440,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_2144]),
[final] ).
cnf(i_0_3441,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_2144]),
[final] ).
cnf(i_0_3442,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_2047]),
[final] ).
cnf(i_0_3443,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_2018]),
[final] ).
cnf(i_0_3444,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_2145]),
[final] ).
cnf(i_0_3445,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_2146]),
[final] ).
cnf(i_0_3446,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_2147]),
[final] ).
cnf(i_0_3447,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_2148]),
[final] ).
cnf(i_0_3448,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_2149]),
[final] ).
cnf(i_0_3449,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_2080]),
[final] ).
cnf(i_0_3450,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_1667]),
[final] ).
cnf(i_0_3451,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk13_1(X1))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[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_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[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_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3454,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_2152]),
[final] ).
cnf(i_0_3455,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_2153]),
[final] ).
cnf(i_0_3456,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_2154]),
[final] ).
cnf(i_0_3457,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_2075]),
[final] ).
cnf(i_0_3458,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_2076]),
[final] ).
cnf(i_0_3459,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_2155]),
[final] ).
cnf(i_0_3460,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_2156]),
[final] ).
cnf(i_0_3461,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_2157]),
[final] ).
cnf(i_0_3462,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_2158]),
[final] ).
cnf(i_0_3463,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_2159]),
[final] ).
cnf(i_0_3464,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_2022]),
[final] ).
cnf(i_0_3465,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_2068]),
[final] ).
cnf(i_0_3466,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_2068]),
[final] ).
cnf(i_0_3467,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_1750]),
[final] ).
cnf(i_0_3468,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_2081]),
[final] ).
cnf(i_0_3469,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_2049]),
[final] ).
cnf(i_0_3470,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_2050]),
[final] ).
cnf(i_0_3471,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_2051]),
[final] ).
cnf(i_0_3472,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_1962]),
[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_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[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_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3475,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_2162]),
[final] ).
cnf(i_0_3476,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_2163]),
[final] ).
cnf(i_0_3477,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_3478,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_3479,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_2077]),
[final] ).
cnf(i_0_3480,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_2078]),
[final] ).
cnf(i_0_3481,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_1926]),
[final] ).
cnf(i_0_3482,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_3483,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_2164]),
[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_2165]),
[final] ).
cnf(i_0_3485,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_2166]),
[final] ).
cnf(i_0_3486,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_2167]),
[final] ).
cnf(i_0_3487,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_2168]),
[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_2169]),
[final] ).
cnf(i_0_3489,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_2170]),
[final] ).
cnf(i_0_3490,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_2171]),
[final] ).
cnf(i_0_3491,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_3492,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_2173]),
[final] ).
cnf(i_0_3493,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_2108]),
[final] ).
cnf(i_0_3494,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_2174]),
[final] ).
cnf(i_0_3495,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_3496,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_2176]),
[final] ).
cnf(i_0_3497,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_3498,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_2178]),
[final] ).
cnf(i_0_3499,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_2179]),
[final] ).
cnf(i_0_3500,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3501,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3502,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3503,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3504,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_2181]),
[final] ).
cnf(i_0_3505,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_2182]),
[final] ).
cnf(i_0_3506,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_2183]),
[final] ).
cnf(i_0_3507,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_2184]),
[final] ).
cnf(i_0_3508,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_2185]),
[final] ).
cnf(i_0_3509,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_2099]),
[final] ).
cnf(i_0_3510,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_3511,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3512,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_3513,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_3514,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_3515,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_3516,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_3517,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_3518,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_2143]),
[final] ).
cnf(i_0_3519,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_2144]),
[final] ).
cnf(i_0_3520,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_3521,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_3522,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_2093]),
[final] ).
cnf(i_0_3523,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_3524,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_3525,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_3526,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_3527,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_3528,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_3529,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_3530,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_3531,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_3532,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_3533,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_3534,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_3535,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_3536,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_3537,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_3538,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_3539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3540,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3541,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_3542,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3543,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_3544,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_3545,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_3546,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_1929]),
[final] ).
cnf(i_0_3547,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_3548,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_3549,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_3550,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_3551,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk14_0),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_3552,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_3553,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_0),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_3554,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_3555,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_3556,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_3557,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_3558,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_3559,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_2136]),
[final] ).
cnf(i_0_3560,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_2136]),
[final] ).
cnf(i_0_3561,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_3562,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_3563,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_3564,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_3565,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_2215]),
[final] ).
cnf(i_0_3566,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_2216]),
[final] ).
cnf(i_0_3567,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_3568,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_3569,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_3570,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_3571,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3572,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3573,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3574,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_3575,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_3576,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_3577,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_3578,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_3579,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_3580,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_3581,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_3582,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_3583,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_3584,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_3585,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_3586,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_3587,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_3588,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_3589,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_2236]),
[final] ).
cnf(i_0_3590,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_2237]),
[final] ).
cnf(i_0_3591,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_2238]),
[final] ).
cnf(i_0_3592,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_2239]),
[final] ).
cnf(i_0_3593,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_2240]),
[final] ).
cnf(i_0_3594,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_3595,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_2242]),
[final] ).
cnf(i_0_3596,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_2243]),
[final] ).
cnf(i_0_3597,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_3598,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_3599,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3600,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3601,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_3602,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3603,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3604,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3605,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_3606,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_3607,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_3608,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_3609,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_2017]),
[final] ).
cnf(i_0_3610,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_2237]),
[final] ).
cnf(i_0_3611,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_2238]),
[final] ).
cnf(i_0_3612,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_2239]),
[final] ).
cnf(i_0_3613,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_2240]),
[final] ).
cnf(i_0_3614,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_2236]),
[final] ).
cnf(i_0_3615,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_2243]),
[final] ).
cnf(i_0_3616,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_3617,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_3618,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_2256]),
[final] ).
cnf(i_0_3619,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_2257]),
[final] ).
cnf(i_0_3620,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_2258]),
[final] ).
cnf(i_0_3621,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_2259]),
[final] ).
cnf(i_0_3622,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_2260]),
[final] ).
cnf(i_0_3623,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_3624,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_2262]),
[final] ).
cnf(i_0_3625,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_2263]),
[final] ).
cnf(i_0_3626,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_2264]),
[final] ).
cnf(i_0_3627,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_3628,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_3629,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_3630,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_2265]),
[final] ).
cnf(i_0_3631,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_2266]),
[final] ).
cnf(i_0_3632,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_2267]),
[final] ).
cnf(i_0_3633,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_2268]),
[final] ).
cnf(i_0_3634,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3635,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3636,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_3637,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_3638,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_1940]),
[final] ).
cnf(i_0_3639,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk16_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3640,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_3641,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_3642,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_3643,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_2273]),
[final] ).
cnf(i_0_3644,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_2274]),
[final] ).
cnf(i_0_3645,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_3646,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_3647,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_3648,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_3649,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_3650,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_3651,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_3652,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_3653,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_3654,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_3655,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_3656,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_3657,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_3658,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_3659,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_3660,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_3661,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_3662,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_3663,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_3664,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_3665,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3666,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[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_2293]),
[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_2294]),
[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_2295]),
[final] ).
cnf(i_0_3670,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3671,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3672,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3673,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3674,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_2300]),
[final] ).
cnf(i_0_3675,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3676,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3677,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3678,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3679,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_3680,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3681,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3682,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3683,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3684,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3685,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3686,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3687,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3688,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3689,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[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_2316]),
[final] ).
cnf(i_0_3691,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3692,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3693,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3694,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3695,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3696,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3697,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_3698,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3699,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3700,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3701,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3702,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3703,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3704,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3705,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3706,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3707,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3708,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_3709,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_3710,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_3711,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_3712,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_3713,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_3714,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_3715,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_3716,plain,
esk24_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_3717,plain,
esk23_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_3718,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_3719,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_3720,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_kas_I1_J]),
[final] ).
cnf(i_0_3721,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w0]),
[final] ).
cnf(i_0_3722,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_kas_I2_J]),
[final] ).
cnf(i_0_3723,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_3724,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_3725,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_3726,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_3727,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_3728,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]),
[final] ).
cnf(i_0_3729,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_3730,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]),
[final] ).
cnf(i_0_3731,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
[final] ).
cnf(i_0_3732,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]),
[final] ).
cnf(i_0_3733,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_3734,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_3735,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
[final] ).
cnf(i_0_3736,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
[final] ).
cnf(i_0_3737,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_3738,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_3739,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]),
[final] ).
cnf(i_0_3740,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_3741,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]),
[final] ).
cnf(i_0_3742,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_3743,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_3744,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_3745,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_3746,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_3747,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_3748,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_3749,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_3750,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_3751,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_3752,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_3753,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_3754,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_3755,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_3756,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_3757,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_3758,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3759,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3760,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3761,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_3762,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_3763,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_3764,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_3765,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_3766,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_3767,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_3768,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
[final] ).
cnf(i_0_3769,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]),
[final] ).
cnf(i_0_3770,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_3771,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_3772,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_3773,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_3774,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_3775,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_3776,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_3777,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_3778,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_3779,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_3780,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_3781,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_3782,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_3783,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_3784,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_3785,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_3786,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_3787,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_3788,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_3789,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_3790,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_3791,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_3792,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_3793,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_3794,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3795,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3796,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3797,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3798,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_3799,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_3800,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_3801,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_3802,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_3803,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_3804,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_3805,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_3806,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_3807,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_3808,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_3809,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_3810,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_3811,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_3812,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_3813,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_3814,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_3815,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_3816,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_3817,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_3818,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_3819,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_3820,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_3821,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_3822,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_3823,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_3824,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_3825,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_3826,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_3827,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_3828,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_3829,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_3830,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_3831,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_3832,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_3833,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_3834,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_3835,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_3836,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_3837,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_3838,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_3839,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_3840,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_3841,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_3842,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_3843,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_3844,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_3845,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_3846,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3847,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3848,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3849,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_3850,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_3851,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_3852,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_3853,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_3854,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_3855,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_3856,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_3857,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
[final] ).
cnf(i_0_3858,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3859,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3860,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3861,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3862,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_3863,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_3864,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_3865,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_3866,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_3867,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_3868,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_3869,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_3870,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_3871,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_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_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3874,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__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_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_3877,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_3878,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_3879,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_3880,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_3881,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_3882,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_3883,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_3884,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_3885,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_3886,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_3887,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_3888,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_3889,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_3890,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_3891,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_3892,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_3893,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_3894,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_3895,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_3896,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_3897,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_3898,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_3899,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_3900,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_3901,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3902,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3903,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3904,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3905,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3906,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_3907,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_3908,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_3909,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_3910,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_3911,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_3912,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_3913,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_3914,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_3915,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_3916,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3917,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3918,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3919,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3920,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3921,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_3922,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_3923,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_3924,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3925,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3926,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3927,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3928,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3929,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3930,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_3931,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_3932,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_3933,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_3934,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_3935,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_3936,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3937,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3938,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_3939,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_3940,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_3941,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_3942,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3943,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3944,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3945,axiom,
X1 = X1 ).
cnf(i_0_3946,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3947,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3948,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3949,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3950,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3951,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3952,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3953,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3954,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3955,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3956,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3957,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3958,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3959,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3960,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3961,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3962,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3963,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3964,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3965,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3966,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3967,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3968,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3969,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3970,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3971,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3972,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3973,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3974,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3975,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3976,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3977,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3978,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3979,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_3980,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_3981,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_3982,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3983,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3984,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3985,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3986,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3987,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3988,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3989,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3990,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3991,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3992,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3993,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3994,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3995,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3996,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3997,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3998,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3999,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4000,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4001,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4002,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4003,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4004,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4005,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4006,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4007,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4008,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4009,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4010,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4011,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4012,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4013,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4014,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4015,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4016,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4017,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4018,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4019,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4020,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4021,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4022,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4023,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4024,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4025,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4026,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4027,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4028,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4029,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4030,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4031,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4032,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4033,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4034,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4035,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4036,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4037,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4038,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4039,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4040,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4041,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4042,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4043,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4044,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4045,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4046,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4047,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4048,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4049,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4050,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4051,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4052,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4053,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4054,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4055,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4056,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4057,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4058,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4059,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4060,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4061,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4062,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4063,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4064,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4065,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4066,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4067,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4068,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4069,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4070,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4071,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4072,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4073,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4074,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4075,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4076,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4077,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4078,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4079,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4080,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4081,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4082,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4083,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4084,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4085,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4086,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4088,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X3,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X4) ) ).
cnf(i_0_4089,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X1,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X2,X4) ) ).
cnf(i_0_4090,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X2) ) ).
cnf(i_0_4091,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4092,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4093,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4094,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4095,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4096,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_3945_001,axiom,
X1 = X1 ).
cnf(i_0_3946_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3947_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3948_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3949_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3950_006,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3951_007,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3952_008,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3953_009,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3954_010,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3955_011,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3956_012,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3957_013,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3958_014,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3959_015,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3960_016,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3961_017,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3962_018,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3963_019,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3964_020,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3965_021,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3966_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3967_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3968_024,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3969_025,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3970_026,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3971_027,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3972_028,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3973_029,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3974_030,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3975_031,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3976_032,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3977_033,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3978_034,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3979_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_3980_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_3981_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_3982_038,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3983_039,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3984_040,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3985_041,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3986_042,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3987_043,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3988_044,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3989_045,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3990_046,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3991_047,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3992_048,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3993_049,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3994_050,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3995_051,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3996_052,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3997_053,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3998_054,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3999_055,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4000_056,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_4001_057,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_4002_058,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_4003_059,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_4004_060,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_4005_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_4006_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_4007_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_4008_064,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4009_065,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4010_066,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4011_067,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4012_068,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4013_069,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4014_070,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4015_071,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4016_072,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4017_073,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4018_074,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4019_075,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4020_076,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4021_077,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4022_078,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4023_079,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4024_080,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4025_081,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4026_082,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4027_083,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4028_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_4029_085,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4030_086,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4031_087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4032_088,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4033_089,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4034_090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4035_091,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4036_092,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4037_093,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4038_094,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4039_095,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4040_096,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4041_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_4042_098,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4043_099,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4044_100,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4045_101,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4046_102,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4047_103,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4048_104,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4049_105,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4050_106,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4051_107,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4052_108,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4053_109,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4054_110,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4055_111,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4056_112,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4057_113,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4058_114,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4059_115,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4060_116,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4061_117,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4062_118,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4063_119,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4064_120,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4065_121,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4066_122,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4067_123,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4068_124,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4069_125,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4070_126,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4071_127,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4072_128,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4073_129,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4074_130,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4075_131,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4076_132,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4077_133,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4078_134,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4079_135,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4080_136,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4081_137,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4082_138,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4083_139,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4084_140,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4085_141,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4086_142,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4087_143,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4088_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_4089_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_4090_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_4091_147,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4092_148,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4093_149,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4094_150,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4095_151,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4096_152,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4097,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_4098,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_4099,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_4100,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_4101,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_4102,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_4103,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_4104,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_4105,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_4106,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_4107,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2433]) ).
cnf(i_0_4108,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_4109,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_4110,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,[],[2592]) ).
cnf(i_0_4111,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_4112,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,[],[2789]) ).
cnf(i_0_4113,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,[],[2868]) ).
cnf(i_0_4114,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,[],[2873]) ).
cnf(i_0_4115,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,[],[2890]) ).
cnf(i_0_4116,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[2891]) ).
cnf(i_0_4117,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[2901]) ).
cnf(i_0_4118,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,[],[2946]) ).
cnf(i_0_4119,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,[],[2947]) ).
cnf(i_0_4120,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,[],[2970]) ).
cnf(i_0_4121,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[2971]) ).
cnf(i_0_4122,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,[],[3001]) ).
cnf(i_0_4123,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,[],[3002]) ).
cnf(i_0_4124,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[3101]) ).
cnf(i_0_4125,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3120]) ).
cnf(i_0_4126,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3121]) ).
cnf(i_0_4127,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3122]) ).
cnf(i_0_4128,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3124]) ).
cnf(i_0_4129,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3125]) ).
cnf(i_0_4130,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3127]) ).
cnf(i_0_4131,plain,
X1 = X1,
inference(equality_inference,[],[3161]) ).
cnf(i_0_4132,plain,
X1 = X1,
inference(equality_inference,[],[3162]) ).
cnf(i_0_4133,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,[],[3167]) ).
cnf(i_0_4134,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,[],[3181]) ).
cnf(i_0_4135,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,[],[3182]) ).
cnf(i_0_4136,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3188]) ).
cnf(i_0_4137,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3189]) ).
cnf(i_0_4138,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3191]) ).
cnf(i_0_4139,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3192]) ).
cnf(i_0_4140,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,[],[3218]) ).
cnf(i_0_4141,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3239]) ).
cnf(i_0_4142,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,[],[3254]) ).
cnf(i_0_4143,plain,
X1 = X1,
inference(equality_inference,[],[3266]) ).
cnf(i_0_4144,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,[],[3280]) ).
cnf(i_0_4145,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(equality_inference,[],[3333]) ).
cnf(i_0_4146,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_4147,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_4148,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_4149,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_4150,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_4151,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_4152,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3360]) ).
cnf(i_0_4153,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3361]) ).
cnf(i_0_4154,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3362]) ).
cnf(i_0_4155,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3363]) ).
cnf(i_0_4156,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(equality_inference,[],[3394]) ).
cnf(i_0_4157,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,[],[3395]) ).
cnf(i_0_4158,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3396]) ).
cnf(i_0_4159,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,[],[3397]) ).
cnf(i_0_4160,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,[],[3398]) ).
cnf(i_0_4161,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3412]) ).
cnf(i_0_4162,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3415]) ).
cnf(i_0_4163,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3417]) ).
cnf(i_0_4164,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3418]) ).
cnf(i_0_4165,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,[],[3427]) ).
cnf(i_0_4166,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,[],[3428]) ).
cnf(i_0_4167,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,[],[3435]) ).
cnf(i_0_4168,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,[],[3442]) ).
cnf(i_0_4169,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,[],[3443]) ).
cnf(i_0_4170,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,[],[3449]) ).
cnf(i_0_4171,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,[],[3457]) ).
cnf(i_0_4172,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,[],[3458]) ).
cnf(i_0_4173,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,[],[3464]) ).
cnf(i_0_4174,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,[],[3465]) ).
cnf(i_0_4175,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,[],[3466]) ).
cnf(i_0_4176,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X2) ),
inference(equality_inference,[],[3467]) ).
cnf(i_0_4177,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,[],[3468]) ).
cnf(i_0_4178,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,[],[3478]) ).
cnf(i_0_4179,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3479]) ).
cnf(i_0_4180,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3480]) ).
cnf(i_0_4181,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,[],[3481]) ).
cnf(i_0_4182,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3501]) ).
cnf(i_0_4183,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3502]) ).
cnf(i_0_4184,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3503]) ).
cnf(i_0_4185,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,[],[3504]) ).
cnf(i_0_4186,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X2 ),
inference(equality_inference,[],[3517]) ).
cnf(i_0_4187,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,[],[3531]) ).
cnf(i_0_4188,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3541]) ).
cnf(i_0_4189,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3542]) ).
cnf(i_0_4190,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,[],[3546]) ).
cnf(i_0_4191,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,[],[3559]) ).
cnf(i_0_4192,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,[],[3560]) ).
cnf(i_0_4193,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,[],[3561]) ).
cnf(i_0_4194,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = X2 ),
inference(equality_inference,[],[3562]) ).
cnf(i_0_4195,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[3563]) ).
cnf(i_0_4196,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3564]) ).
cnf(i_0_4197,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3566]) ).
cnf(i_0_4198,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(equality_inference,[],[3582]) ).
cnf(i_0_4199,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(equality_inference,[],[3584]) ).
cnf(i_0_4200,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,[],[3586]) ).
cnf(i_0_4201,plain,
X1 = X1,
inference(equality_inference,[],[3587]) ).
cnf(i_0_4202,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,[],[3609]) ).
cnf(i_0_4203,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,[],[3610]) ).
cnf(i_0_4204,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,[],[3611]) ).
cnf(i_0_4205,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,[],[3612]) ).
cnf(i_0_4206,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,[],[3613]) ).
cnf(i_0_4207,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,[],[3614]) ).
cnf(i_0_4208,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,[],[3615]) ).
cnf(i_0_4209,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,[],[3616]) ).
cnf(i_0_4210,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,[],[3617]) ).
cnf(i_0_4211,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,[],[3627]) ).
cnf(i_0_4212,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,[],[3628]) ).
cnf(i_0_4213,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,[],[3629]) ).
cnf(i_0_4214,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,[],[3642]) ).
cnf(i_0_4215,plain,
$false,
inference(scs_inference,[],[i_0_2342,i_0_3864,i_0_2353,i_0_3252,i_0_2609]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW263+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n027.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:31:19 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.79/5.79 % Version : CSE_E---1.7
% 0.79/5.79 % Problem : theBenchmark.p
% 0.79/5.79 % SZS status Theorem for theBenchmark.p
% 0.79/5.79 % SZS output start CNFRefutation
% See solution above
% 6.19/5.94 % Total time : 5.449s
%------------------------------------------------------------------------------